2.2.4. Complete Prototype

All the mechanical parts that make up the sensing device were produced using a 3D printer. After that, the two mechanical parts and the electronic board described above were assembled with the use of the magnetic anchor and positioned on the EndoWrist tool of the dVRK system. Figure 5 clearly shows how the first version of the prototype guarantees a minimum footprint and better compactness. This support configuration is to be taken into consideration in cases where there is no need to detect objects placed on the workspace using the integrated sensors. For example, in the case in question, it is possible to refer to this first version to demonstrate the potential of the BLE connection between two boards placed on two arms of the dVRK. Furthermore, during the validation phase of the device on dVRK instrumentation, it was found that the friction between the surface of the instrument and the inside of the device prevents any movement of the support; therefore, the stability of the electronic component is guaranteed.

**Figure 5.** Complete prototype of the first version of the detection device connected to the EndoWrist tool of dVRK system.

The second assembled version of the prototype, unlike the first, allows the board to be kept parallel to the work surface. The main limitation of this configuration is the larger footprint, as shown in Figure 6, which could constitute an obstacle for the other tools of the robotic system during the execution of the tasks. Furthermore, it may seem less stable than the first configuration, but it has been tested that using magnets, the sensing device remains perfectly in position during the entire procedure carried out with the dVRK system.

**Figure 6.** Complete prototype of the second version of the detection device connected to the EndoWrist tool of dVRK system.

#### *2.3. Experimental Evaluations*

This section presents the experiments conducted to verify the possibility of introducing a proximity and color sensor on the EndoWrist instrument.

#### 2.3.1. Proximity Detection and Experiments with Organs

Proximity calibration was performed using the embedded APDS9960 unit of the Arduino Nano 33 BLE Sense. The path of the IR receive signal begins with the IR detection using four photodiodes, and ends with an 8-bit proximity result (256 values) in the PDATA register. So, we focused on proximity readings, which were based on sensing a tissue on photodiodes, and were then converted to millimeters within the sensor for our use. The board has been programmed to print out simple proximity detections and control the RGB LED accordingly, and to change the colors of the RGB LED according to the proximity of a tissue to the sensor. To take advantage of the functions of the APDS9960 detection unit, the <Arduino\_APDS9960.h> library was used. In particular, the LED lights up green if the object is far from the sensor (proximity value >150), blue in the case of intermediate distance (60 < proximity value < 150), and red if the object is very close to the sensor (proximity value < 60). The threshold values shown in parentheses have been implemented in the code. The first test performed concerns the evaluation of the proximity between the tissues and the sensor. This allows the surgeon to work in a safer environment with the sensorization of the instrument, which gives a sound or visual feedback based on the

distance of the instrument to the tissue. This aspect is very important during abdominal surgery procedures, where the various organs are very close to each other. Before getting to the heart of the testing phase, a connection was created between the Arduino Nano 33 BLE Sense board and the Matlab software through a serial communication protocol to manage the data collected by the proximity sensor directly in the Matlab environment. Subsequently, we moved on to the real-time display of the proximity values read by the sensor, which allowed for an instant evaluation of the trend of the data collected in relation to the distance in centimeters. Proximity data acquisition was performed with the MELFA RV3-SB industrial robot. For the execution of the tests, a support for the Arduino board to be fixed to the end effector of the robot was designed and built using a 3D printer. The support was fixed to the robot using two M5 screws, as shown in Figure 7.

**Figure 7.** (**a**) Support for the Arduino board fixed to the end effector of the MELFA RV3-SB industrial robot by means of two M5 screws. (**b**) View of the support with an integrated board made with a 3D printer.

The robot was programmed to perform movements along the z axis, allowing the sensor to move away from and approach the tissue sample. Once we acquired the initial position (minimum distance from the tissue) desired, we decided to make the robotic arm move by 13 cm by making vertical movements of 0.5 mm intervals. All the positions necessary for the desired movement were implemented manually using the robot programming language with a structure that is very simple and intuitive; for example, the command MOV was used to manage the movement of the robot from one position to the next. Slices of tissues with a thickness of about six millimeters were obtained from the organ. Obviously, since these are soft and/or spongy organs, it is not possible to consider a precise and absolute measure of thickness, as the tissue surfaces have protuberances and depressions. This condition was considered relevant for an optimal and faithful representation of the operational reality; therefore, no corrections were made. These slices of tissue were placed on a rigid plate on the workstation below the sensor. As shown in Figure 8, a safety space was left between the sensor and the surface of the tissues to ensure the cleanliness and integrity of the detector. During the testing phase, the same environmental lighting conditions were always maintained. Furthermore, the tests on the samples were carried out on the same day that the tissues were taken from the slaughterhouse; in this way, the freshness of the sample was guaranteed to preserve its color and consistency, to better respect the conditions in vivo.

**Figure 8.** Tissue samples from the pig, placed on the plate below the sensor for the testing phase with the robot MELFA RV3-SB. (**a**) Liver. (**b**) Gut. (**c**) Stomach.

#### 2.3.2. Classification of Tissues by Color

This subsection presents the implementation of a TensorFlow model to classify tissues, based on color detection. The main objective is to be able to distinguish normal tissue from one with characteristics that are not typical of physiological tissue, evaluating the color differences that characterize the two types of tissue. For example, it is possible to define the area of the tissue affected by cancerous manifestations that lead to an alteration of the color, compared to that of normal tissue.

To demonstrate this concept, we limited ourselves to verifying that it is possible, based on color, to distinguish two different tissues, i.e., liver and stomach. In particular, the procedure for the identification and classification of tissues was based on the use of the TensorFlow Lite Micro library and the Arduino Nano 33 BLE Sense colorimetric sensor. To do this, a simple neural network was implemented on the board, combining machine learning with integrated systems to develop an intelligent device. For the first phase of collecting the color data from the two portions of tissues, the Arduino Nano 33 BLE Sense board was first programmed. The colorimetric sensor was integrated inside the APDS9960 unit. This allowed the detection of the intensity of the red, green, and blue colors of each tissue subjected to the sensor. For correct data acquisition, it is advisable to move the sensor around the surface of the tissue to capture the variations of color, as shown in Figure 9. RGB color values were captured as comma separated data grouped in CSV format. This procedure was repeated for both organs, which we were decided to classify by capturing the color data.

**Figure 9.** Frames concerning the acquisition of color data from the stomach and liver to detect the intensity of the red, green, and blue colors of each tissue subjected to the sensor.

Following the data acquisition phase, the model training phase was implemented. The model training phase represents the process by which a model learns to produce the correct output for a given set of inputs. This phase involved feeding training data through the model, making small changes until the most accurate predictions were possible. A model was a network of simulated neurons represented by arrays of numbers arranged in various layers. As data are fed into the network, it is transformed by successive mathematical operations involving weights and distortions at each level. The output of the model was the result of executing the input through these operations. Training stopped when the model's performance stopped improving. For the training phase of the machine learning model, reference was made to the Google Colaboratory, an interactive environment that provides a notepad that allows the writing and execution of code in Python, using the data collected in the previous phase. Before TensorFlow Lite ran the model that was trained, it needed to be converted to the TensorFlow Lite format, and then a model.h file would be generated to be downloaded and included in the final Arduino code, to classify fabrics based on color. Finally, after loading this code on the Arduino board, it was possible, by approaching the RGB sensor close to the object to be classified with which the model was trained, to view the percentage relating to the two classes implemented in the model.


**4. Risk factors for bovine cysticercosis (BCC)**

Bovine cysticercosis is a disease that affects cattle and is caused by a parasite called *T. saginata.* Identified risk factors include herd/farm-related, feed-related, and animal-related factors. Age and gender of animals are correlated with the occurrence of bovine cysticercosis. Environmental contamination is the main cause of BCC cases (**Figure 3**).


3.1. The desertification dynamic in Inner Mongolia from 1981 to 2010

From 1981 to 2010, the area of deserts and desertified land in Inner Mongolia expanded from 555.3 km2 in 1981 to 624.5 km2 in 2010. Except for a decrease of 28,000 km2 in deserts, the area of land with low, medium, high, and severe desertification all showed different increases. The largest increment is caused by medium desertification, which increased 48.77% over 1981. Reversion and expansion between lands with different desertification degrees and between desertified and non-desertified lands are equally significant, which showed a significant spatial heterogeneity. In the 30 years, the area of desertification reversion in Inner Mongolia was 170,900 km2 , with an expansion area of 204,300 km2 (Figure 2).

The area of desertification reversion was mainly distributed in erdos, alsh, bash, and other areas in southwest Inner Mongolia. Among them, the area of desertification reversion in erdos accounted for 8.71% of the desertified land area of Inner Mongolia. The area of desertification reversion in alsh and bash also reached 8.33 and 5.1% of the total desertification area, respectively. The reversal area among different degrees of desertification accounted for 17.98% of the total desertification area. The reversal area from deserts and desertified land to non-desertified

Figure 2. Land use and desertification change in Inner Mongolia autonomous region from 1980s to 2010s. (a) Land use and desertification map in 1981, (b) land use and desertification map in 2010, (c) desertification reversion and (d) desertification expansion.

lands accounts for 9.38% of total desertification area, which was dominated by the reversion to undegraded grassland. The expansion of desertification mainly occurred in central-northern Inner Mongolia, such as southwestern hlbr, hsdk, and char. The desertification expansion in hsdk accounted for the largest proportion of total desertification area, reaching 13.76%. The expansion area among differing degrees of desertification accounted for 12.28% of the whole deserts and desertified land, and the area of land that expanded from non-desertified lands to deserts and desertified land was nearly twice as much as the area of desertification expansion among different degrees, which was mainly attributed to the expansion from undegraded grassland to desertification.


3.1.1. ISO 11863:2011

ISO 11863:2011 (ISO/TC 59/SC 15) [121], specifies the basic requirements and principles to determine and check the basic requirements of structural performance. This is very important to a SHM system since it can help to restrain the scope of the SHM system and select proper vibration parameters to be monitored. It also specifies the thresholds for capability, which is in fact essential for a SHM system since automated alert algorithm highly depends on the pre-defined thresholds. In addition, it provides guidelines on assessing the difference between designed and measured capabilities, which is helpful to generate the maintenance strategy in SHM system. However, it does not provide any detailed feasible procedures for any specific structures. Therefore, it is difficult to construct a SHM system

for a specific building or structure by just following ISO 11863. For example, it requires "the threshold level is a minimum level of demand", but the statement is quite general because for different buildings or structural components the requirements may be quite different, hence it is difficult to be applied in real application directly.


**2. Genetic syndromes**

Genetic syndromes are defined as a consistent pattern of malformation caused by a genetic alteration. A malformation syndrome consists of multiple structural defects that are thought to be due to a single cause, even if the suspected cause has not yet been identified [24].

#### **2.1. Noonan's syndrome**

The Noonan phenotype includes characteristic facies (ptosis, hypertelorism, low set ears, and low posterior hairline), short stature, webbed neck and cardiac anomalies. Noonan syndrome occurs in I per 1000 to 1 per 2500 live births diagnosed clinically [25–27]. Cardiac anomalies are present in 80% of individuals [28]. In 70–80% of cases, the lesion is pulmonary stenosis, usually due to dysplastic pulmonary valve leaflets [25]. In 20–30% of affected individuals, the cardiac anomaly is in the form of a cardiomyopathy, which may be present at birth or develop later [25, 29].

Most of the cases of Noonan syndrome are sporadic, although families with a pattern of autosomal dominant inheritance are well known. Mutation in the gene PTPN11 on the chromosome locus 12q24.1 was noted in 45% of cases. Gelb et al. demonstrated a positive association between those with PTPN11 mutations and pulmonary stenosis [30]. Maternal transmission of the gene is three times more common than paternal transmission [28]. Prenatal testing can be established by chorionic villus sampling or amniocentesis, fetal ultrasound can show increased nuchal translucency, increased nuchal thickening, pleural effusions and generalized hydrops [31]. Developmental delays are always present, and intellectual disability is typically in the range of moderate mental retardation [28, 29]. Diagnosis in newborn baby may be difficult unless the cardiac lesion is severe, with either significant pulmonary stenosis or severe cardiomyopathy. The diagnosis can only be confirmed genetically if there is an affected parent with a recognized mutation [25, 27, 30].


**3. Effects of active elements**

A number of active soldering filler metals for direct soldering of difficultto-wet materials have been reported. S-Bond technologies LLC has developed a series of active solder metals and an active soldering process [25]. In a prior study, the active filler metallic alloy Sn–Ag–Ti(Ce, Ga) was successfully used to join indium tin oxide (ITO) targets with Cu backing plates at 250°C in air [26]. Moreover, a lower-melting-point-active-filler metal Sn56Bi4Ti(Ce, Ga) with a low bonding temperature of 180°C was used to join ZnS–SiO2 targets with Cu backing plates [27]. Due to the high chemical activity of Ti, it can easily form the required subsequent chemical reaction between filler metal and substrate. Fu et al. [28] studied the effect of Ti content on the wetting behavior of the Sn0.3Ag0.7Cu/AlN system. They demonstrated that the addition of Ti to Sn–Ag–Cu filler resulted in a significant enhancement of wettability for Ti content of 4–10%. Chang et al. [24, 26, 29, 30] have shown that the affinity of rare earth elements to oxygen gives rise to the reaction of Ti with some difficult-to-wet materials at a low temperature. Moreover, rare earth elements have a very strong affinity for oxygen, nitrogen, carbon, or almost all metals and hence create chemical reactions at the interface [31]. Qu et al. [32] investigated the effect of Ti content and Y additions on the oxidation behavior of Sn–Ag–Ti solder. Their results indicated that the addition of Y significantly improved the oxidation resistance of Sn–Ag–Ti solder. Due to the higher affinity of Y for oxygen than Ti, the Y added to the solder efficiently inhibited the oxidation of Ti during the soldering process. Many researchers have demonstrated that rare earth element dopants can significantly enhance solder bonding with difficult-to-wet materials [33–36]. The addition of Ti and rare earth elements to Sn or In alloys improves the solderability by increasing the wettability on difficult-to-wet materials. Furthermore, the oxidation resistances of these soldering filler metals are somewhat limited. For example, the addition of the rare earth element Ce to Sn3.5Ag4Ti solder protects Ti from oxidation and enhances the activity of Ti [26, 28, 32]. Magnesium is also very chemically active and has good electric and thermal conductivity. It is also a suitable additive active element for Sn or In alloys used to increase the wetting in some applications of electronic packaging [37, 38]. Chang et al. [39, 40] have also developed a series of magnesium-containing active solders, as listed in **Tables 2–4**. Sn3.5Ag0.5Cu1Mg filler metal was used for joining alumina with alumina at 250°C in air. The microstructure of the bonding interface of Al2O3/Al2O3 joint is shown in **Figure 4**, which demonstrates a good wettability of the filler metal on the alumina. Hence, a satisfactory joint can be obtained using the magnesium-containing active filler. A good bonding strength of 6.54 MPa can be achieved using the Sn3.5Ag0.5Cu1Mg filler metal.

**53**

**Solder**

M–S M–SA M–SAC

M–SB M–SC M–SP M–SZ

**Table 2.**

*Magnesium-containing Sn-based active solders and melting ranges.*

Bal.

0

0

0

1–15

0

0

0.1–5

Bal.

0

0

0

0

10–50

0

0.1–5

Bal.

0

0

0.1–2

0

0

0

0.1–5

Bal.

0

0

0

0

0

10–60

0.1–5

Bal.

0

0.5–5

0.1–2

0

0

0

0.1–5

Bal.

0

0.5–5

0

0

0

0

0.1–5

Bal.

0

0

0

0

0

0

0.1–5

**Sn**

**In**

**Ag**

**Cu**

**Zn**

**Pb**

**Bi**

**Mg**

**Melting range, °C**

220–232 220–232 220–232 140–220

220–232

180–220

180–232

*Active Solders and Active Soldering*

*DOI: http://dx.doi.org/10.5772/intechopen.82382*


*Article* **Combined Optimal Torque Feedforward and Modal Current Feedback Control for Low Inductance PM Motors**

## **Roland Kasper \* and Dmytro Golovakha**

Chair of Mechatronics, Otto von Guericke University, 39106 Magdeburg, Germany<EMAIL_ADDRESS>**\*** Correspondence<EMAIL_ADDRESS>
Received: 7 October 2020; Accepted: 22 November 2020; Published: 25 November 2020

**Abstract:** Small sized electric motors providing high specific torque and power are required for many mobile applications. Air gap windings technology allows to create innovative lightweight and high-power electric motors that show low phase inductances. Low inductance leads to a small motor time constant, which enables fast current and torque control, but requires a high switching frequency and short sampling time to keep current ripples and losses in an acceptable range. This paper proposes an optimal torque feedforward control method, minimizing either torque ripples or motor losses, combined with a very robust and computation-efficient modal current feedback control. Compared to well-known control methods based on the Clarke-Park Transformations, the proposed strategy reduces torque ripples and motor losses significantly and offers a very fast implementation on standard microcontrollers with high robustness, e.g., against measurement errors of rotor angle. To verify the accuracy of the proposed control method, an experimental setup was used including a wheel hub motor built with a slotless air gap winding of low inductance, a standard microcontroller and GaN (Gallium Nitride) Power Devices allowing for high PWM switching frequencies. The proposed control method was validated first by correlation of simulation and experimental results and second by comparison to conventional field-oriented control.

**Keywords:** optimal control; modal current control; feedforward torque control; feedback current control; torque ripples and loss minimization; low inductance permanent magnet motor

## **1. Introduction**

Manufacturers of electric vehicles or electric planes require electric motors with small size, lightweight construction and maximum efficiency, providing at the same time high torque and power. For low-power applications (<200 W), electrical motor weight can be reduced by air gap winding designs offered, e.g., by Faulhaber and Maxxon [1]. A new slotless air gap winding design for a 15-inch wheel-hub motor providing high power of 40 kW at a speed of 1500 rpm and a very low weight of 20 kg is presented in References [2–4]. Wheel hub motors take a new step in technology of electric vehicles as they allow to create completely new designs of mobile applications without a lot of the mechanics used today and a lot more room for passengers and baggage. High specific power and torque densities are the main indicators of the quality of wheel hub motors. This way, the very lightweight wheel hub motors based on air gap windings [2–4] are most promising.

Usually, motors are based on slotted windings, which significantly increase the motor weight and reduce specific torque and power density. Slotless air gap winding design reduces the weight of electric motors, as it avoids a big part of stator back-iron needed for conventional slotted machines. Additionally, a very high torque can be generated without any torque ripple induced by slotted geometry. However, low number of turns and low iron volume in air gap winding designs lead to very low phase inductances of only several μH, which makes control a challenge [4,5]. For this

reason, a high pulse width modulation (PWM) switching frequency of about 100 kHz is needed to keep current ripples, and accordingly torque ripples and associated losses, in a demanded range. In addition, the motor control must be adapted to low phase inductance and high PWM frequency for microcontrollers with a very small sampling step size.

Depending on the phase current waveform, conventional control methods for permanent magnet (PM) motors can be divided into two groups: based on the block commutation [5–9] and based on the Clarke-Park Transformations [10–16]. The first one is usually used for low-cost and low-power applications because of low manufacturing costs and simple design. On the other hand, this leads to a high torque ripple waveform caused by non-ideal commutation currents [5–9]. This disadvantage is even more significant for PM motors with low inductance due to the inverse relationship between phase inductances and current ripples. Trigonometric Clarke-Park Transformations transfer phase currents into a torque generating Q-part and a field generating D-part (DQ control), dependent on rotor position [10–16]. This gives the opportunity for smoother phase commutations, which decreases current and torque ripple but assumes pure sinusoidal waveforms for B-field (magnetic flux density) and phase currents. For high sampling frequencies, calculation of transformations is a high burden for the microcontroller. If the B-field consists of significantly higher harmonics, they should be compensated by adding additionally higher harmonic parts to the phase currents. This method may be unacceptable for high-frequency control, and only iterative approaches are known [10–14].

This article proposes a combined optimal torque feedforward and modal current feedback control method for PM motors with very low phase inductance. Previously, in References [17,18], a high-frequency Combined Optimal Torque and Modal Current Control (OTMIC) was proposed for low inductance PM motors focused on the minimization of motor losses. In this article, this method for loss minimization is described as mathematically complete. Further, it is extended to torque ripple minimization to give a powerful optimization method flexibly adaptable to different goals. Limitations of References [17,18] given by growing size of symbolic expressions will be avoided by a new matrix formulation of the algorithm that allows for adaptive real-time applications. It is possible to switch online between both optimization strategies to fulfill changing demands depending on certain operation points (e.g., low speed → minimal torque ripple, high speed → minimal loss). In case of motors based on air gap winding designs, motor B-field is nearly independent of speed, torque and phase currents. This conclusion was used to explicitly take into consideration all harmonics of B-field for torque control. In an off-line optimization step, optimal current values for a set of electric angles are stored in a table for on-line usage under hard real-time conditions. By means of a very robust modal current control approach, which works independently on rotor angle, the 3-phase current control problem can be reduced to a 2-phase modal one, based on a linear model of the PM machine with constant coefficients. It becomes evident that the non-controllable state (one of the 3-phase currents) can be eliminated without any pre-conditions, e.g., on B-field waveform, and all statements on stability are global using this approach. Additionally, modal transformation matrices are constant, especially independent of electrical angle and any physical parameter. This reduces computation effort significantly compared, e.g., to Park-Clarke Transformation, where transformation matrices change with the angle. Errors of angle measurement or estimation have only a very limited effect on current control. Thus, independence of motor parameters increases the robustness of the transformation due to any physical changes, further allowing for a very fast software implementation on a low-cost microcontroller with an acceptable sampling step size. Optimization as well as control problem can be solved symbolically, allowing for very fast and adaptive implementations.

In the second section of this article, a new approach of PM motor control based on the mathematical model of slotless air gap winding PM motor with very low phase inductance is presented. The proposed method combines modal feedback control to guarantee the desired stability, dynamics and robustness margins with optimal feedforward control to minimize important motor features like ohmic losses or torque ripple. The last section shows the experimental and simulation results of the proposed method and comparison of the proposed control with conventional Field-Oriented Control (FOC) based on DQ Clarke-Park Transformations (DQ control). A PM wheel hub motor with slotless air gap windings and very small inductances (near 1.5 μH per phase) was used as a test object.

## **2. Design of the Proposed Combined Optimal Feedforward Torque and Modal Current Feedback Control for Low Inductance PM Motors**

## *2.1. Operation Principle of PM Motor with Very Low Phase Inductance*

The dynamic model of a PM motor with slotless air gap winding is obtained considering the following assumptions [3]:

A model is shown in Figure 1, where *R*—phase resistance, *L*, *M*—phase self and mutual inductance, *e* = - *ea eb ec T* —phase back-EMFs (back electromotive force), *u* = - *ua ub uc T* , *i* = - *ia ib ic T* —phase voltages and currents, *uS*—voltage at star point and *uDC*, *iDC*—input direct voltage, current to PM motor inverter [2–4].

**Figure 1.** B6-bridge-fed 3-phase permanent magnet (PM) drive connections.

Considering the Y-connection, Kirchhoff's first Law

$$i\_a + i\_b + i\_c = 0 \tag{1}$$

and Kirchhoff's second Law

$$
\begin{bmatrix} u\_d \\ u\_b \\ u\_c \end{bmatrix} = \begin{bmatrix} \text{R} & 0 & 0 \\ 0 & \text{R} & 0 \\ 0 & 0 & \text{R} \end{bmatrix} \begin{bmatrix} i\_d \\ i\_b \\ i\_c \end{bmatrix} + \begin{bmatrix} \text{L} & -M & -M \\ -M & \text{L} & -M \\ -M & -M & \text{L} \end{bmatrix} \begin{bmatrix} di\_d/dt \\ di\_b/dt \\ di\_c/dt \end{bmatrix} + \begin{bmatrix} e\_d \\ e\_b \\ e\_c \end{bmatrix} + \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} u\_S \tag{2}
$$

or more compact

$$
\underline{\mathbf{u}} = \underline{\mathbf{R}}\,\underline{\mathbf{i}} + \underline{\mathbf{L}}\,d\underline{\mathbf{i}}/dt + \underline{\mathbf{e}} + \underline{\mathbf{u}}\_{\mathcal{S}}\tag{3}
$$

state the mathematical model of a 3-phase PM motor. The 3-phase back-EMF values

$$
\underline{e} = \omega \, k\_M \, \underline{B}(\varphi),
\tag{4}
$$

depend on ω—the mechanical angular velocity of the rotor, *kM*—a motor geometric constant and *B* = - *Ba*(ϕ) *Bb*(ϕ) *Bc*(ϕ) *T* —the vector of averaged B-fields acting on air gap winding phases [3], which itself depends on ϕ—the electrical angle. Obviously, *Ba*(ϕ) = *B*(ϕ), *Bb*(ϕ) = *B* ϕ − 2π 3 and *Bc*(ϕ) = *B* ϕ − 4π 3 are given by the harmonic magnetic field density generated by permanent magnets, calculated by:

$$B(\varphi) = \sum\_{k} b\_{k} \sin(k \,\varphi). \tag{5}$$

as a function of electric angle and odd harmonic coefficients, *bk*. Either FE analysis of the underlying magnetic circuit or line-fitting of measured back-EMF values give the B-field harmonic coefficients with very good accuracy [2–4].

Electrical torque is generated by Lorentz force [2–4]:

$$T\_E = k\_M \begin{bmatrix} B\_d & B\_b & B\_c \end{bmatrix} \begin{bmatrix} i\_d \\ i\_b \\ i\_c \end{bmatrix} = k\_M \underline{B}^T \dot{\underline{t}} \tag{6}$$

acting on the airgap winding. Loss torque:

$$T\_L = d\,\,\omega + c\,\,\tag{7}$$

collects linear mechanical friction together with back-iron and airgap winding eddy losses into the linear friction coefficient *d* and mechanical coulomb friction together with back-iron hysteresis losses into the constant friction coefficient *c*. It will be noted that loss torque *TL* and resulting loss power depends only on speed and is independent of motor current. Electrical torque *TE* reduced by loss torque *TL* gives motor output torque:

$$T\_M = T\_E - T\_L.\tag{8}$$

Equations (1)–(8) describe the motor model in terms of back-EMF, output torque and phase currents based on information of angular position ϕ, angular velocity ω, B-field harmonics and motor parameters *kM*, *d* and *c*. Torque Equation (6) shows that the adaptation of phase current waveforms taking into account the B-field harmonics is the key to motor torque control [2–4].

Phase currents *i*(ϕ), like B-field, can also be defined as harmonic functions of electrical angle ϕ:

$$i(\boldsymbol{\varphi}) = \sum\_{k} a\_{k} \sin(k \, \boldsymbol{\varphi}).\tag{9}$$

Cosine terms are omitted. If included, they would vanish during optimization. From (1), we get additional constraints:

$$a\_{\mathfrak{A}} = 0\tag{10}$$

for current coefficients. Average electrical torque:

$$T\_A = \frac{1}{2\pi} \int\_0^{2\pi} T\_E \, d\varphi = \frac{3}{2} \, k\_M \sum\_k a\_k b\_k \tag{11}$$

can then be expressed by Fourier coefficients of phase current and B-Field. Using Equations (5) and (8)–(11), in this paper will be proposed a new method to generate optimal phase currents to generate a given torque *TRe f* for an arbitrary harmonic B-field, while minimizing either the motor losses or alternatively while minimizing the output torque ripples.

## *2.2. Optimal Control for Minimal Motor Losses*

Generation of a given torque *TRe f* with maximum efficiency or, equivalently expressed, with minimum losses *PL* is a typical design requirement of an electrical motor. Averaged total motor losses consist of ohmic and non-ohmic losses [3]:

$$\begin{aligned} P\_L &= \frac{1}{2\pi} \int\_0^{2\pi} \left( R \left( \dot{i}\_a^2 + \dot{i}\_b^2 + \dot{i}\_c^2 \right) + d \,\omega^2 + c \,\omega \right) d\phi\\ P\_L &= \frac{3R}{2} \sum\_k a\_k^2 + d \cdot \overline{\omega} \,^2 + c \cdot \overline{\omega} \end{aligned} \tag{12}$$

where non-ohmic losses depend only on the average angular speed in a pole pair segment:

$$
\overline{\omega} = \int\_0^{2\pi} \omega d\varphi \quad \text{and} \quad \overline{\omega}^2 = \int\_0^{2\pi} \omega^2 d\varphi \tag{13}
$$

and ohmic losses can be expressed by Fourier coefficients of phase currents according to (9). Given demands lead to the mathematical optimization problem for minimization of motor losses *PL* while generating a demanded torque *TRe f* :

$$Min = P\_L \quad \text{with constraint} \quad T\_A = T\_{Ref} \tag{14}$$

for unknown parameters *ak* of the phase current harmonics based on the given harmonics *bk* of the B-field. The solution of this quadratic optimization problem can be determined analytically, e.g., by combining cost function and constraints in a Lagrange function, calculating derivatives and solving first-order conditions for unknown coefficients:

$$a\_{\rm ml} = \frac{2}{3} \frac{T\_{\rm Ref}}{k\_{\rm M}} \frac{b\_{\rm m}}{\overline{b}^2} \tag{15}$$

with the sum of squares of selected harmonics of B-field:

$$\left|\overline{b}^2 = \sum\_{m} b\_{m}^2\right.\tag{16}$$

and the selection indices:

$$m = 1, 5, 7, 11, 13, 17, 19, 23 \dots \text{ } \tag{17}$$

Remaining parameters *ak* are zero. Selection indices show that some odd harmonics of phase current {3, 9, 15, ... } will not contribute to torque. The optimal current waveforms can be calculated from (15) for each electrical angle taking into account the harmonics of B-field, motor constant *kM* and given reference torque *TRe f* . This approach achieves that each demanded torque can be generated with minimum motor losses for arbitrary B-field and regardless of motor speed. Air gap winding PM motor design allows to have nearly ideally constant B-field harmonics with minor sensitivity to temperature changes. If necessary, e.g., for application to other motor types, the effect of temperature on B-field and phase resistances can be easily incorporated into the model and adapted online.

### *2.3. Optimal Control for Minimal Torque Ripples*

Generation of a given torque *TRe f* with minimum torque ripples is another typical design requirement of an electrical motor, especially if vibrations and noise are critical. Torque ripple is defined as mean square deviation between electrical torque *TE* and average torque *TA*:

$$T\_R^2 = \frac{1}{2\pi} \int\_0^{2\pi} \left(T\_E - T\_A\right)^2 d\varphi \tag{18}$$

In this case, optimal current can be determined solving the optimization problem:

$$M\dot{m} = T\_R^2 \quad \text{with constraint} \quad T\_A = T\_{Ref} \tag{19}$$

Inserting current definition (9) into the integral (18), the optimization problem stated in (19) again can be solved analytically by formulating Lagrange function, calculating derivatives and solving the first-order conditions. Besides this straightforward path, there exists another approach, which leads to more simple expressions and allows further insight into the solution. Starting from (5), (6) harmonics

$$t\_k = \frac{1}{\pi} \int\_0^{2\pi} T\_E \cos(\theta \, k \, \varphi) d\varphi \tag{20}$$

of electrical torque *TE* can be determined and collected in vector

$$
\underline{t} = \underline{A}\,\underline{a}\tag{21}
$$

with matrix

$$
\underline{A} = \frac{2}{3}k\_{\rm M} \begin{bmatrix} 2b\_{1} & 2b\_{5} & 2b\_{7} & 2b\_{11} & 2b\_{13} & 2b\_{17} & 2b\_{19} & 2b\_{23} \\ \mathbf{b}\_{7} - b\_{5} & b\_{11} - b\_{1} & b\_{13} + b\_{1} & b\_{17} + b\_{5} & b\_{19} + b\_{7} & b\_{23} + b\_{11} & b\_{13} & b\_{17} \\ \mathbf{b}\_{13} - b\_{11} & b\_{17} - b\_{7} & b\_{19} - b\_{5} & b\_{23} - b\_{1} & b\_{1} & b\_{5} & b\_{7} & b\_{11} \\ \mathbf{b}\_{19} - b\_{17} & b\_{23} - b\_{13} & -b\_{11} & -b\_{7} & -b\_{5} & -b\_{1} & b\_{1} & b\_{5} \\ -b\_{23} & -b\_{19} & -b\_{17} & -b\_{13} & -b\_{11} & -b\_{7} & -b\_{5} & -b\_{1} \\ \mathbf{0} & \mathbf{0} & -b\_{23} & -b\_{19} & -b\_{17} & -b\_{13} & -b\_{11} & -b\_{7} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & -b\_{23} & -b\_{19} & -b\_{17} & -b\_{13} \\ \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & \mathbf{0} & -b\_{23} & -b\_{19} \end{bmatrix} \tag{22}
$$

and vector of current harmonics

$$\underline{a} = [a\_{1\prime}, a\_{5\prime}, a\_{7\prime}, a\_{11\prime}, a\_{13\prime}, a\_{17\prime}, a\_{19\prime}, a\_{23}] \tag{23}$$

for an example with 23 harmonics. Only average value at zero and multiples of the sixth harmonic appear. All other coefficients are zero. Matrix *A* is square and has full rank. Defining the torque harmonics

$$\underline{t} = \begin{bmatrix} 2 \ T\_{\text{Ref}}, 0, 0, 0, 0, 0, 0, 0, 0 \end{bmatrix} \tag{24}$$

in a way that the zero coefficient is given by the demanded torque *TRe f* and all other torque harmonics vanish, delivers the solution for the above-mentioned optimization problem by solving the linear system of equations defined by (21). For practical applications, a much smaller number of harmonics than given in (23) will be sufficient. The larger number presented here helps to demonstrate the structure of the matrix. It is important to state that also the torque ripples minimization leads to an analytical solution for optimal currents that is well suited for online and adaptive applications.

#### *2.4. Modal Current Control*

So far, we have two feedforward strategies to implement either loss minimal or torque ripples minimal operation of the motor. Both strategies rely on current control, which is able to deal with higher current harmonics, which means also with higher frequencies. A modal current control method, exploiting all structural benefits of given control problem and allowing for very high-speed control, will be presented in more detail in this section. The complete model of the PM motor with air gap winding is defined by (1)–(3). Node Equation (1) shows that only 2 of the 3 phase currents are independent. Taking this dependency into account, (3) can be written as

$$
\underline{G}(\underline{u} - \underline{e}) = \underline{R}\,\underline{i} + \underline{\mathbf{L}}d\underline{i}/dt\tag{25}
$$

with

$$
\underline{G} = \frac{1}{3} \begin{bmatrix} 2 & -1 & -1 \\ -1 & 2 & -1 \\ -1 & -1 & 2 \end{bmatrix} . \tag{26}
$$

For simplicity, back-EMF *e* can be neglected and later added to input voltage *u* as a feedforward compensation or simply treated as a disturbance for the controller. This coupled system for the 3 phase currents *i* can be completely decoupled with a modal transformation

$$
\begin{bmatrix} f\_{\Sigma} \\ f\_1 \\ f\_2 \end{bmatrix} = \underbrace{\frac{1}{3} \begin{bmatrix} 1 & 1 & 1 \\ -1 & -1 & 2 \\ -1 & 2 & -1 \end{bmatrix}}\_{\underline{W}} \begin{bmatrix} i\_a \\ i\_b \\ i\_c \end{bmatrix} \tag{27}
$$

applied to system (25) in a way that modal inductance matrix

$$
\underline{\Lambda} = \underline{\underline{W}} \underline{L} \, \underline{\underline{W}}^{-1} = \begin{bmatrix} L - 2M & 0 & 0 \\ 0 & L + M & 0 \\ 0 & 0 & L + M \end{bmatrix} \tag{28}
$$

gets diagonal. Phase currents *i* are transformed to modal currents *J* = - *J*Σ *J*1 *J*2 *T* . Considering (1) and the first row of the transformation matrix defined in (27), modal current *J*Σ will be zero. Thus, only 2 out of 3 modal currents associated with the modal inductances *L* + *M* are relevant. The decoupled modal system

$$
\begin{bmatrix} 1 & 0 & 0 & 0 \\ -1 & -1 & 2 & \\ -1 & 2 & -1 & \end{bmatrix} \begin{bmatrix} u\_d \\ u\_b \\ u\_c \end{bmatrix} = \begin{bmatrix} R & 0 & 0 \\ 0 & R & 0 \\ 0 & 0 & R \end{bmatrix} \begin{bmatrix} J\_\Sigma \\ J\_1 \\ J\_2 \end{bmatrix} + \begin{bmatrix} L - 2M & 0 & 0 \\ 0 & L + M & 0 \\ 0 & 0 & L + M \end{bmatrix} \begin{bmatrix} dJ\_\Sigma/dt \\ dJ\_1/dt \\ dJ\_2/dt \end{bmatrix} \tag{29}
$$

shows that modal current *J*Σ is not controllable as the associated row of the modal input matrix is completely zero. The remaining 2 modal currents, *J*1 and *J*2, come from 2 identical first-order systems with time constant *L*+*M R* . Eliminating non-controllable current *J*Σ gives the reduced controllable system

$$
\underbrace{\frac{1}{3}\begin{bmatrix}-1 & -1 & 2 \\ -1 & 2 & -1 \end{bmatrix}}\_{\mathbb{E}}\begin{bmatrix}u\_d\\u\_b\\u\_c\end{bmatrix} = \begin{bmatrix}R & 0\\0 & R\end{bmatrix}\begin{bmatrix}f\_1\\f\_2\end{bmatrix} + \begin{bmatrix}L+M & 0\\0 & L+M\end{bmatrix}\begin{bmatrix}dI\_1/dt\\dI\_2/dt\end{bmatrix}\tag{30}
$$

Thus, the 3-phase current control problem is reduced to the control of two completely identical but decoupled first-order systems, associated with modal currents *J*1 and *J*2. The redundant total current *J*Σ displays any errors in current control loop and can be used as an indicator of the quality of the system online. Modal currents *J*1 and *J*2 are not connected and can be controlled completely independent by modal input voltages

$$
\underline{V} = \begin{bmatrix} V\_1 \\ V\_2 \end{bmatrix} = \underline{\Gamma} \cdot \underline{\omega} \tag{31}
$$

as shown in Figure 2. This simple separation based on the modal transformation given in (27) does not use any trigonometric calculations based on the rotor angle as in conventional Clarke-Park Transformations, is independent of motor parameters and is well defined for any shape of B-field.

**Figure 2.** Modal control loop for modal currents *J*1,2.

According to (30). motor transfer function is given by

$$G\_M(s) = \frac{1/R}{1 + \frac{L+M}{R}s}.\tag{32}$$

For high-speed control of low inductance PM motors with high number of poles, current sensor dynamics must be included in the control loop with a first-order sensor model

$$G\_S(s) = \frac{1}{1 + T\_S s} \tag{33}$$

and sensor time constant *TS*. As a microcontroller-driven B6-bridge generates PWM pulses at frequency *fPWM* = 1/Δ*t* to control motor input voltage and ADC (Analog-to-Digital Converter) samples current sensor signals with the same rate, time continuous transfer function

$$\mathbf{G\_{MS}(s)} = \mathbf{G\_M(s)} \mathbf{G\_S(s)}\tag{34}$$

has to be discretized with that frequency to get the discrete transfer function

$$D\_{MS}(z) = \frac{(\beta - 1 + (1 - \alpha)\delta)z + ((\alpha - 1)\delta - \alpha)\beta + \alpha}{R(\delta - 1)(z - \alpha)(z - \beta)}\tag{35}$$

with sampling time Δ*t*, discrete eigenvalues of motor α = *e* − RΔ*t* L+M , sensor β = *e* − Δ*t TS* and motor/sensor speed ratio δ = L+M R *TS* . Very small motor time constant due to low phase inductance allows to achieve very fast current and electrical torque response with requested time constant *TReq*, which expands the possibilities of design for more complex control systems like dynamic stability control or autonomous driving. To get a controlled system of first order

$$D(z) = \frac{1 - z\_R}{z - z\_R} \tag{36}$$

with requested eigenvalues *zR* = *e* − Δ*t TReq* , it is necessary to use a discrete PID (Proportional-Integral-Derivative) controller with filtered derivative action:

$$D\_{\mathbb{C}}(z) = K\_P + \frac{K\_I}{z - 1} + \frac{K\_D}{N\_D + \frac{1}{z - 1}}.\tag{37}$$

Control parameters can be determined by comparison of coefficients of discrete closed loop

$$D(z) = \frac{D\_{\mathbb{C}}(z)D\_{\text{MS}}(z)}{1 + D\_{\mathbb{C}}(z)D\_{\text{MS}}(z)}\tag{38}$$

and reference transfer function given in (36), as

$$\begin{array}{l} \mathcal{K}\_{P} = \frac{(1 - \alpha + \delta(\beta - 1))R(z\_{R} - 1)}{(\delta - 1)(\beta - 1)(\alpha - 1)}; \\\\ \mathcal{K}\_{I} = R(z\_{R} - 1); \\\\ \mathcal{K}\_{D} = \frac{R\delta(z\_{R} - 1)(\beta - \alpha)^{2}}{(\delta - 1)^{2}(\beta - 1)^{2}(\alpha - 1)^{2}}; \\\\ \mathcal{N}\_{D} = \frac{\beta - 1 + \delta(1 - \alpha)}{(\delta - 1)(\beta - 1)(\alpha - 1)}. \end{array} \tag{39}$$

A saturation of output and I-part of the PID controller guarantees safe operation in the case of limited supply voltages. Outputs from PID controllers *DC*(*z*) are two modal control voltages, *V*1 and *V*2. According to (31), *V*1 and *V*2 must be transformed back to three control voltages *u* by means of a Moore Penrose pseudo-inverse transformation matrix Γ+

$$
\begin{bmatrix} u\_a \\ u\_b \\ u\_c \end{bmatrix} = \underbrace{\begin{bmatrix} -1 & -1 \\ 0 & 1 \\ 1 & 0 \end{bmatrix}}\_{\underline{\mathbf{L}}^+} \begin{bmatrix} V\_1 \\ V\_2 \end{bmatrix}. \tag{40}
$$

Modal current control ensures system stability regardless of fluctuations in system parameters caused by changes of motor temperature and other factors. Moreover, it can be implemented for PM synchronous motors with any waveform of B-field. However, it should be noted, that the motor model should satisfy the mathematical model described with Equations (1)–(3), which can be very good when performed for PM motors with air gap windings and also other PM motors.

## *2.5. Control Diagram of OTMIC*

The proposed control diagram of Combined Optimal Torque and Modal Current Control (OTMIC) is shown in Figure 3. The control algorithm uses a torque reference *TRe f* and measured electrical angle ϕ to estimate optimal phase current waveforms for motor loss or torque ripples minimization, *i Re f* = - *iaRe f*(ϕ) *ibRe f*(ϕ) *icRe f*(ϕ) *T* , based on one of the optimization methods described in Sections 3.1 and 3.2. The optimal currents *i Re f* are used as a reference for measured phase currents *i*. Current errors Δ*i* as differences between reference and measured currents are fed to the Modal Current Control described in Section 2.4 and used to generate the control voltages *u*, which set PM motor in motion with the optimal torque waveform via a SVPWM (Space Vector Pulse Width Modulation) and a B6-bridge. Architecture of OTMIC control allows to simplify the microcontroller torque/current control loop by using constant matrices with simple coefficients for modal transformation.

**Figure 3.** Proposed Combined Optimal Torque and Modal Current Control (OTMIC) diagram of PM motor drive system.

In addition, optimal reference currents according to (9) and (15)–(17) for minimal Loss Control or from (9) and (21)–(24) for minimal Torque Ripple Control can be calculated off-line for a set of angles and stored in a table. These simplifications allow to implement the control loop with very small step size of Δ*t* < 10 μ*s* on a common low-cost microcontroller.

## **3. Units Simulation and Experimental Results**

## *3.1. Motivation and Experimental Setup*

A wheel hub motor for a hub-less scooter, shown in Figure 4 on the experimental setup (left above) and in the dissembled state (right) for better demonstration of the air gab winding, will be used for verification of OTMIC control method. The motor has a very low total weight of 2.7 kg, a high nominal power of 4.8 kW and a nominal torque of 80 Nm. More motor data is given in Table 1, where B odd Harmonics are 1st, 3rd, 5th and 7th harmonic numbers. The experimental platform shown in Figure 4 was used to verify the proposed OTMIC method with either minimized motor losses or minimized torque ripples for low inductance PM motors.

**Figure 4.** Experimental setup for OTMIC verification [18].

**Table 1.** Air gab winding wheel-hub motor parameters [17,18].

Due to elimination of stator iron, motor inductance is very low (near 1.5 μH per phase). Thus, motor needs an adapted control with high switching frequency of about 100 kHz to keep current ripples and total losses in an acceptable range. Control parameters calculated according to (39) are also given in Table 1.

To drive the motor, six GS61008P MOSFETs (metal–oxide–silicon transistors) from company GaN Systems, able to switch up to 90 A at a rate up to 300 kHz, were connected as a B6-bridge. Due to limited MOSFETs cooling of experimental boards, phase current was restricted to 20 A for the experiments. Hall-effect-based sensors from Allegro ACS730 were used for phase current measurement with a very small sensor time constant of 1 μs. Rotor angle is delivered by an encoder using 5 k increments. 100 kHz PWM switching frequency to power the B6-bridge requires a very small step size in the microcontroller (lower than 10 μs). To achieve this requirement, an ARM Cortex-M4F has been used running at 200 MHz. It allows to implement the control loop shown in Figure 3 in 8.3 μs. In comparison to the proposed method, a conventional DQ control needs a minimum of 9.4 μs, which underlines the effectiveness of the proposed method. This comparison can be seen in Figure 5.

**Figure 5.** Step response of simulated and measured torque for OTMIC and FOC (DQ).

This means that OTMIC control can be calculated faster and in addition, gives the optimal torque in contrast to FOC (DQ) based on the Clarke-Parke Transformations.

#### *3.2. Verification of the Proposed Method*

The simulation results presented in this study have been performed through Matlab/Simulink environment based on the mathematical model of the PM motor described in Section 2 and the control model presented in Section 3. Conventional DQ field-oriented vector control used as a reference to the proposed OTMIC was also implemented in the experiment to control the wheel hub motor, with the parameters in Table 1.

The motor dynamic behavior can be verified by means of step response of electrical torque *TE*. As shown in Figure 6, measured and simulated torque of proposed OTMIC and conventional DQ methods were carried out according to zero velocity, mechanically fixed rotor and 5 Nm reference torque *TRe f* (green). Because torque sensor bandwidth was too low for this experiment, electrical torque generated in air gap winding (grey) was calculated using (6) based on the values of measured currents and the electric angle with a given motor geometric constant *kM*, and compared with the simulation for OTMIC (blue) and DQ (red) control methods. As can be seen form Figure 6, the difference between both methods is minimal due to the very low motor time constant. The exciting fast torque step response within 35 μs underlines the very high dynamics of this type of motor. The slight difference between simulation and measurement is due to parasitic inductances and capacitances in power lines

and supply. This can be easily considered in the motor model but was not done in this experiment to show the robustness of the control.

**Figure 6.** Step response of simulated and measured torque for OTMIC and DQ.

For a more detailed demonstration of the basic principles of the proposed control algorithm, Figure 7 shows the results of modeling the ideal optimal current waveforms to minimize the torque ripples (OTMIC TRO) and losses (OTMIC LO) for two waveforms of B-Field (Case A with odd harmonic coefficients *bk* from Table 1 and Case B with *bk* from Reference [19], which result from a change in the air gap between stator and rotor). For a more detailed analysis, the torque RMS (root mean square) and efficiency value are also presented for a sinusoidal current of conventional DQ control based on the Clarke-Park Transformations. Figure 7 shows the simulation results of an ideal system without any errors in the phase current or rotor position measurements. As can be seen, the optimal phase current waveforms are able to the minimize torque ripples or maximize motor efficiency based on the Equations (6) and (12). The advantages of the OTMIC TRO are seen very well in Figure 7. In an ideal system, OTMIC TRO eliminants any torque fluctuations for any waveform of the B-field. OTMIC with loss optimization (LO) changes the phase current waveform and improves loss rates and efficiency of the system with increased torque ripples. The advantages of the OTMIC LO in comparison with the standard DQ method are visible only in the presence of significant parasitic harmonics in the form of a B-field. Simply said, the ideal sinusoidal B-field leads to the same torque ripples and motor loss for every method.

**Figure 7.** Working principles of the proposed OTMIC control algorithm for two B-Field waveforms.

Simulated and measured phase currents and torque results during normal operation of proposed OTMIC control with minimization of torque ripple (TRO Figure 8a—simulation, Figure 9a—measurement) and losses (LO Figures 8b and 9b) as well as a conventional vector DQ control (DQ Figures 8c and 9c) correspond to the references: ω = 8 rad/s and TRef = 10 Nm. The behavior of phase currents and torque for both OTMIC optimizations given in Figure 9a,b has a slight asymmetry caused by speed fluctuations of load machine and errors in angle measurements, which could not be completely avoided in experimental setup. The current and torque harmonic distribution for the aforementioned control approaches are shown in Figure 8d for simulation and in Figure 9d for measured results. The amplitude of each harmonic component is normalized relative to that of a fundamental one. The FFT (Fast Fourier transform) analyses of simulation currents and torques underline the main idea of the proposed method. As shown in Figure 8d (left), the phase current waveforms of OTMIC have 5th and 7th harmonics expected to conventional control. On the other hand, the torque waveform of OTMIC with torque ripple optimization TRO (blue) is deprived of such harmonics, which leads to the very small torque fluctuations as opposed to DQ control, as shown in Figure 8d (right).

**Figure 8.** Simulation results of stator current and torque of: (**a**) OTMIC with torque ripples optimization, (**b**) OTMIC with losses optimization, (**c**) conventional DQ control and (**d**) harmonic spectrum of phase current (left) and torque (right) for every method [18].

The harmonic spectrum of measured phase current with OTMIC control shown in Figure 9d (left) has parasitical 2nd, 4th and 6th harmonics due to inaccuracies in experimental setup, mainly caused by interactions of control system and load machine, but they are less than 1% of that of the fundamental one. The necessary 5th and 7th harmonics have a slight deviation of about 0.5% of the fundamental one compared to simulation results. The current waveform of conventional DQ control should be quite similar to a sinusoidal, as shown in the simulation results in Figure 8c and harmonic analyses in Figure 8d (left). However, the harmonic spectrum of measured phase currents by the conventional method consist of high 3rd and 4th harmonics due to the high sensitivity of the standard method based on the trigonometric transformations to errors in the control system, especially errors in angle measurement.

**Figure 9.** Experimental results of stator current and torque of: (**a**) OTMIC with torque ripples optimization, (**b**) OTMIC with losses optimization, (**c**) conventional DQ control and (**d**) harmonic spectrum of phase current (left) and torque (right) for every method [18].

The measured torque harmonic distribution shown in Figure 9d (right) consists of a large number of harmonics due to speed errors in rotating shaft and additional torque produced by load machine. However, the 6th and 12th harmonics retain their tendency and can be compared with the simulation. In addition, the FFT analyses of measured torques in Figure 9d (right) shows that the proposed OTMIC control with torque ripple minimization is able to compensate additional harmonics in B-field. Summarized, the measured results show very good correspondence to theoretical calculations. As opposed to OTMIC, the Clarke-Park Transformations need a very accurate rotor angle measurement, which can be seen in the larger asymmetries given in Figure 9c. Thus, the proposed OTMIC method is less sensitive to speed fluctuations and angle errors due to the absence of trigonometric transformations of phase currents based on the electric angle.

Figure 10 compares the measured values of motor efficiency for OTMIC control with LO and TRO and conventional DQ control. Motor efficiency was measured with given constant velocity of 30 rad/s, variable torque from 1 to 10 Nm and output power from 30 to 300 W. Results show that OTMIC control with loss minimization increases the system efficiency by 0.7% in compassion to the conventional method, while delivering the same torque. However, for a correct analysis of the proposed control in case of a motor loss and efficiency, any errors in the measurement system should be avoided and motor torque and current should be increased to the rated values, which could not be fully realized in our experimental setup. More detailed analyses of the system efficiency should be investigated in the future work.

**Figure 10.** Motor efficiency for OTMIC and DQ control.

Simulation and experimental results show that the OTMIC control system is less sensitive to errors in the electrical angle and phase currents measurements compared to FOC. In addition, the proposed method worked very robustly independent of deviations of motor parameters like phase resistance due to the temperature and the speed of fluctuations due to the load motor.

## **4. Conclusions**

This paper proposed a Combined Optimal Torque feedforward and Modal Current feedback Control architecture (OTMIC) for PM motors with very low inductance and higher harmonic B-field, which minimizes motor losses or torque ripples/motor noise by means of offline calculation of optimal current waveform. Optimal three-phase currents are used as reference values to the measured currents. The optimization algorithm considers all relevant coefficients of B-field harmonic distribution to calculate the appropriate current waveform off-line and employs an extremely fast table-lookup for real-time implementation in the microcontroller. Modal current feedback control provides stability, high system dynamics without deviation of a given reference and high robustness against variation of motor parameters or errors in rotor angle measurement.

Compared to classical field-oriented control methods based on the cumbersome and complex Clarke-Park Transformations, the proposed control is simpler for implementation on the microcontroller and allows to minimize either torque ripples or motor losses. As a result, the proposed OTMIC control can reach its full potential in high-frequency systems, where simplicity of the control algorithm and microcontroller calculation time matters. Due to the transformations used in the conventional DQ method, the phase currents' waveforms have to be nearly ideally sinusoidal. This means that conventional methods to achieve the specified requirements of motor torque or total losses demand the special concepts and additional real-time calculations to adapt the phase current waveform to the non-sinusoidal waveform of the magnetic field. It complicates the control system and increases the calculation time in the microcontroller. Moreover, in real high-frequency control systems with errors in current and angle measurements, this problem can be more significant. Experimental results show that the Clarke-Park Transformations for electric drives with a very small motor time constant and high number of poles introduces significant current deviations from the values given. In this case, the proposed OTMIC control method used for PM synchronous motors with a very low phase inductance and tested experimentally shows a very good match between simulated and measured waveforms of phase current and torque. The proposed control can also be applied to other electric motors such as brushless DC (BLDC), asynchronous or PM motors, with any waveform of B-field waveform.

**Author Contributions:** Conceptualization, R.K. and D.G.; methodology, R.K.; software, R.K. and D.G.; validation, D.G.; formal analysis, R.K. and D.G.; writing—original draft preparation, R.K. and D.G.; writing—review and editing, R.K. and D.G.; funding acquisition, R.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported in part by the European Commission under Grant ERDF (European Regional Development Fund) and the County of Saxony-Anhalt.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

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A search of PubMed, Google Scholar, and Science Direct was performed for studies published in 2020, 2021, and 2022 and studies that were published before this period using pre-defined terminology. The search terms (COVID-19) and (Food Choice Motives) and (lockdown); (Food Habits) and (Lockdown); (Dietary change) and (COVID-19) and (lockdown); and (COVID-19) and (nutrition or diet) were used initially in the three databases to obtain an understanding of the current research on this topic area. Following this, an alternative phrasing search in relevant publications and a guidance on the search strategy were finalized. The search terms were then finalized with the 10 search terms (research themes) used in this systematic review. This search took place in September and October of 2022. No restrictions and filters were used to avoid excluding any papers of interest. The results were evaluated for eligibility based on the title, abstract, and full text. Two researchers independently screened the articles for eligibility (DS and ZCK) following these inclusion criteria:

The search was broad to identify all studies fitting the review's aim. No authors were contacted for further information.

The limitations of the review process included the following factors:

#### **3. Results**

After reviewing all eligible papers and exploring changes in FCM caused by the pandemic, ten research themes were extracted from each publication for evaluation (Table 1). These included health, convenience, sensory appeal, nutritional quality, moral concerns, weight control, mood and anxiety, familiarity, price, and shopping frequency behavior.

#### *3.1. Food Consumption and Health*

Food consumption and consumer health have always been one of the main issues that all countries have to address in the new post-COVID-19 era [20]. In recent decades, trends in food consumption have been linked to an increase in chronic food-related diseases, such as obesity, cancer, and coronary heart disease [21]. Experts have focused on promoting medical rules about nutrient intake and proper consumption, while avoiding targeting foods. They, thus, issued guidelines for a balanced diet that does not exclude the consumption of specific food products [22]. Consumption of foods high in fat, sugar, and sodium, and low in fiber, are considered to be risk factors for hypertension, cardiovascular disease, diabetes, breast cancer, colon cancer, rectal cancer, prostate cancer, and obesity [23].

Studies that occurred during the pandemic have shown that energy intake exceeding energy expenditure is a major risk factor for a wide range of medical conditions, ranging from diabetes and cancer to musculoskeletal disorders [24,25]. Health attitudes have changed during the COVID-19 era. Due to long periods of limited mobility, consumers were more prone to unhealthy lifestyles, such as reduced or no physical activity and excessive sedentary behavior, which had negative effects on eating habits as well as on body composition [25,26].

The post-COVID-19 era seems to have altered the lives of people, leading to significant changes in various health behaviors. In particular, according to Drieskens et al. [27], increased consumption of sweet or salty snacks and less physical activity have led to an increase in body weight during pandemic-related confinement among adults in Belgium, and more measures are needed to support individuals to achieve healthier behaviors to tackle overweight and obesity. Furthermore, Martínez-de-Quel et al. [28] showed that pandemic-related confinement caused a drawback on the levels of physical activity and sleeping on Spanish citizens, while body weight and self-perceived well-being were also adversely affected, indicating that those with an active life were more susceptible to such disruptions. Robinson et al. [29] reported perceived negative changes in weight-related eating behaviors and physical activity and perceived negative changes in the barriers that adults living in the UK faced in the management of their weight (e.g., motivation problems and control around eating), compared to pre-lockdown. A study on the effect of quarantine on the diet and exercise of Lithuanians and the association between health behaviors and changes in body weight by Kriaucioniene et al. [30] showed a decrease in the consumption of carbonated or sugary drinks, fast foods, and sweets and an increase in the consumption of homemade sweets and fried foods. This was combined with a decrease in physical activity, resulting in an increase in body weight. Huber et al. [31] in a cross-sectional study from Bavarian universities showed that an increase in food consumption, mainly bread and sweets, combined with a lower level of physical activity led to a reduction in weight maintenance during the pandemic. Poelman et al. [32] analyzed consumer behavior in

the Netherlands where they demonstrated that consumers kept their eating behavior or food purchases during COVID-19 lockdown, thus keeping their eating habits; however, in people with overweight and obesity, the lockdown had a negative effect on healthy food choices. A Polish study showed that health and weight control were more important during the pandemic compared to the period before it [33].

Although the short-term effects of lockdown practices differ between countries, women seem to be most affected [34]. Jaeger et al. [35], in a propositions to relevant authorities, proposed the need for educational programs to increase physical activity and to teach basic principles of healthy eating and the construction of a healthy food "plate" in case of a possible future lockdown.

**Proposition 1.** *The present data on health motives indicate that consumers decreased physical activity during the COVID-19 pandemic, with parallel increase in consumption of unhealthy foods which had negative effects on their health. A minority of consumers, though, preferred to choose homemade cooked meals for better results.*

#### *3.2. Food Consumption and Convenience*

The term 'convenience' is associated with 'convenience foods'—that is, those foods prepared and made available to shoppers designed for easy and quick consumption. Such foods include frozen or chilled foods, ready meals, confectionery, snacks and beverages, processed meat and cheese, canned products, and ready-to-eat foods for sale [36]. The convenience factor has always influenced the choice of food, with the result that the consumption of ready-made food is the outcome of the strategy followed by households to cope with time pressure [37]. However, Botonaki et al. [38] in their study on whether or not to choose a ready meal, which included spouse's work status and socio-demographic characteristics of consumers as the control variables, showed that the convenience of cooked meals may be negatively assessed as their consumption is connected with emotions of guilt, regret, and neglect.

Since the beginning of the pandemic, lifestyle and eating habits have been greatly affected [39]. An increase in the use of convenience foods, such as instant and frozen foods, has been recorded worldwide [40]. According to the study by Ko et al. [41], there was a significant decrease in visits to markets, fast food restaurants, catering restaurants, buffet restaurants, and snack bars, while food deliveries and home-cooked meals increased significantly during the pandemic period. The study by Marty et al. showed that the importance of convenience, familiarity, and price decreased during the pandemic [13]. Liu and Chen reported that the young Chinese have normalized takeaway food consumption and developed their own ways of reducing food/food-related waste, which reflect young people's lifestyles [36].

**Proposition 2.** *The present data clearly indicate an increase in the purchase of takeaway food and ready-to-go meals during the pandemic to avoid visits to supermarket or elsewhere.*

#### *3.3. Food Consumption and Sensory Appeal*

Sensory appeal is the taste, smell, texture, and appearance of food [42]. It is crucial in directing consumers' selection for various foods. Groups of consumers, such as consumers attaching high importance to all determinants ("demanding consumers" with high significance for all determinants), consumers attaching low importance to all determinants ("indifferent consumers" with low significance for all determinants), "healthy eaters" (health as the most important determinant of food choices), and "hedonists" (convenience, sensory appeal, and price as the most important determinants) experienced specific changes in their food consumption during COVID-19 [43]. Moreover, the "healthy eaters" were identified as those who preferred mostly vegetables; the "hedonists" showed a preference for meat/fish, dairy, and snacks; the "demanding consumers" showed a preference for

all food categories; and the "indifferent consumers" showed a low preference for all food categories [44]. Sensory appeal seemed to be unaffected by "coronavirus pandemic" of rural China households [45]. Mood and sensory appeal became less important in Polish citizens [33] and Croatian males [46], but more important in French [13] and British people (except sensory appeal which was unchanged) [47].

**Proposition 3.** *The present data show that sensory appeal motives have not been a priority for consumers during COVID-19 and beyond; therefore, their preferences have not significantly changed for this motive.*

#### *3.4. Food Consumption and Nutritional Quality*

The health effect of food prevention is undeniable. The combination of food and drink in a concentrated period, combining taste and consumption, is called a meal. Analyzing meals and identifying what foods and drinks are consumed allows nutritionists to understand how different combinations of foods and drinks, throughout the day, affect overall diet quality and health [48]. The nutrients in foods combined with their effects can be interactive because, when consuming foods, humans primarily select to mix foods in meals or snacks according to their own formulations. Dietary advice and other nutritional recommendations are given on a daily basis to consumers so that they can understand and follow them [49]. However, the quality, food safety, and nutritional value of foods vary widely around the world. Serious constraints on global production include contamination of the food chain and water by persistent pesticide residues, and reduction in nutrient content and flavors due to intensive production and/or low-cost food processing [50].

During the pandemic, consumers chose healthy, safe, and better quality food compared to their previous practices [51]. However, in some countries, such as Greece [52] and UK [29], studies showed a consumer preference for unhealthy products, such as snacks and pre-packaged 'over-processed' foods high in fats, sugars, and salt. Ruiz-Roso et al. [53] reported a diversification in dietary habits and altered consumption of processed foods, fruits, and vegetables for consumers in Italy, Spain, Chile, Colombia, and Brazil. They further demonstrated new purchasing habits, such as 'conscious shopping', 'bartering' for cheap items, and attention on 'basics' [53]. Alternatively, consumers preferred groceries as the food of choice and consistently anticipated spending most of their money on foods since they are one of the basic human needs [54]. Finally, studies by Ellison et al. [55] and Huang et al. [56] showed that consumers spent money on foods with a longer shelf life and easier access to the market. Rahman et al. found significant differences in food and nutrient consumption, with marked differences in 'fruits and vegetables', vitamin A, folic acid, calcium, iron, magnesium, phosphorus, and potassium, resulting in higher rates of inadequate nutrient intake for those consumers who frequently consumed take-out foods [40].

**Proposition 4.** *Current results show that consumers with a preference for nutritional quality of foods became more sensitive during the pandemic and beyond, spending more money and consuming more nutritional foods, such as grocery and fruits.*

#### *3.5. Food Consumption and Ethical Concern*

Nowadays, environmental aspects are of main concern for consumers, such as pollution, food production, environment, and food waste, which are ethical issues related to the impact of food consumption on the environment or society [57]. Climate activists, who are concerned about the deterioration of the planet from consumption, food choosers who are vegetarians and vegans, and conservation activists who have concerns about the preservation of existing goods via their reuse and repair are three of the five types of anti-consumers that have emerged following the pandemic with ethical concerns about the conservation of the planet [58].

Food waste can be approached from an ethical perspective. The awareness, understanding, and embracing of ethical attitudes related to food waste may lead to a consumer's behavior change. Crisis, such as the COVID-19 pandemic, has curbed food waste, which can have an impact on climate change and environmental pollution, according to a study by Caloran [59]. Young people seem to be sensitive to food waste effects on the planet, and how this generates an environmental impact in large cities [57]. In addition, this generation will try to change their attitudes to the requirements of environmental conservation and generate innovative solutions to ease the negative impact of an increased population on the planet.

Food consumption behavioral changes have altered the variety of foods [60]. The impact that food waste has on the environment has also been changed by the pandemic as reflected by the fluctuations and short-term alternatives in the consumption of foods [54]. Not only these changes have exacerbated food waste, such as overcooked foods, foods exceeding long-term storage in the freezer, and overbuying, but they have also favored a decrease in food waste, including less frequent shopping, more carefully planned meals, and consumption of the long-term stored food [57].

Above all, food shopping in the context of COVID-19 is now a more careful process, with close attention to one's need and money available. Health maintenance concerns as well as ethical concerns can lead to better behavior on food waste and environmental footprint [59].

**Proposition 5.** *Overall, the data show that food waste and environmental effects are two ethical parameters receiving increased attention from consumers during COVID-19 and beyond.*

#### *3.6. Food Consumption and Weight Control*

Older people and women have always been more concerned about controlling their weight and following diet and exercise programs [61]. With increased exercise and eating low-calorie, portion-controlled meals, including liquid meal replacements, they try to maintain weight loss [62].

Stress and boredom were two factors that led to overweight as consumers ate 'comfort foods' with sugar and consumed more energy/calories during the COVID-19 period [63]. This is a type of emotional state driven by affective (strong eating desire), behavioral (food seeking), cognitive (thoughts about food), and physiological (salivation) sensations. Fattysweet products and sweet-tasting beverages were consumed (including fruit juices) during snacking. Sweets, biscuits, cakes, soft drinks, and sugary foods led to an increase in energy intake and, thus, an increase in body weight during the pandemic [13]. Warning elements in body weight have been recorded during lockdown worldwide [64], probably due to physical activity reduction and increased consumption caused by isolation measures during the pandemic, which resulted in a higher incidence of overweight, obesity, and relevant comorbidities [65]. Only half of the adult population, with increased sweet consumption and less exercise, kept their body weight during the first six months of pandemic-related confinement in Belgium [27]. According to Kalligeros et al. [66], cardiometabolic disorders caused by weight and body fat gain following physical inactivity increased among patients with coronavirus disease. Furthermore, the studies by Wiklund et al. [67] and Lighter et al. [68] have shown that obesity is associated with more severe disease and COVID-19 outcomes. An unhealthy diet is known to lead to chronic inflammation and reduced defense against viruses [69]. In addition, unhealthy eating habits during the pandemic led to increased obesity and caused a chronic systemic inflammatory condition that, along with other chronic non-communicable diseases, such as dyslipidemia, hypertension, heart disease, diabetes, and lung disease, increased the risk of severe complications [70,71]. These studies showed an increase in body weight of women during the Coliform pandemic. Social support during COVID-19 was part of many obesity management programs and was connected with better dietary adherence, better weight management, and even a lower risk of mortality [72]. For both sexes, it may be necessary to improve and adapt weight management goals. Ultimately, the best way to obtain all the necessary nutrients is a balanced diet to ensure normal immune system function while reducing the risk of obesity [72].

**Proposition 6.** *The present data indicate that lockdown resulted in an increase in overall food consumption and consumption of junk food on many occasions, which led to unbalanced body weight and disorders.*

#### *3.7. Food Consumption and Mood and Stress*

According to Singh and Mood [73], overeating and obesity are the results of changing food choice and intake due to changing mood and emotional eating, where these psychological "pathways" influence not only food choice but also the quantity and frequency of meals. Individuals are unable to perceive their state of hunger and satiety and show preference for palatable 'comfort foods' as a means of relieving their negative emotions. Furthermore, sweets, chocolate, cakes, and biscuits are more frequently consumed under stressful conditions, especially high-fat and energy-dense foods are chosen by people during stressful life events [74–76]. Food consumption has also been considered as a strategy for coping with stressful situations [77]. Indeed, it has been observed that anxiety and depressive symptoms lead to poorer food choices [78]. Moreover, it appears that individuals who experience periods of stress over-consume foods that they would usually avoid and this consumption makes them feel better [79].

The COVID-19 pandemic has drastically influenced consumers' consumption and food choice behavior in relation to depression, stress, and anxiety [80]. The huge disruption in social interactions, contacts, and daily lives of consumers, increased unemployment, and business disruption have caused increased loneliness, fear of illness, financial stress, food insecurity, and insecurity about the future and livelihood [81]. Even families were affected and put under a lot of pressure when parents educated their children at home during lockdown and fed their children more often than usual. In addition, stress and negative emotions led to emotional eating, i.e., eating as a result of negative emotions without any real evidence of hunger [82]. Larger amounts of foods, such as sweets, fatty foods, and salty snacks, were reported to be consumed during the pandemic for emotional reasons. The negative impact on normal food consumption was fully mediated by emotional distress during the pandemic [63]. The role of emotional distress as a key mechanism to explain coping behaviors, such as comfort food consumption, which were adopted as a consequence of the economic, interpersonal, and health impact of the pandemic, was also revealed. In another study comparing behaviors among different sexes, women consumed larger amounts of high-sugar and high-calorie foods during COVID-19 for reasons of emotion, leading to greater weight gain compared to men [83].

**Proposition 7.** *The present data show an increase in food consumption during COVID and beyond due to a deterioration in mental health, such as depression, stress, and anxiety, which has continued globally to date.*

#### *3.8. Food Consumption and Familiarity*

Familiarity is the cognitive ability to apply knowledge acquired via experience to objects or stimuli [84]. Regarding everyday food choices, familiarity is important as it relates to the close relationship between a person's eating habits during childhood, adolescence, and adulthood. Moreover, familiarity is due to previous personal experiences and tends to be linked to tradition, as many consumers prefer to choose foods that are familiar to them [85]. Still, familiarity is significant among those who have a relatively strong focus on prevention, who tend to be in good health, responsible, and safety oriented, and who consider their food a factor to cope with their stress and bad mood. However, consumers are demanding healthier food and, to meet this demand, technological solutions (such

as reduced-fat and functional foods) have been implemented, together with a return to naturalness and purity of food [86].

During COVID-19, familiarity helped consumers address anxiety and mood when choosing foods, sustaining a healthy diet through adherence to personal nutrition by selecting foods they know and trust [87]. The lockdown led consumers to become familiar with the internet and other technologies to order the foods that they knew and consumed, demonstrating that familiarity depends also on personal past experiences [20]. Familiarity, convenience, and price became more important in Croatian adults [46], but less so in French [13] and British adults (except price more) [47], and remained the same for Polish adolescents [33].

**Proposition 8.** *Overall, the present data prove that familiarity is a motive that has helped consumers cope with the pandemic as far as food choice is concerned and will also help them with online purchase, which has drastically increased to date.*

#### *3.9. Food Consumption and Price*

One of the most important determinants of consumption patterns and living standards is food prices. In particular, high prices can have a significant negative impact on nutritional status and health, especially among poor people [88]. Green et al. [89] showed that price changes in the global food market have a greater impact on low-income countries and the poorest households within these countries. In addition, interferences in the purchase and consumption of goods due to self-control problems or temporally inconsistent preferences of consumers, who derive direct satisfaction from food consumption itself, influence future health costs [90]. Low-income consumers have lower fruit and vegetable consumption and reduced intake of nutrients (e.g., calcium and vitamins) [91].

During the pandemic and periods of lockdowns, the global restriction on 'normal' economic production affected all aspects of life, including decisions regarding food purchase, leading to an unstable food chain [92]. The consequence of this situation was that prices increased, and many consumers were unable to buy enough essentials and foods. In addition, jobs were lost and consumers cooked more at home in order to reduce the cost of their daily meals [93]. The crisis revealed the compromises that households were willing to make in times of shortages [94]. What led many households to consume less and make more careful food choices was the increase in food prices combined with any loss of disposable household income [95]. The International Food Security Assessment model that estimates changes in food consumption and food gaps in developing countries uses gross domestic product (GDP) and food price changes as the main inputs for its predictions. The results show that the lockdowns led to a decrease in global GDP of 7.2 per cent, and an increase in grain prices of 9 per cent. These changes led to an increase in the number of food-insecure people in 2020, totaling 211 million (a 27.8 per cent increase) [95]. In the post-COVID-19 era, price promotion policies are a common practice worldwide in order to control the price increase; however, this results in food waste by encouraging over-purchase, according to half of the reported studies [96]. In contrast, the other half of the studies prove that consumers buying price-promoted foods show average or even lower levels of household food waste [96]. Low-income households, due to the pandemic, may not have the financial resources to engage in any stockpiling behavior compared to higher-income households. In addition, important price shocks negatively affect household consumption patterns of low-income groups [97].

**Proposition 9.** *The findings indicate that price remains a major food choice motive during COVID and beyond, with low-income groups being more affected by the foreseeable economic global recession. Therefore, it may be the most important selection criterion, among the 10 presented motives, for food choice in the new era.*

#### *3.10. Food Consumption and Shopping Frequency Behavior*

Consumers' low income leads them to shop less and at longer intervals, which affects the sustainability and shelf life of perishable foods, such as vegetables and fresh fruits [98,99]. There are also those consumers who either do not have access to a supermarket or grocery store [100], or do not have transport to make it easier for them to buy foods from the store they want themselves after comparing prices [101].

During the pandemic, consumers were forced to adapt their behaviors, including their food purchasing habits and their preferences, to the new routine. Schools were closed, homework was imposed, and except in certain specific occupational areas (e.g., working in hospital, in grocery stores), leaving home was only allowed under restricted conditions following the completion of special certificates [82]. Consumers' eating habits were significantly affected by perceived risk and precautions related to the COVID-19 virus, resulting in major changes in consumers' shopping behavior [102].

Children's eating behavior and feeding practices changed through changes in their appetite, enjoyment of food, responsiveness to food, and emotional overeating, as well as frequency of snacking between meals which was enhanced by parents who became more indulgent [103]. Furthermore, as demonstrated by Moynihan et al. [104] an increased intake in energy was connected with high levels of boredom. The COVID-19 pandemic altered the content of meals for a proportion of consumers [105] as well as the frequency of their consumption [82], leading to an increase in demand for food [106]. As a consequence, the food industry and food production chain have been adapted to the new situation and consumers' demands [106].

In addition, online shopping had become the first choice during the home restriction, and the demand for online food shopping increased significantly for both food and wine [107,108]. As the COVID-19 pandemic had completely disrupted food production and food supply chains due to unavailable labor, lack of transport, and closure of various food services, such as restaurants [109], it is inevitable that a major change has been observed in the way households buy, prepare, and consume food [110]. A significant shift to traditional foods has also been studied with similar results [111,112]. Consumers must learn how to use e-commerce, ICT technologies, and credit card payment in order to facilitate food shopping and avoid crowding. This also demands the presence of an online mechanism for protection of personal and transactional data to avoid online attacks [113].

**Proposition 10.** *Overall, it appears that, due to lockdown, shopping frequency decreased with a parallel increase in online purchase and delivery, a tendency which has continued to date.*

A main limitation of this scoping review is the short-term nature of the studies included (2020/2021/2022) and, therefore, there is limited literature available based upon which a discussion of the findings was presented. However, the review type chosen was viewed as the most appropriate for the current topic.

**Table 1.** One hundred and seven papers in this review divided by theme and sub-theme.

**Table 1.** *Cont.*

#### **4. Conclusions**

FCMs, based on the reviewed data, have been affected by the COVID-19 pandemic in certain ways, which are affecting consumers' choice beyond the pandemic in the new economic era. Of the ten motives presented in this review, food price seems to be the most important motive for consumers during and post-COVID-19 periods and will be more significant if a global recession is under way. Decreased physical activity, as well as increased mental disorders related to stress and anxiety, had a negative effect on health, weight control, and mood and stress motives, along with increased food consumption, especially junk food. On the other hand, the lockdowns had a positive impact on other motives, such as convenience and familiarity, and a negative impact on shopping frequency motive, with increased online and takeaway purchase of foods. Food waste and its effects on the environment seem to be the parameters concerning motives such as ethics and nutritional status. Nutritional quality and sensory appeal are two consumer motives which have not been affected significantly by the pandemic.

Raising consumer awareness of the incentives for food choice is of paramount importance in the new post-COVID-19 era where the world is changing drastically. Motivations, such as sensory appeal, taste, and food presentation, can act as a one-way street for emotional eating in the new era since they remain as important as before the pandemic. Family members, feeling secure and having high feelings of self-esteem when preparing a pleasant dish, bring the family together and create a context of daily stability, where people know what to expect with familiar dishes and can assess whether hunger and nutritional needs

will be met. In addition, price as an incentive for food choice becomes important due to uncertainty about work and economic future and a sense of impending precariousness experienced by affected consumers. Still, changes in food choice incentives have led to an increased awareness of food choices, with the aim of sustaining health through quality food, ensuring healthy eating behaviors and attitudes toward food waste, and meeting environmental footprint and ethical concerns. In addition, online shopping is a rising choice for consumers, a habit that has emerged due to home confinement and the demand for online shopping has increased significantly.

Finally, could the pandemic be assumed to be the threshold at which the usual rules behind food choices are suspended? The definite answer will be known in three to five years when the new worldwide economic and social condition will be clear and stable, and an adequate number of studies will be published by then. In this review, we present the studies that have reported to date, with the above conclusions derived from their results so far.

It would be more workable if consumers are encouraged to explore healthier food options, such as fresh fruits, vegetables, and whole foods. In addition, when purchasing foods, they should be informed about the foods and their beneficial properties (e.g., vegetables, fruits, and organic wine) and reflect more on the importance of certain foods to themselves and their families through their cultural identity. Online food shopping can surely contribute to a reduction in food waste thanks to the elimination of frenzied shopping routines at supermarkets or groceries and can open up space to new fields of study. On the other hand, defining a "new" index of consumer satisfaction can alter the sale strategies of retail managers and entrepreneurs.

The present review, which is based on the findings reported so far, offers 10 specific propositions for each one of the 10 main food choice motives examined, which can be used as a practical and theoretical basis for the development of a "new" FCM index that can be used by retail managers, food companies, and any other parties involved in the agri-food chain.

Despite the abovementioned conclusions, more studies are needed in the years to come to ensure their validity since only studies from a three-year period are recorded so far (2020–2022).

Furthermore, studies with longer time periods beyond the pandemic should be performed to ensure the long-term validity of the conclusions.

Finally, studies on consumer segments, such as young adults, older people, and children, will be very important to verify these findings and their applications to food choice motives.

**Author Contributions:** Conceptualization and methodology, D.S. and Z.C.K.; writing—original draft preparation, Z.C.K.; supervision and editing, D.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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