**Abstract**

Tamarillo has a unique flavor and rich history. South American fruit is popular in New Zealand. Tamarillo is commercially grown in New Zealand and South America. It grows best under sub-tropical areas. It matures in 18 months. It's 2 m tall and has lifespan of about 7 years. For propagation, seeds or cuttings are employed, and plant trimming for effective output varies according to propagation method. Tamarillo plants are wind-sensitive and need cover or windbreaks. It's a beautiful fruit with smooth, shining skin. Yellow, red, and purple fruits are available. This fruit contains vitamins, minerals, fiber, and antioxidants. It has a very low-calorie count. Breeding focuses on fruit quality through selection, hybridization, and biotechnological treatments for plantation and post-harvest management. Diseases, pests, viruses, and physiological abnormalities can be treated with plant protection techniques. Like other fruits, it's edible after harvesting. Made into juices, concentrates, jams, gelatins, and sweets. If processing facilities and transport are available, it can be exported as pulp or concentrate. The tamarillo can diversify sub-tropical fruit production as a high-value cash crop, with excellent fruits commanding premium prices in Europe, North America, and Japan.

**Keywords:** botany, breeding, biotechnology, cultivation, composition, diseases, origin, production, processing, pests, trade, value addition


*4.1.1 Flavonols*

Flavonols are O-glycosidic, ketonic chemicals with a 3-position sugar fraction. Flavonols are antioxidants that prevent the development of ROS. Due to UV, ozone radiation, and other damaging substances, the skin is the most prevalent target for oxidative stress. The combination of conjugated double bonds in the C-ring and adjacent hydroxyl groups in the B-ring gives flavonols their antioxidant properties [24]. Quercetin, kaempferol, myricetin, and other compounds are included in this class.

#### *4.1.2 Quercetin*

Quercetin is a flavonol in various foods, including leafy greens, citrus fruits, berries, and other fruits and vegetables. Quercetin inhibits edema, leukocyte production,

#### *Recent Advances in Flavonoid Metabolism: An Updated Review DOI: http://dx.doi.org/10.5772/intechopen.106243*

and irritation. It helps reconstruct the skin's structure by endorsing the synthesis of new collagen fibers and generating ground substances [25]. Inflammatory mediators such as interleukins (IL) and prostaglandins (PGs), which are generated by COX, LOX, and LPS, are likewise suppressed by quercetin. The enzyme nitric oxide synthase, which also creates reactive nitrogen species like peroxynitrite, produces nitric oxide (NO), an inflammatory mediator. Quercetin is an antioxidant that prevents oxidative stress by inhibiting all of the mediators that cause it [26]. It avoids cell death by inhibiting the caspase-3 pathway and lowers mast cell development by inhibiting mast cell synthesis has an anti-allergic impact on histidine decarboxylase, IL-6, and monocyte chemoattractant protein (MCP-1).

#### *4.1.3 Kaempferol*

Kaempferol is primarily present in berries and plants of the allium and brassica family. It has antineoplastic, anti-inflammatory, and anti-allergic properties. It works as an anti-inflammatory drug by inhibiting NO synthase, which produces NO, a pro-inflammatory mediator. With the help of nuclear factor-inducing kinase (NIK) and mitogen-activated protein kinase (MAPKs), it also suppresses (NF-kappa B) [27]. It also inhibits COX-2 via decreasing nitric oxide synthase and TNF-, resulting in anti-inflammatory action. However, because kaempferol suffers significant first-pass metabolism and has a bioavailability of about 2%, topical application is preferable. UVB-induced cancer and photo-inflammation are treated with kaempferol, a new drug. It has been tested in skin cancer patients who have high levels of COX 2 enzymes. JB6 P+ mouse epidermal cells reduce AP-1 (Activator protein) activity via reducing COX-2. To test for AP-1 transactivation, JB6 P+ mouse epidermal cells were transfected with a luciferase reporter plasmid containing AP-1, and it was discovered that kaempferol reduces COX and AP-1 activities in a dose-dependent way, assisting in anticancer activity. The protooncogene tyrosine protein-kinase Src (Src) is a protooncogene that plays a key role in cell propagation, differentiation, and survival. Src activity is inhibited by kaempferol, which strives with ATP for the Src requisite position.

#### **4.2 Flavanones**

Consequent to the flavones origin, these fragrant ketones in citrus fruits like oranges and lemons. As a byproduct of citrus farming, a substantial quantity of hesperidin is produced. They are cytotoxic and inhibit tumor development; therefore, they might be used as anticancer drugs. Flavanones also serve as an anti-inflammatory and constrain protein tyrosine kinase, affecting cell development, distinction, mitosis, and death [28].

#### *4.2.1 Hesperetin and hesperidin*

Hesperidin has anti-inflammatory, antidiabetic, neuroprotective, and other properties. The aglycone component of hesperidin has antioxidant and anti-inflammatory properties by intruding with arachidonic acid, inhibiting COX and LOX enzymes, and limiting inflammatory mediator production [29]. It can whiten skin by reducing hyperpigmentation caused by UV radiation. Hesperetin and hesperidin generate anti-allergic action by constraining the issue of histamine from mast cells. They can also lower HMG CoA reductase and acyl CoA levels, resulting in a hypolipidemic effect. Hesperetin has a log P value ranging from 1.7 to 2.20, making it lipophilic and hard to absorb orally.

#### *4.2.2 Naringenin*

Naringenin has numerous properties, including antioxidant, antidiabetic, anti-inflammatory, and antineoplastic properties. It demonstrates antioxidants. MC1R: Melanocortin 1 receptor, MSH: Melanocyte stimulating hormone, MiTF: Microphthalmia associated transcription factor, Type-1: Tyrosinase related protein 1, Type-2: Tyrosinase related protein 2, ASIP: Agouti signaling protein] [− MSH: Melanocyte stimulating hormone, MC1R: Melanocortin 1 receptor, MiTF: Microphthalmia associated transcription factor, Type-2: Tyrosina Journal of Controlled Release 296 (2019) 190–201 R.L. Nagula, S. Wairkar 195 acts via chelating metal ions and constraining xanthine oxidase, averting oxygen radical generation and lipid peroxidation. It can also scavenge ROS through the ∙OH substitution. Because naringenin is hydrophobic and has low solubility and bioavailability, it can be used topically to create an effective formulation [30].

#### **4.3 Flavanols**

They are not to be mistaken with flavonol since they lack the ketone group. Epigallocatechin-3-gallate, proanthocyanidins, and other members of this class are included. Tea, chocolate, and a variety of vegetables and fruits contain them naturally [31]. The FDA, for use in a variety of medicinal formulations, has approved catechins and their derivatives.

#### *4.3.1 Catechins*

Catechins have antioxidant, photoprotective, anti-aging, anti-inflammatory, anticancer, neuroprotective, cardioprotective, antiviral, and antibacterial properties, among others. Epigallocatechin and epicatechin are abundant in grape seed extract and tea polyphenols. By scavenging free radicals, it has an antioxidant action [32]. Anti-inflammatory action is induced via inhibiting the COX enzyme, NO, PGs, and H2O2 production. Catechins help wounds heal faster by foraging free radicals at the wound site.

#### *4.3.2 Anthocyanins*

Anthocyanins are colorful glycosylated, water-soluble pigments that give fruits and vegetables their blue, red, and purple hues. They have been revealed to have antioxidant, anti-inflammatory, and depigmentation qualities in numerous scientific research.

Delphinidin contains anti-inflammatory, antioxidant, antitumorigenic, and antiangiogenic effects and is identified to suppress osteoclastogenesis in osteoporosis. Delphinidin inhibits the production of seditious intermediaries such as iNOS, NO, IL-6, MCP-1, and TNF-, which are produced when LPS inhibits the NF-B pathway and MEK1/2-ERK1/2 signaling [33]. It was tested for psoriasis on flaky skin mice and shown to reduce epidermal thickness. Infiltrating macrophages and caspase 14 downregulation were also seen. Keratin-14, which induces hyperproliferation, was also reduced. By inhibiting keratin-14, delphinidin serves as an antiproliferative. The level of pathological indicators of psoriasis lesions is reduced when delphinidin is applied to flaky mouse skin.


**Author details**

Han-Yong Jeon Department of Chemical Engineering, Inha University, Incheon, South Korea

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© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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*Review of Sustainable Geosynthetic Development Trend with Environmental Adaptive… DOI: http://dx.doi.org/10.5772/intechopen.90336*


**1. Introduction**

Three-phase asynchronous motors are commonly used in industrial and agricultural production due to their advantages of simple structure, ruggedness, and low price [1–4]. The emergence of vector control allows the AC speed regulation system to have good speed regulation performance, just like a DC speed regulation system [5]. However, vector control has disadvantages, such as dependence on accurate mathematical models, poor adaptability to instruction changes, and sensitivity to changes in the system parameters. Even if the motor parameters and rotor flux linkage are known accurately, decoupling can be achieved under steady-state conditions, and there are still couplings during the field-weakening speed regulation. The nonlinearity of the magnetization curve of the ferromagnetic material in the motor [6] leads to the nonlinearity of the motor inductance, and the change of the inductance parameter reduces the speed control effect of the vector control. The AC control system has the characteristics of non-linearity [1,4], strong couplings, and having multiple variables, which means the traditional control method based on a precise mathematical model faces severe challenges.

The active disturbance rejection control (ADRC) theory was proposed for the control of nonlinear uncertain systems. The system is linearized by compensating for the observed total disturbance. The compensated system can be converted into an integrator series independent of whether the object is deterministic, linear, or nonlinear, or whether it is time-varying or time-invariant. At present, the ADRC theory has been applied to a six-rotor aircraft [7], a permanent magnet synchronous motor [8], DC–DC boost converter [9], and other fields. Abdul-Adheem et al. [10] applied the improved ADRC to the decoupling control of multivariable systems. The coupling is divided into two parts: static coupling (control input of the system) and dynamic coupling (parts other than the control input to the system). All ADRC pass a reversible static matrix (approximately reversible also applies) that is used for decoupling. Compared with the traditional decentralized control method (an automatic disturbance rejection controller designed independently for each part of the system), the improved ADRC decoupling algorithm uses part of the system model information, easing the burden of the extended state observer (ESO) such that the decoupling e ffect is better. Although both numerical simulations and physical verification show that the ADRC controller has a good control e ffect, the large number of modeled non-linear links between the ADRC require high system hardware requirements and increases the di fficulty of real-time control. The second-order auto-disturbance rejection controller has 15 parameters that need to be adjusted, and the direction of the parameter adjustment is di fficult to determine, which brings certain di fficulties in the practical application of the controller. In short, many factors limit the popularity and engineering application of ADRC.

American scholar Gao Zhiqiang explored the connotation and meaning of the idea of auto-disturbance control. He was inspired by the concept of "time scale" [11] proposed by Han Jingqing researchers and proposed the concept of "frequency scale." The parameter setting is carried out through the pole configuration in the frequency domain, and the parameters to be set are reduced to three, which greatly promotes the development and application of the auto-disturbance control theory. Since then, the linear auto-rejection controller has been used in fault detection [12], a wind energy conversion system [13], maximum power point tracking [14], and other fields. Li et al. [15] adopted the concept of "relative order" to determine the order of the linear ADRC (LADRC) controller and designed a second-order LADRC controller to suppress the harmonics to the grid in the AC microgrid. Laghridat et al. [13] applied LADRC to the control of generators and grid-side converters. Compared with the ADRC, an LADRC has the advantages of a fixed structure, an independent object model, clear physical meaning, easy theoretical analysis [13,16], and easy engineering application. However, in practical applications, it is found that the anti-interference performance of LADRC decreases rapidly with the increase of interference and input frequency, which is related to the insu fficient performance of a traditional ESO [17].

This study took the three-phase cage asynchronous motor as the control object, established a mathematical model for it according to the rotor flux linkage orientation, and introduced the structure of the ADRC controller and the role of each component. First, the structure and function of each part of the ADRC controller are introduced. Then, based on the basic principle of deviation control, the adjustment process of each state variable of traditional LESO is discussed and improved. Through theoretical analysis, the stability proof and precision analysis of an improved LESO are given. From the frequency domain, the convergence, tracking, and immunity of the improved linear auto-disturbance controller are analyzed. In the time domain, a large deviation band of the initial value of the internal state variable of the observer is seen and the corresponding value of the system's overshooting is compared. Finally, the control e ffects of the two controllers are compared based on results from Matlab/Simulink digital simulation software (Developed by MathWorks in Natick, MA, USA, and dealt by MathWorks Software (Beijing) Co., Ltd. in Beijing, China).

### **2. Mathematical Modeling of an Asynchronous Motor and Introduction to Classic LADRC**

### *2.1. Mathematical Modeling of the Rotor Flux Orientation of Induction Motor*

To facilitate the research, it was necessary to treat the motor as an ideal motor; therefore, it was necessary to make the following assumptions [18]:

The three-phase winding voltage balance equation in the three-phase stationary coordinate system is shown in Figure 1:

**Figure 1.** Physical model of an asynchronous motor.

The three-phase winding voltage balance equation in the three-phase stationary coordinate system is shown in Equation (1):

$$
\begin{bmatrix} u\_A \\ u\_B \\ u\_C \\ u\_d \\ u\_b \\ u\_c \\ u\_c \end{bmatrix} = \begin{bmatrix} R\_s & 0 & 0 & 0 & 0 & 0 \\ 0 & R\_c & 0 & 0 & 0 & 0 \\ 0 & 0 & R\_s & 0 & 0 & 0 \\ 0 & 0 & 0 & R\_r & 0 & 0 \\ 0 & 0 & 0 & 0 & R\_r & 0 \\ 0 & 0 & 0 & 0 & 0 & R\_r \end{bmatrix} \begin{bmatrix} i\_A \\ i\_B \\ i\_C \\ i\_B \\ i\_B \\ i\_c \end{bmatrix} + \frac{d}{dt} \begin{bmatrix} \psi\_A \\ \psi\_B \\ \psi\_C \\ \psi\_B \\ \psi\_B \\ \psi\_C \end{bmatrix} \tag{1}
$$

where *uA*,*uB*,*uC*,*ua*,*ub* and *uc* are the instantaneous values of the stator (A, B, C) and rotor phase (a, b, c) voltages; *iA*,*iB*,*iC*,*ia* ,*ib* , and *ic* are the instantaneous values of the stator (A, B, C) and rotor (a, b, c) phase currents; and ψ*A*,ψ*B*,ψ*C*,ψ*a*,ψ*b*,ψ*c* are the full flux of each phase winding. *Rs* and *Rr* are the resistances of the stator and rotor windings, respectively.

The flux of each winding of an asynchronous motor is the sum of its own self induction flux and the mutual inductance flux of other windings. Therefore, the flux of the six windings can be expressed as follows:

$$
\begin{bmatrix}
\psi\_s \\
\psi\_r
\end{bmatrix} = \begin{bmatrix}
L\_{ss} & L\_{sr} \\
L\_{rs} & L\_{rr}
\end{bmatrix} \begin{bmatrix}
i\_s \\
i\_r
\end{bmatrix} \tag{2}
$$

where ψ*s* = + ψ*A* ψ*B* ψ*C* ,*T*,ψ*r* = + ψ*a* ψ*b* ψ*c* ,*T*,*is* = + *iA iB iC* ,*T*, and *ir* = + *ia ib ic* ,*T*. The stator inductance matrix is:

$$\mathbf{L}\_{\rm ss} = \begin{bmatrix} L\_{\rm ms} + L\_{\rm ls} & -\frac{1}{2}L\_{\rm ms} & -\frac{1}{2}L\_{\rm ms} \\ -\frac{1}{2}L\_{\rm ms} & L\_{\rm ms} + L\_{\rm ls} & -\frac{1}{2}L\_{\rm ms} \\ -\frac{1}{2}L\_{\rm ms} & -\frac{1}{2}L\_{\rm ms} & L\_{\rm ms} + L\_{\rm ls} \end{bmatrix} . \tag{3}$$

The rotor inductance matrix is:

$$\mathbf{L}\_{rr} = \begin{bmatrix} L\_{\rm wss} + L\_{\rm lr} & -\frac{1}{2}L\_{\rm sws} & -\frac{1}{2}L\_{\rm sws} \\ -\frac{1}{2}L\_{\rm ms} & L\_{\rm ms} + L\_{\rm lr} & -\frac{1}{2}L\_{\rm ms} \\ -\frac{1}{2}L\_{\rm ms} & -\frac{1}{2}L\_{\rm sws} & L\_{\rm ms} + L\_{\rm lr} \end{bmatrix}. \tag{4}$$

The mutual inductance matrix of the stator and rotor is:

$$\mathbf{L}\_{rs} = \mathbf{L}\_{sr}^T = L\_{ms} \begin{bmatrix} \cos\theta & \cos(\theta - \frac{2\pi}{3}) & \cos(\theta + \frac{2\pi}{3}) \\ \cos(\theta + \frac{2\pi}{3}) & \cos\theta & \cos(\theta - \frac{2\pi}{3}) \\ \cos(\theta - \frac{2\pi}{3}) & \cos(\theta + \frac{2\pi}{3}) & \cos\theta \end{bmatrix} . \tag{5}$$

The voltage equation of the asynchronous motor in the rotating orthogonal coordinate system can be obtained from a Park transform:

$$
\begin{bmatrix} u\_{sd} \\ u\_{sq} \\ u\_{rd} \\ u\_{rq} \end{bmatrix} = \begin{bmatrix} R\_s & 0 & 0 & 0 \\ 0 & R\_s & 0 & 0 \\ 0 & 0 & R\_r & 0 \\ 0 & 0 & 0 & R\_r \end{bmatrix} \begin{bmatrix} i\_{sd} \\ i\_{sq} \\ i\_{rd} \\ i\_{rq} \end{bmatrix} + \frac{d}{dt} \begin{bmatrix} \psi\_{sd} \\ \psi\_{sq} \\ \psi\_{rd} \\ \psi\_{rq} \end{bmatrix} + \begin{bmatrix} -\omega\_1 \psi\_{sq} \\ \omega\_1 \psi\_{sd} \\ -(\omega\_1 - \omega) \psi\_{rq} \\ (\omega\_1 - \omega) \psi\_{rd} \end{bmatrix} \tag{6}
$$

where *usd*, *usq*, *urd*, and *urq* are the components of the voltage of the stator and rotor sides along the d and q axes; *isd*, *isq*, *ird*, *irq* are the components of the current of the stator and rotor sides along the d and q axes; ψ*sd*, ψ*sq*, ψ*rd*, and ψ*rq* are the components of the magnetic flux of the stator and rotor sides along the *d* and *q* axes; and ω1 and ω are the synchronous angular velocity and the rotor angular velocity, respectively.

The flux equation of the asynchronous motor in the synchronous rotation orthogonal coordinates system is:

$$
\begin{bmatrix}
\psi\_{sd} \\
\psi\_{sq} \\
\psi\_{rd} \\
\psi\_{rq}
\end{bmatrix} = \begin{bmatrix}
L\_s & 0 & L\_m & 0 \\
0 & L\_s & 0 & L\_m \\
L\_m & 0 & L\_r & 0 \\
0 & L\_m & 0 & L\_r
\end{bmatrix} \begin{bmatrix}
i\_{sd} \\
i\_{sq} \\
i\_{rd} \\
i\_{rq}
\end{bmatrix}' \tag{7}
$$

where *Ls*, *Lr*, and *Lm* are stator inductance, rotor inductance, and mutual inductance between the stator and rotor, respectively. ψ*rd* = ψ*r* when the rotor flux is oriented as in Figure 2.

**Figure 2.** Rotor flux orientation.

Selecting the stator currents and rotor flux as the state variables, and the stator voltages as the control variables, a fourth-order simplified nonlinear differential equation can be given as follows:

$$\begin{cases} \dot{\omega}\_{r} = k\_{1}\psi\_{r}i\_{sq} - \frac{n\_{p}}{f}T\_{L\_{r}}\\ \dot{\psi}\_{rd} = \frac{L\_{m}}{T\_{r}}i\_{sd} - \frac{1}{T\_{r}}\psi\_{r},\\ \dot{i}\_{sd} = -k\_{2}i\_{sd} + k\_{3}\psi\_{r} + \omega\_{1}i\_{sq} + \frac{1}{\sigma L\_{s}}u\_{sd},\\ \dot{i}\_{sq} = -k\_{2}i\_{sq} - \frac{L\_{m}}{\sigma L\_{r}L\_{r}}\psi\_{r}\omega\_{r} - \omega\_{1}i\_{sd} + \frac{1}{\sigma L\_{s}}u\_{sq}. \end{cases} \tag{8}$$

In the above state equations, *np*, *Tr*, and *TL* represent the number of pole pairs of the motor, the load torque, and the rotor time constant, respectively. The coupling between the state variables in Equation (8) causes the nonlinearity of the system [4,10]. The vector control block diagram of the asynchronous motor is shown in Figure 3, in which automatic speed regulator (*ASR*), the automatic current torque regulator (*ACTR*), and the automatic current magnetic regulator (*ACMR*) are the controllers of the vector speed regulation system.

**Figure 3.** Vector control structure of an asynchronous motor. ASR: automatic speed regulator, ACTR: Automatic torque current regulator, ACMR: Automatic magnetic field current regulator SVPWM: Space Vector Pulse Width Modulation.

In Equation (8), there is a cross-coupling term in the state equation of the asynchronous motor, thus resulting in the mutual effect of control of the torque component and the excitation component of the stator current, which further affects the dynamic and static performance of the system. The graphical representation of the coupling term is shown in Figure 4. Decoupling can be achieved if the coupling terms are observed and compensated for [19].

**Figure 4.** Coupling structure of an asynchronous motor.

### *2.2. LADRC Introduction and First-Order LADRC Design*

The ADRC consists of a tracking differentiator (TD) [20,21], an extended state observer (ESO) [22,23], and a nonlinear states error feedback control laws (NLSEF) . Among them, the TD can arrange the transition process for the given input, reduce the "impact" of the original error on the system caused by the given mutation, and realize the differential signal extraction; ESO can observe the state variables and total disturbances (unmodeled dynamics and external disturbances) of the controlled object in a real-time manner; and the NLSEF is used to improve the dynamic characteristics of the closed-loop system. The linear ADRC only replaces the nonlinear part of the original controller with the linear part, where the structure of the controller is shown in Figure 5.

**Figure 5.** Structure of an active disturbance rejection controller (TD: tracking differentiator, NLSEF: nonlinear state error feedback, ESO: extended state observer).

Consider the first-order system [24]:

$$
\dot{y} = -ay + w + bu\_\prime \tag{9}
$$

where *u* is the output of the controller, *y* is the system output, *w* is the external disturbance, *a* is the system parameter, *b* is the controller gain that satisfies *b* ≈ *b*0; the parameters *a* and *b* are unknown. Let *x*1 = *y* and *x*2 = *f*(*y*, *w*) = −*ay* + *w* + (*b* − *b*0)*u*, where *x*1 represents the system output and *x*2 represents the total disturbance of the system. Assuming that *f*(*y*, *w*) is derivable and satisfies . *f*(*y*, *w*) = *h*, the state variables *x*1 = *y* and *x*2 are selected to establish the continuous extended state equation s shown in Equation (10):

$$\begin{cases} \begin{bmatrix} \dot{\mathbf{x}}\_1\\ \dot{\mathbf{x}}\_2 \end{bmatrix} = \begin{bmatrix} 0 & 1\\ 0 & 0 \end{bmatrix} \begin{bmatrix} \mathbf{x}\_1\\ \mathbf{x}\_2 \end{bmatrix} + \begin{bmatrix} b\_0\\ 0 \end{bmatrix} u + \begin{bmatrix} 0\\ 1 \end{bmatrix} \dot{f},\\ y = \begin{bmatrix} 1 & 0 \end{bmatrix} \begin{bmatrix} \mathbf{x}\_1\\ \mathbf{x}\_2 \end{bmatrix}. \end{cases} \tag{10}$$

The corresponding continuous expansion state observer can be established as:

$$\begin{cases} \varepsilon = z\_1 - y\_1\\ \left[\begin{array}{cc} \dot{z}\_1\\ \dot{z}\_2 \end{array}\right] = \left[\begin{array}{cc} -\beta\_1 & 1\\ -\beta\_2 & 0 \end{array}\right] \left[\begin{array}{cc} z\_1\\ z\_2 \end{array}\right] + \left[\begin{array}{cc} b\_0 & \beta\_1\\ 0 & \beta\_2 \end{array}\right] \left[\begin{array}{cc} u\\ y \end{array}\right]. \tag{11}$$

In Equation (11), *z*1 and *z*2 are the state variables of the linear extended state observer, which can be adjusted using the difference between the state variables *z*1 and the system output *y*. By selecting the appropriate observer gain coefficients β1 and β2, the observer state variables can be used to observe the system output *y* and the total disturbance *f*(*y*, *w*).

Estimate the total disturbance of the system through the expanded state variables, and compensate for the input side of the system:

$$
\mu = \frac{(-z\_2 + u\_0)}{b\_0}.\tag{12}
$$

If the estimation error of *z*2 to *f*(*y*, *w*) is excluded, Equation (9) is simplified to a pure integral link:

$$\dot{y} = (f(y, w) - z\_2) + u\_0 \approx u\_0. \tag{13}$$

The linear feedback control law uses proportional links:

$$
u\_0 = kp(\upsilon - z\_1). \tag{14}$$

In Equation (14), *kp* is the controller bandwidth and *v* is the given reference input. Pole assignment of the parameters of the observer and controller is performed using the bandwidth method [10]:

$$\begin{cases} \beta\_1 = 2\omega\_{0\prime} \\ \beta\_2 = \omega\_{0\prime}^2 \\ k\_p = \omega\_c. \end{cases} \tag{15}$$

where ω*c* is the controller gain and ω0 is the observer gain. The bandwidth ω0 of the observer is about 3 to 5 times that of the controller ω*c*.

### **3. Design and Performance Analysis of ADRC**

### *3.1. Design and Stability Proof of the Improved State Observer*

The traditional observer estimates the internal state variables of the system using the difference *e* between the estimated value *z*1 of the system output and the output *y* of the system. In Sun [25], it is pointed out that the observer should first track the output *y* of the system with *z*1, and then track the output *f* with *z*2. Before the tracking of the estimated value *z*1 to the system output *y* is completed, other state variables of the observer cannot complete the tracking of the corresponding state variables of the system. However, when the observation variable *z*1 can better track the output *y* of the system, the smaller error *e* makes it difficult to adjust other observation variables; therefore, we have to use a larger coefficient β2 to speed up the tracking of the observation variables to the real value. Meanwhile, to ensure the stability of the system, the value of β2 cannot be too large. In general, the gain coefficient of the observer β*i* increases by an order of magnitude, which is more serious in the higher-order ADRC. Yang et al. [26] mentioned that the extended observer could be improved by introducing the differential of the observation error, but the parameters of the controller were doubled and the parameters of the observer needed to be configured; therefore, it had to be further simplified.

From Equation (11), we can get:

$$\begin{cases} z\_1 = x\_1 + \mathfrak{e}\_r \\ z\_2 = \dot{z}\_1 + \beta\_1 \mathfrak{e} - b\_0 \mu. \end{cases} \tag{16}$$

The following equation can be obtained by sorting Equation (16):

$$\begin{cases} z\_1 = x\_1 + \mathfrak{e}\_\prime \\ z\_2 = x\_2 + \dot{\mathfrak{e}} + \beta\_1 \mathfrak{e}. \end{cases} \tag{17}$$

It can be seen from Equation (17) that the error between *z*2 and *x*2 is .*e* + β1*e*, and adjusting *z*2 by using it as a correction amount can speed up the convergence without significantly increasing the observer gain. Therefore, the classic LESO can be modified as follows:

$$\begin{cases} \varepsilon = z\_1 - \mathbf{x}\_1, \\ \dot{z}\_1 = z\_2 - \beta\_1 \varepsilon + b\_0 u\_\prime \\ \dot{z}\_2 = -\beta\_2 (\dot{\varepsilon} + \beta\_1 \varepsilon). \end{cases} \tag{18}$$

Equations (12), (14), and (18) form the improved Linear Active Disturbance Rejection Controller of Equation (8), whose structure is shown in Figure 6.

**Figure 6.** Structure of the improved controller.

### 3.1.1. Improved Stability Proof of LESO

Let *e*1 = *z*1 − *x*1 and *e*2 = *z*2 − *x*2. From Equations (10) and (18), we obtain:

$$\begin{cases}
\dot{\varepsilon}\_1 = \varepsilon\_2 - \beta\_1 \varepsilon\_1, \\
\dot{\varepsilon}\_2 = -\beta\_2 \varepsilon\_2 - w.
\end{cases} \tag{19}$$

Let *Y*1 = *e*1 and *Y*2 = *e*2 − β1*e*1 to obtain the error equation of the LESO system:

$$\begin{cases}
\dot{Y}\_1 = Y\_{2\prime} \\
\dot{Y}\_2 = -(\beta\_1 + \beta\_2)Y\_2 - \beta\_1\beta\_2Y\_1 - w.
\end{cases} \tag{20}$$

The characteristic equation of Equation (20) is:

$$
\lambda^2 + (\beta\_1 + \beta\_2)\lambda + \beta\_1\beta\_2 = 0.\tag{21}
$$

The necessary and sufficient conditions for the stability of the second-order system are β1 + β2 > 0 and β1β2 > 0. The zero solution (*e*1 = 0, *e*2 = 0) of the second-order constant-coefficient differential equation shown in Equation (20) is globally asymptotically stable because ω0 > 0 and ω*c* > 0 are stable.

When considering the disturbance *w*, the system has a steady-state error. Specify *w*0 = *const* > 0 when |*w*| ≤ *w*0 . When the system reaches a steady-state, then:

$$\begin{cases} \dot{Y}\_1 = Y\_2 = 0, \\ \dot{Y}\_2 = 0. \end{cases} \tag{22}$$

The steady-state error is calculated according to Equation (19):

$$\begin{cases} \left| \left| \boldsymbol{e}\_{1} \right| \leq \frac{\text{uv}\_{0}}{\beta\_{1} \beta\_{2}} \prime \\ \left| \left| \boldsymbol{e}\_{2} \right| \leq \frac{\text{uv}\_{0}}{\beta\_{2}} \right. \end{cases} \tag{23}$$

### 3.1.2. Observation Errors of the Classical First-Order LESO

Stability and error analyses are performed on the traditional first-order LESO represented by Equation (11). Let *Y*1 = *e*1 and *Y*2 = *e*2 − β1*e*1 be used to obtain the equation of the traditional LESO error system:

$$\begin{cases}
\dot{Y}\_1 = Y\_2, \\
\dot{Y}\_2 = -\beta\_1 Y\_2 - \beta\_2 Y\_1 - w.
\end{cases} \tag{24}$$

 The characteristic equation of Equation (24) is given as follows:

$$
\lambda^2 + \beta\_1 \lambda + \beta\_2 = 0.\tag{25}
$$

Using the Hurwitz theorem, the necessary and sufficient conditions for the stability of the second-order system are β1 > 0 and β2 > 0. The zero solution (*e*1 = 0, *e*2 = 0) of the second-order constant-coefficient differential equation shown in Equation (24) is globally asymptotically stable because ω0 > 0 and ω*c* > 0 are stable.

When considering the disturbance *w*, the system has a steady-state error. Specify *w*0 = *const* > 0 when |*w*|≤ *w*0 . When the system reaches a steady-state, then:

$$\begin{cases} \dot{Y}\_1 = Y\_2 = 0, \\ \dot{Y}\_2 = 0. \end{cases} \tag{26}$$

The steady-state error of the observer can be expressed as:

$$\begin{cases} \left| \left| e\_1 \right| \le \frac{\overline{\mu\_0}}{\overline{\beta\_2}}, \epsilon \\ \left| \left| e\_2 \right| \le \frac{\overline{\beta\_1} w\_0}{\overline{\beta\_2}}. \end{cases} \right. \tag{27}$$

According to the above analysis, the modified LESO shown in Equation (18) can exhibit a better dynamic regulation performance and a smaller steady-state observation error than the traditional LESO when the parameters β1 and β2 are the same. Compared with Equations (23) and (27), the improved LESO exhibits a higher observation accuracy than the traditional LESO when the observer and controller bandwidths are the same.

### *3.2. Performance Index Analysis of the Improved Linear ADRC*

### 3.2.1. Convergence and Estimation Error of the Improved LESO

The Laplace transform of Equation (18) can be used to obtain the transfer function of the observer:

$$\begin{cases} Z\_1(\mathbf{s}) = \frac{(\beta\_1 + \beta\_2)s + \beta\_1\beta\_2}{(s + \beta\_1)(s + \beta\_2)} Y(\mathbf{s}) + \frac{b\_0 s}{(s + \beta\_1)(s + \beta\_2)} \mathrm{l}I(\mathbf{s}),\\ Z\_2(\mathbf{s}) = \frac{\beta\_2 s}{s + \beta\_2} Y(\mathbf{s}) - \frac{b\_0 \beta\_2}{s + \beta\_2} \mathrm{l}I(\mathbf{s}). \end{cases} \tag{28}$$

Taking *e*1 = *z*1 − *y* and *e*2 = *z*2 − .*y* into account for analyzing a typical *y*, and *u* as the amplitude *K* step signal, then the steady-state error of LESO is given as:

$$\begin{cases} \mathcal{e}\_1 = \lim\_{s \to 0} E\_1(s) = 0, \\\mathcal{e}\_2 = \lim\_{s \to 0} E\_2(s) = 0. \end{cases} \tag{29}$$

Equation (29) shows that the improved LESO has a good convergence performance for realizing the invariant estimation of the system state variables and generalized disturbances. Further analyzing its dynamic process, the response of *z*1 under the step signal when *b*0 = 0 is as follows:

$$z\_1(s) = K(\frac{1}{s} + \frac{2}{(s + 2\omega\_0)(\omega\_0 - 2)} - \frac{\omega\_0}{(s + \omega\_0^2)(\omega\_0 - 2)}).\tag{30}$$

The time-domain response of *z*1 under the action of a step signal can be obtained using an inverse Laplace transform:

$$z\_1(t) = \begin{cases} K(1 + \frac{2\varepsilon^{-2u\omega\_0} - \omega\eta e^{-4t}\overline{0}}{\omega\eta - 2}) & \omega\eta\_0 \neq 2, \\\ K(1 + 4te^{-4t} - e^{-4t}) & \omega\eta\_0 = 2. \end{cases} \tag{31}$$

In Equation (30), for *t* > 0, the derivative of *t* and taking .*z*1(*t*) = 0 can produce the extreme point of *t*0:

$$t\_0 = \begin{cases} \frac{2(\ln a\_0 - \ln 2)}{\omega\_0^2 - 2\omega\_0} & a\_0 \neq 2, \\\frac{1}{2} & a\_0 = 2. \end{cases} \tag{32}$$

The extreme value of *z*1 is obtained by substituting the extreme value *t*0 into Equation (30):

$$z\_1(t\_0) = \begin{cases} K(1 + \frac{\frac{-4(\ln^{40} - \ln^2)}{\omega\_0 - 2} - \frac{2\omega\_0(\ln^{40} - \ln^2)}{\omega\_0 - 2}}{-a\nu\_0 - 2}) & a\_0 \neq 2, \\ K(1 + e^{-2}) \approx 1.135K & a\_0 = 2. \end{cases} \tag{33}$$

The trajectory of *z*1(*t*0) with the observer bandwidth value ω0 can be obtained via digital simulation. According to Figure 7, when ω0 = 2, the tracking overshoot of observer *z*1(*t*0) to *y* is the largest. At this time, the system overshoot is equal to the traditional LESO overshoot. The traditional LESO has a 13.5% overshoot at *t*0 = 2/ω0 and the amount of overshoot is independent of the value of the observer bandwidth ω0.

**Figure 7.** Relation curve between the system overshoot and observer bandwidth.

The overshoot of the improved LESO varies with the observer bandwidth ω0. The maximum overshoot of the observer state variable *z*1 is equal to that of the traditional observer. The corresponding speed of the system can be increased and the amount of overshoot is reduced by selecting a larger observer bandwidth ω0. Although the observer bandwidth ω0 is larger and the tracking speed is faster, it will lead to noise amplification. The ability of LESO to suppress noise needs to be analyzed.

### 3.2.2. Improved Disturbance Immunity Analysis of LESO

The closed-loop transfer function of the improved LADRC can be obtained by combining Equations (12), (14), and (18):

$$
\mu = \frac{1}{b\_0} G\_1(s) (k\_p v - H(s)y). \tag{34}
$$

The transfer functions of *G*1(*s*) and *H*(*s*) in Equation (34) are as follows:

$$\begin{array}{l} \mathcal{G}\_{1}(\mathbf{s}) = \frac{(s + \beta\_{1})(s + \beta\_{2})}{s^{2} + (\beta\_{1} + k\_{\mathcal{P}})\mathbf{s}},\\ H(\mathbf{s}) = \frac{\beta\_{2}s^{2} + (\beta\_{1}\beta\_{2} + \beta\_{1}k\_{\mathcal{P}} + \beta\_{2}k\_{\mathcal{P}})s + \beta\_{1}\beta\_{2}k\_{\mathcal{P}}}{(s + \beta\_{1})(s + \beta\_{2})}. \end{array} \tag{35}$$

According to Equation (34), the diagram of the system structure shown in Figure 8 is obtained [24]:

**Figure 8.** Equivalent system structure diagram.

Now the effect of the observation noise δ0 at the output *y* of the system and the disturbance δ*c* at the output *u* of the controller for the improved LESO will be discussed. Based on Equation (28), the transfer function of the improved LADRC is:

$$\frac{z\_1}{\delta\_0} = \frac{(2\omega\_0 + \omega\_0^2)s + 2\omega\_0^3}{(s + 2\omega\_0)(s + \omega\_0^2)}.\tag{36}$$

Similarly, the transfer function of δ0 of the traditional LESO's observation noise can be obtained as follows:

$$\frac{z\_1}{\delta\_0} = \frac{2a\nu s + a\_0^2}{\left(s + a\_0\right)^2}.\tag{37}$$

The transfer function of the disturbance δ*c* at the output of the LESO controller can be improved according to:

$$\frac{z\_1}{\delta\_c} = \frac{b\_0 s}{(s + 2\omega\_0)(s + \omega\_0^2)}.\tag{38}$$

The transfer function of the disturbance δ*c* at the output of a traditional LESO controller is:

$$\frac{z\_1}{\delta\_c} = \frac{b\_0 s}{\left(s + w\_0\right)^2}.\tag{39}$$

Figure 9 shows the characteristic amplitude and phase–frequency curves for the improved and traditional LESOs. The bandwidth of the improved LESO was higher than that of the traditional LESO, and the phase lag of the intermediate frequency segment was improved. Unlike Figure 9, the improved LESO with the same observer bandwidth in Figure 10 is basically the same as the traditional LESO in the high frequency band, but it has better noise immunity in the low frequency band compared with the traditional LESO, and can more effectively suppress the interference at the input end.

**Figure 9.** Frequency-doman characteristic curves of the observed noise.

**Figure 10.** Frequency-domain characteristic curves of the input disturbance.

3.2.3. Immunity Analysis of the Improved Self-Disturbance Rejection Controller

According to Equation (10), the control object can be written as:

$$s\mathcal{Y}(\mathbf{s}) = F(\mathbf{s}) + b\eta \mathcal{U}(\mathbf{s}).\tag{40}$$

Combined with Figure 8, the closed-loop transfer function of the system is as follows:

$$Y(s) = \frac{k\_p}{s + k\_p} V(s) + \frac{s^2 + (\beta\_1 + k\_p)s}{(s + \beta\_1)(s + \beta\_2)(s + k\_p)} F(s). \tag{41}$$

The closed-loop transfer function of the system includes the tracking term and the disturbance term. If the state variable of the observer can be used to accurately estimate the total disturbance of the system, the closed-loop transfer function of the system is simplified to the first-order inertial link. At this time, it relates the corresponding speed of the system to the bandwidth of the controller, and the larger the bandwidth, the faster the system.

It can be seen from the closed-loop transfer function that the disturbance term impacts the observer and controller bandwidths. The same observer and controller bandwidths were selected for comparing the improved LESO with the traditional LESO. It can be seen from Figure 11 that under the same bandwidth, the immunity of the improved LESO in the middle- and low-frequency bands were better than that of the traditional LESO, and it improved the phase lag of the middle-frequency band.

**Figure 11.** Logarithmic phase–frequency characteristic curves of the disturbance term.

In particular, if the disturbance *f* is taken as the unit step signal, we can obtain the output response using Equation (41):

$$Y(s) = \frac{a}{(s + a\iota\_0)} + \frac{b}{(s + a\iota\_0^2)} + \frac{c}{(s + a\iota\_0)}\,\tag{42}$$

$$\begin{cases} a = \frac{a\eta + \omega\_{\!\!k}}{(\omega\_0^2 - \omega\_0)(\omega\_{\!\!k} - \omega\_0)}, \\\ b = \frac{2\omega\eta + \omega\_{\!\!k} - \omega\_0^2}{(\omega\_0 - \omega\_0^2)(\omega\_{\!\!k} - \omega\_0^2)}, \\\ c = \frac{2\omega\_0}{(\omega\_0 - \omega\_{\!\!k})(\omega\_0^2 - \omega\_{\!\!k})}. \end{cases} \tag{43}$$

The time domain for the anti-Laplace transformation to obtain system output can be expressed as:

$$y(t) = ae^{-a\nu\_0 t} + b\nu^{-\omega\_0^2 t} + c e^{-a\nu\_0 t}.\tag{44}$$

It is easy to find lim*t*→∞*y*(*t*) = 0, i.e., the steady-state output of the system is zero under the external step disturbance.

### **(a) Controller Stability with an Unknown Input Gain**

Considering only the influence of the input gain on the stability of the system, i.e., if *f* = (*b* − *b*0)*u*, then Equation (40) can be simplified to:

$$s\mathcal{Y}(\mathbf{s}) = b\mathcal{U}(\mathbf{s}).\tag{45}$$

The following equation can be obtained by combining Equations (26) and (30):

$$Y(s) = \frac{a\iota\_{\mathbb{H}}(s + 2a\iota\_{0})(s + a\_{0}^{2})}{a\_{3}s^{3} + a\_{2}s^{2} + a\_{1}s + a\_{0}}V(s). \tag{46}$$

In Equation (46), the coefficients are as follows: *a*3 = *b*0/*b*,*a*2 = 2*a*0ω0 + *a*0ω*c* + ω20, *a*1 = 2ω30 + 2ω0ω*c* + ω20ω*c*, and *a*0 = 2ω30ω*c*. As ω0 and ω*c* are greater than zero, it is easy to see that *a*3,*a*2,*a*1 and *a*0 are all positive numbers. The necessary and sufficient condition for the stability of the Leonard qipat stability criterion (Equation (46)) is that all odd or even Hurwitz determinants are positive.

$$\begin{array}{c|cccc} \Delta\_3 &=& \begin{vmatrix} a\_2 & a\_0 & 0\\ a\_3 & a\_1 & 0\\ 0 & a\_2 & a\_0 \end{vmatrix} = a\_0(a\_1a\_2 - a\_0a\_3) \\ &= a\_0^2(4\omega\_0^4 + 2\omega\_0^3\omega\_\varepsilon + \omega\_\varepsilon^2\omega\_\varepsilon^2 + 4\omega\_0^2\omega\_\varepsilon + 2\omega\_0\omega\_\varepsilon^2) + (2\omega\_0^5 + \omega\_0^4\omega\_\varepsilon + 2\omega\_0^3\omega\_\varepsilon)a\_0 \end{array} \tag{47}$$

Since *b*, *b*0, ω0 and ω*c* are all positive numbers, Δ3 > 0 is true, i.e., the improved LADRC can be stable for any parameter greater than zero.

### **(b) Stability of the Controller when the System Parameters are Unknown**

Set the controlled object as the following:

$$y = \frac{b\_0}{s + k\_c} u\_\prime \tag{48}$$

where *kc* in Equation (48) is an unknown system parameter, and the closed-loop transfer function of the system is obtained by combining with Figure 8:

$$Y(s) = \frac{a\iota\_{\mathfrak{c}}(s+a\eta)(s+a\iota\_{0}^{2})(s+2a\eta)}{s^{4}+a\_{4}s^{3}+a\_{3}s^{2}+a\_{2}s+a\_{1}}V(\mathfrak{s}),\tag{49}$$

$$\begin{cases} a\_4 = \omega\_\emptyset^2 + 4\omega\_0 + \omega\_\varepsilon + k\_{\varepsilon\prime} \\ a\_3 = \omega\_0^2 \omega\_\varepsilon + 4\omega\_0^2 + 3\omega\_0^3 + 4k\_\varepsilon a\_0 + k\_\varepsilon a\_\varepsilon + 4\omega\_0 a\_\varepsilon \\ a\_2 = 4k\_\varepsilon \omega\_0^2 + 2\omega\_0^2 \omega\_\varepsilon + 3\omega\_0^3 \omega\_\varepsilon + 2\omega\_0^4 + 2k\_\varepsilon a\_0 \omega\_\varepsilon \\ a\_1 = 2\omega\_0^4 \omega\_\varepsilon. \end{cases} \tag{50}$$

The necessary and sufficient conditions for the stability of Equation (49) are:

$$a k\_c^3 + b k\_c^2 + c k\_c + d \gg 0,\tag{51}$$

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩*a* = 4ω50ω*c*(4ω0 + ω*c*)(2ω0 + ω*c*), *b* = (72ω90ω*c* + 68ω80ω2*c* + 128ω80ω*c* + 14ω70ω3*c* + 160ω70ω2*c* + 52ω60ω3*c* + 4ω50ω4*c* , *c* = 52ω110 ω*c* + 62ω100 ω2*c* + 176ω100 ω*c* + 16ω90ω3*c* + 252ω90ω2*c* + 128ω90ω*c*+ 104ω80ω3*c* + 272ω80ω2*c* + 10ω70ω4*c* + 144ω70ω3*c* + 20ω60ω4*c* , *d* = 12ω130 ω*c* + 18ω120 ω2*c* + 56ω120 ω*c* + 6ω110 ω3*c* + 96ω110 ω2*c* + 64ω110 ω*c*+ 48ω100 ω3*c* + 160ω100 ω2*c* + 6ω90ω4*c* + 124ω90ω3*c* + 64ω90ω2*c* + 24ω80ω4*c*+ 72ω80ω3*c* + 16ω70ω4*c* . (52)

If the roots of Equation (51) are *kc*1, *kc*2, and *kc*3 (*kc*1 < *kc*2 < *kc*3), the conditions of system stability are *kc*1 < *kc* < *kc*2 or *kc* > *kc*3.

According to the digital simulation results, the equation had a pair of conjugate complex roots and a real root. Figure 12 shows the boundary curve for ensuring the system stability when ω0 = 30 and ω0 ∈ [0, 60], and Figure 13 shows the boundary curve for ensuring the system stability when ω0 = 30 and ω*c* ∈ [0, 60]. From Figures 12 and 13, it can be seen that the stability region of the system increased with an increase of the observer bandwidth ω0 and the controller bandwidth ω*c*

**Figure 12.** System stability region under different observer bandwidths ω0.

**Figure 13.** System stability region under different controller bandwidth ω*c*.


**Design of an Aftermarket Hybridization Kit: Reducing Costs and Emissions Considering a Local Driving Cycle**

#### **Jony Javorski Eckert 1,\*, Fabio Mazzariol Santiciolli 1, Ludmila Corrêa de Alkmin e Silva 1, Fernanda Cristina Corrêa 2 and Franco Giuseppe Dedini 1**

Received: 22 December 2019; Accepted: 6 March 2020; Published: 11 March 2020

**Abstract:** For decades, drivers and fleet managers have been impacted by the instability of fuel prices, the need to save resources and the duty to meet and attain environmental regulations and certifications. Aiming to increase performance and efficiency and reduce emissions and mileage costs, plug-in electric vehicles (PHEVs) have been pointed out as a viable option, but there are gaps related to tools that could improve the numerous existing conventional vehicles. This study presents the design of an aftermarket hybridization kit that converts a vehicle originally driven by a combustion engine into a PHEV. To achieve this goal, an optimization was conducted with the objective of decreasing the cost (regarding fuel consumption and battery charging) to perform a local driving cycle, while attenuating the tailpipe emissions and reducing the battery mass. The torque curves of the electric motors, the battery capacity, the parameters for a gear shifting strategy and the parameters for a power split control were the design variables in the optimization process. This study used the Campinas driving cycle, which was experimentally obtained in a real-world driving scenario. The use of a local driving cycle to tune the design variables of an aftermarket optimization kit is important to achieve a customized product according to the selling location. Among the optimum solutions, the best trade-off configuration was able to decrease the mileage cost in 22.55%, and reduce the tailpipe emissions by 28.4% CO, 33.55% NOx and 19.11% HC, with the addition of a 137 kg battery.

**Keywords:** aftermarket hybridization kit; emissions mitigation; local driving cycle; plug-in hybrid electric vehicles; vehicle efficiency

#### **1. Introduction**

Local and global environmental issues have resulted in the establishment of regulations to reduce vehicle emissions worldwide [1,2]. On the other hand, the instability of fuel prices leads customers to react by reducing consumption [3] or by changing energy source [4] when it is possible. Plugin hybrid electric vehicles are driven by electric motors (EMs) and internal combustion engines (ICE) and can be connected to the grid [5]. They are one of the solutions for mitigating local emissions [6] and absorbing fuel and electric energy price instabilities.

The relevance of the plug-in electric vehicles (PHEVs) in the current engineering is reflected by the recent scientific activities. Du et al. [7] optimized a plug-in hybrid bus to avoid excessive changes of operation modes, reducing the number of engine startups, the clutch abrasion and the jerk. Golpîra and Khan [8] pointed that the increasing use of PHEVs is an important issue to be taken into account in

domestic energy power management, while Li et al. [9,10] investigated the advantages for the power distribution systems due to the optimum coordination of the PHEVs charging times. Furthermore, Mohammadi et al. [11] asserted that if the PHEVs are able to work in a bidirectional power mode (draining power from and supplying power to the grid), they can collaborate to regulate the grid voltage and frequency along a day. Zhang et al. [12] studied the integration between PHEVs, other kinds of electric vehicles and the road to achieve global ecodriving conditions. Liu et al. [13] proposed a mixed mutation strategy for a multiobjective optimization algorithm and demonstrated its effect by applying it on a PHEV problem. Wang et al. [14] optimized a 4-wheel drive PHEV considering the Federal Test Procedure (FTP) 72 driving cycle and achieved good results in three antagonistic objectives: −1.21% electric energy consumption, −6.18% fuel consumption and −5.49% acceleration time. Fu et al. [15] optimized a front traction PHEV under the New European Driving Cycle (NEDC), resulting in reductions about 3.45% fuel consumption, 6.15% NOx, 3.71% CO, and 3.57% HC.

Although in general, research is focused on the production and application of new hybrid vehicles, there are good results regarding the installation of aftermarket hybridization kits on combustion vehicles, turning them into PHEVs. Some of these solutions have already been patented [16–19], and companies are selling and installing such kits [20].

Researchers of the University of Salermo have developed an aftermarket hybridization kit by installing EMs in the rear wheels of a combustion vehicle originally driven only through the front wheels. The batteries of this kit can be loaded by regenerative braking, by plugging the kit to the grid, and by the energy acquired through solar panels installed on the vehicle roof [21]. In the best conditions, the resulting vehicle would have the fuel economy improved by 11% under the NEDC and 20.5% considering the FTP 72 driving cycle [21]. It is expected that 10% of vehicle owners are interested in installing this kit [22]. Furthermore, the kit improves the life cycle assessment of the vehicle in which it is installed, and the overall environmental impact is better than the purchase of a brand-new hybrid vehicle [23].

The Integrated System Laboratory (LabSIn) of the University of Campinas has worked on vehicle longitudinal dynamics issues and on the development of an aftermarket hybridization kit for the Brazilian scenario. The regional market is dominated by conventional vehicles, which are numerous (in 2018 there were 600,000 samples in Campinas City [24]; 18,200,000 in the São Paulo State [25]; and 54,700,000 in the whole country [26]).

Key contributions of LabSIn arose from the addition of two EMs to the rear wheels of a conventional vehicle (front wheel ICE traction); the effects on fuel consumption and on gear shifting strategy were experimentally evaluated [27,28]. Such experimental data were input to virtual analysis regarding the hybridization of a conventional vehicle [29,30]. As a result, suitable configurations were able to decrease by up to 34.18%, the cost of performing the combination of the FTP 75 and US06 driving cycles. However, the mentioned studies did not analyze the hybridization kit's influence on the engine emissions. The increase in the ICE warm-up period is amplified by the addition of the extra electric traction system, which supplies a parcel of the power demand and therefore decreases the ICE torque that can increase the generated emissions if the power split between ICE and EMs is not properly defined [31]. Modifications in the standard driving behavior, e.g., changing the gear shifting strategy, can decrease the ICE fuel consumption and emissions [32,33].

In 2019, LabSIn [34] proposed and simulated an aftermarket hybridization kit shown in Figure 1. The EMs are powered by a battery that is charged by the electrical grid when the vehicle is parked. The optimization was conducted to find out the best gear shifting strategy, EMs torque curves and battery size according to different fuel and electric energy cost scenarios, and the robust solutions regarding cost variations were selected. It also was not considered a local driving cycle that may differ from the standard ones, and may result in further optimized vehicle solutions [35–37].

**Figure 1.** Proposed assembly for the hybridization kit.

Therefore, the aim of the present study is to conduct a multi-objective optimization of the aftermarket hybridization kit. The optimization problem is formulated to decrease the mileage cost (in terms of fuel consumption and battery charging), mitigating the tailpipe emissions and decreasing the battery mass. The selected design variables are the EMs' torque curves, the battery capacity, the parameters of the gear shifting strategy and the parameters of the power split control. Moreover, this study is based on the Campinas driving cycle [38], which was experimentally obtained in a real-world driving scenario. Local driving cycles allow a more realistic analysis of the possible gains of the aftermarket hybridization vehicle, focusing on the local costumer.

#### **2. Simulation Model**

In the literature, models of vehicle longitudinal dynamics and vehicle components are often implemented in MATLABTM [37,39–41]. All the equations presented here have been implemented by the authors by means of MATLAB/SimulinkTMblock diagrams. In this study, the vehicle longitudinal dynamics are modeled based on the equations presented by Gillespie [42]. However, some modifications were required to include the electric drive train in the model.

The vehicle required traction torque *Treq* (Nm) is defined by Equation (1) as a function of the movement resistance forces caused by the gravitational acceleration *g* (m/s2), vehicle mass *M* (kg) and required acceleration *areq* (m/s2), the aerodynamic drag *DA* (N), the tires rolling resistance *Rx* (N) and the climbing resistance that varies according to the road angle *α* (rad).

$$T\_{\rm req} = r(D\_A + R\_{\rm x} + M\left(g\sin(a) + a\_{\rm req}\right))\tag{1}$$

The tire dynamic radius *r* (m) can be defined as proposed by Genta and Morello [43] as 98% of the geometric radius *rg* (m), that varies according to the tire standard geometry. The vehicle speed effects are also considered by means of the *kv* factor [44].

$$r = 0.98r\_{\mathcal{X}}(1 + 0.01kv) \tag{2}$$

The rolling resistance *Rx* (Equation (3)) and the aerodynamic drag *DA* (Equation (4)) increase with the vehicle speed *V* (m/s). Moreover, *DA* varies as a function of the air density *ρ* (kg/m3), the projection of the vehicle frontal area *A* (m2) and the *CD* coefficient that represents the vehicle shape.

$$R\_x = 0.0981 \left( 1 + \frac{2.24 \text{ V}}{100} \right) M \tag{3}$$

*Vehicles* **2020**, *2*

$$D\_A = \frac{1}{2} \rho V^2 \mathbb{C}\_D A \tag{4}$$

(5)

The required acceleration *areq* represents the driver behavior. In this paper, a local driving cycle of the city of Campinas, Brazil [38], is applied (Figure 2). The target speed *Vc* (m/s) is defined as the cycle speed at one time step Δ*t* (s) ahead of the current simulation time. Therefore, the requested acceleration can be calculated by Equation (5).

*areq* = *Vc* − *V*

**Figure 2.** Campinas Driving cycle [38].

As aforementioned, the main objective of the aftermarket hybridization kit is to add an extra propelling system in the conventional vehicle. Therefore, the power management control (PMC) defines the traction torque required by the engine *Teng* (Nm) and the electric motors *Tel* (Nm). In the

same way, as presented by Eckert et al. [34], the extra electric motors act only as an auxiliary propelling system. Thus, the throttle pedal signal is acquired and the PMC splits the requested traction torque *Teng* according to the *PE* factor (defined in the optimization problem). The engine torque *Teng* and torque of the electric motors *Tel* are defined by Equations (6) and (7) respectively, according to the engine inertia *Ie* (kgm2); gearbox and differential gear ratios *Nt* and *Nd*; inertia *It* (kgm2) and *Id* (kgm2); the frontal and real wheels inertia *Iw f* (kgm2) and *Iwr* (kgm2); and the overall powertrain efficiency *ηtd*.

$$T\_{\rm eng} = \frac{T\_{\rm req}(1 - P\_{\rm E})}{N\_l N\_d \eta\_{td}} + \left( (I\_\varepsilon + I\_t)(N\_l N\_d)^2 + I\_d N\_d^2 + I\_{wf} \right) \frac{a\_{\rm req}}{r} \tag{6}$$

$$T\_{cl} = P\_{\rm E} T\_{\rm req} + I\_{\rm uvr} a\_{\rm req} \tag{7}$$

#### *2.1. ICE System Restrictions*

Once the required traction torque parcel exerted by the engine is defined, it has to be compared to the available traction torque *Tav* (Nm) that corresponds to the 100% throttle curve (Figure 3a). Moreover, the clutch transmissible torque limit *Tcl* (Nm) (that acts during the gear shifting) also is considered in the definition of the available traction torque.

**Figure 3.** Engine torque curve and clutch normal force *Fn* (N) [45].

The clutch transmissible torque is calculated according to its friction coefficient *μcl*, the number of clutch faces *N* (-) and internal and external disks radii *Ri* (m) and *Ro* (m) (see Equation (8)). Moreover, the spring force *Fn* (N) (Figure 3b) controls the torque transmission according to the clutch pedal displacement (CPD).

$$T\_{cl} = \frac{2}{3} \mu\_{cl} F\_{\text{n}} N \frac{R\_o^3 - R\_i^3}{R\_o^2 - R\_i^2} \tag{8}$$

It can be seen in Figure 3b that the clutch maximum *Fn* value is applied when it is closed (CPD = 0). In this condition, the total engine output torque is transmitted to the gearbox. On the other hand, during the gear shifting process, the clutch disconnects the ICE from the gearbox (CPD = 0 to CPD = 100 mm) in 0.3 s. After the clutch fully opened (CPD = 100 mm), the gear ratio is changed in 0.2 s; then, the ICE is reconnected to the gearbox (CPD = 100 to CPD = 0 mm) in 0.5 s [32]. Therefore, the gearbox input torque *Tgb* (Nm) is defined according to the rules presented in Equation (9) and the available traction torque at the vehicle frontal wheels *Ta f* (Nm) is then defined by Equation (10).

$$T\_{\lg b} = \begin{cases} \begin{array}{c} T\_{av} \text{ if } T\_{cl} > T\_{av} \\\ T\_{cl} \text{ if } T\_{cl} \le T\_{av} \end{array} \end{cases} \tag{9}$$

*Vehicles* **2020**, *2*

$$T\_{af} = T\_{\mathfrak{g}b} N\_l N\_d \eta\_{td} - \left( (I\_\varepsilon + I\_l)(N\_l N\_d)^2 + I\_d N\_d^2 + I\_{wf} \right) \frac{a\_{req}}{r} \tag{10}$$

#### *2.2. Electric Drivetrain Restrictions*

As the frontal propelling system, the electric drivetrain is also limited by the maximum torque of the EMs curves *Tev* (Nm) according to their current speed. Therefore, if the required torque *Tel* is higher than the sum of available torques *Tev* of both in-wheel EMs, there will be performance losses. The available traction torque of the rear-drive system *Tar* (Nm) is defined by the combination of Equations (11) and (12).

$$T\_{rl} = \begin{cases} \begin{array}{l} 2T\_{\text{ev}} \text{ if } T\_{cl} > 2T\_{\text{ev}} \\ T\_{cl} \quad \text{if } T\_{cl} \le 2T\_{\text{ev}} \end{array} \end{cases} \tag{11}$$

$$T\_{ar} = T\_{rl} - I\_{wr}a\_{req} \tag{12}$$

#### *2.3. Traction Restrictions*

Once the available traction torques *Ta f* and *Tar* are defined, it is possible to verify whether the available torque can be transmitted through the tire/ground contact. The maximum transmissible torque for the frontal *TF*(*max*) (Nm) and rear *TR*(*max*) (Nm) wheels are defined by Equations (13) and (14) respectively [46]. *μ* represents the tire-ground peak friction coefficient, and *L* (m), *h* (m), *b* (m) and *c* (m) correspond respectively to the vehicle's wheelbase; the height of its center of gravity; and the longitudinal distance between its front and rear axles.

$$T\_{\rm F(max)} = \mu \left( \frac{Mg \cos \alpha \ c - h \sin \alpha - Mh \ a\_{req}}{2L} \right) r \tag{13}$$

$$T\_{R(max)} = \mu \left(\frac{Mg\cos\alpha \; b + h\sin\alpha + Mh \; a\_{req}}{2L}\right)r\tag{14}$$

Therefore, the effective traction torque of the frontal *TF* (Nm) and rear *TR* (Nm) propelling system are defined by Equations (15) and (16).

$$T\_F = \begin{cases} \begin{array}{l} T\_{af} \qquad \text{if } T\_{\mathcal{F}(\max)} \ge T\_{af} \\\ T\_{\mathcal{F}(\max)} \text{ if } T\_{\mathcal{F}(\max)} < T\_{af} \end{array} \end{cases} \tag{15}$$

$$T\_R = \begin{cases} \begin{array}{l} T\_{ar} \qquad \text{if } T\_{R(max)} \ge T\_{ar} \\\ T\_{R(max)} \text{ if } T\_{R(max)} < T\_{ar} \end{array} \end{cases} \tag{16}$$

#### *2.4. Acceleration Iterative Process*

With both effective traction torques, it is possible to define the vehicle current acceleration *ax* (m/s2) by means of Equation (17), which is integrated by ODE5 of the SimulinkTM, to find out the current vehicle speed *V* and also the displacement.

$$a\_{\overline{x}} = \frac{\frac{T\_F + T\_R}{r} - D\_A - R\_{\overline{x}} - Mg\sin(\alpha)}{M} \tag{17}$$

Due to the many constraints presented, the vehicle acceleration *ax* may become lower than the requested *areq*. Therefore, it is necessary to perform an iterative process among Equations (1), (6), (7) and (9)–(17), considering *areq* = *ax* until the convergence of the *ax* value. Moreover, the tire slipping has to be corrected in this iterative process. The coefficient *e* (Figure 4) estimates the difference between the tire tangential speed and the vehicle displacement speed as a function of the traction torque *TF*/*R*. This parameter changes the engine and EMs speeds, and therefore the maximum available torques according to the drivetrain respective curves.

**Figure 4.** Tire slip coefficient in function of the traction torque *TF*/*R*.

#### *2.5. Fuel Consumption and Emissions*

After the convergence, the engine effective torque *Te* (Nm) and speed *ωe* are defined by the Equations (18) and (19).

$$T\_c = \frac{F\_l r}{N\_l N\_d \eta\_{td}} + \left( (I\_c + I\_l)(N\_l N\_d)^2 + I\_d N\_d^2 + I\_w \right) \frac{a\_x}{r} \tag{18}$$

$$
\omega\_{\varepsilon} = \frac{V N\_d N\_t}{r(1-\varepsilon)}\tag{19}
$$

These values correspond to the engine operation point, and are input to the ADVISORTMfuel converter block, which defines the ICE fuel consumption *FC* (l) and the tailpipe emissions HC (g/km) NOx (g/km) and CO (g/km) according to the ICE maps shown in Figure 5. ADVISORTM [47] is a free vehicular simulation tool that considers the ICE transient regimes, simulating the combustion heat and its influence in the catalyst efficiency that significantly changes the generated tailpipe emissions [32].

**Figure 5.** *Cont.*

**Figure 5.** Engine maps for fuel consumption and emissions [32,47].

#### *2.6. Battery and Equivalent Fuel Consumption*

As initially proposed by Eckert et al. [34], the hybridization kit contains a lead-acid battery pack with a nominal voltage of 48 V. This voltage value was selected because the hybridization kit must be adapted to conventional vehicles. Electrical systems above 60 V can represent a potential danger to the passenger [48], and therefore require a shock protection system [49] that would increase the cost of the kit. Furthermore, the lead-acid batteries were selected due to their maintenance-free, good recycling capacity [50] associated with easy manufacture and high-volume production [51] that decrease the final cost of the kit.

In the simulations, the lead-acid battery block from SimulinkTMdatabase [34] is used. The developed control stops the use of the auxiliary electric drive train system when the battery state of charge *SoC* is under 40% to avoid fatigue caused by deep discharge [34]. Aiming to define the best battery pack for the hybridization kit, its capacity *Bc* (Ah) has to be defined and included as input to the SimulinkTMbattery block. Moreover, the battery mass *Mbat* (kg) is also calculated by Equation (20) as a function of the lead-acid specific energy *SE* = 40 (Wh/kg) and added to the vehicle mass *M*. Thus, the resulting *Mbat* is added to the vehicle overall mass *M*.

$$M\_{bat} = \frac{V\_{bat}B\_c}{S\_E} \tag{20}$$

Once the driving cycle is simulated, the final battery *SoC* is used as an input to the charge simulation, which infers the cost of recharging the battery from the electric grid. As in Eckert et al. [34], the battery is recharged at constant current [52]—the maximum *I* (A) value that does not overcome the allowed battery voltage *Vbat* (V). The power consumption *Pc* (W) to return the battery *SoC* to 100% is defined by Equation (21), considering a charge efficiency *ηc* that concerns the conversion from AC to DC and the heat losses.

$$P\_{\mathcal{C}} = \eta\_{\mathcal{C}} IV \tag{21}$$

Differences in the cost of the energy sources may impact the result of the optimization of vehicle solutions [53]. To allow a fair comparison between the conventional vehicles and the hybridized one, the cost of battery charge is converted in a equivalent fuel consumption *Feq* (l) by Equation (22) according to the charging time *Ct* (s) and the ratio between the fuel *Fcost* (\$/l) and electric

energy *Ecost* (\$/Ws) costs. Finally, the *Feq* is added to the engine fuel consumption *FC*, resulting in the total fuel consumption *FT* (l) used to compare the results.

$$F\_{c\eta} = P\_c C\_t \frac{E\_{cost}}{F\_{cost}} \tag{22}$$

$$F\_T = F\_C + F\_{\text{eq}} \tag{23}$$

#### *2.7. Electric Motors*

One of the goals of this study was to find out optimum in-wheel EMs to be applied in the aftermarket hybridization kit; a generic torque curve and efficiency map are presented in Figure 6 [34,54,55]. This approach allows for the definition of a theoretical torque curve, based on three main points. The first one is the EM maximum torque *Tmax* (Nm) and its respective speed *ωTc* (rad/s) at the constant torque phase. The second point is defined at the constant power phase, according to Tong [56], which defines the EM best operating region between 0.1*Tmax* and 0.3*Tmax*. In this paper, we adopt the upper limit of 0.3*Tmax*, as shown in Equation (24), and the EM speed of this point is defined by Equation (25). Finally, the last torque curve point represents the speed at which the EM reaches null torque, and it is defined by linear progression of the previously defined points (*Tmax*, *ωTc*) and (*TPc*, *ωPc*).

**Figure 6.** Electric motor efficiency map and torque curve [34,54,55].

$$T\_{Pc} = 0.3 T\_{\text{max}} \tag{24}$$

$$
\omega\_{Pc} = \frac{T\_{\text{max}} \omega\_{Tc}}{T\_{Pc}} \tag{25}
$$

With the EM torque curve fully defined, the map that defines the EM efficiency *ηEM* is interpolated based on the data presented in Figure 6. Moreover, the EM inertia is interpolated based on some values presented by Corrêa et al. [57]. Finally, the inverter efficiency *ηinv* is obtained from Table 1 and the electric current *I* (A) results from the Equation (26).

$$I = \frac{T\_R V}{r(1 - \varepsilon) \ V\_{\text{bat}} \ \eta\_{EM} \ \eta\_{inv}} \tag{26}$$

**Table 1.** Inverter efficiency *ηinv* map adapted from [58].

The EMs are able to regenerate some part of the kinetic energy during the braking. In this paper, the regenerative braking is limited to 10% of the EM maximum torque [54,59]. If the required braking torque exceeds the bounded, the remaining parcel is dissipated by the conventional brake of the vehicle [59].

#### *2.8. Vehicle Parameters*

The simulated vehicle is based on the 1.0L engine frontal traction Brazilian Chevrolet CeltaTM. The parameters used to model this conventional vehicle and the aftermarket hybridization kit in the simulations are presented in Table 2.

**Table 2.** Simulated vehicle parameters [44,45].

#### *2.9. Gear Shifting Strategy*

Finally, the simulation parameters related to the applied gear shifting strategy have to be defined; they significantly influence the energy management [60], the vehicle performance, the fuel consumption and the emissions [32,33]. The use of an adequate gear shifting strategy improves the gains reached by the vehicle hybridization, once the electric motors decrease the ICE torque demand, allowing for the anticipation of the upshifts, moving the engine to a lower fuel consumption/better efficiency operation point [34]. On the other hand, anticipating the upshifts increases the ICE warm-up period, leading to poor catalyst efficiency and higher tailpipe emissions.

Therefore, the applied shifting strategy has to be carefully defined. The hybridization kit was developed to be adapted to a conventional vehicle a manual gearbox; the most adequate gear will be shown to the driver by means of a user interface adapted to the vehicle. As in previous works [32,34,45], the gear shifting strategy is based on speed limits; in other words, when the vehicle reaches one of these limits, the gear will be changed to the next (upshift) or previous gear (downshift). In the simulation the shifting process is controlled by the vector **Vshift** (Equation (27)) that contains the upshift speeds *Vu*(*i*) (km/h) and the speed interval *VD* (km/h) used to define the downshift speeds *Vd*(*i*) (km/h) (Equation (28)). This difference between *Vu*(*i*) and *Vd*(*i*) is necessary to prevent gear shifting instabilities, as highlighted by Xi et al. [61].

$$\mathbf{V\_{shift}} = \begin{bmatrix} V\_{u1} & V\_{u2} & V\_{u3} & V\_{u4} & V\_{D} \end{bmatrix} \tag{27}$$

$$V\_{d(i)} = V\_{u(i)} - V\_D \tag{28}$$

The gearbox transmission ratio *Nt* is then defined according to the shifting rule present in Equation (29).

$$N\_{t} = \begin{cases} \text{Neutral} & \left\{ 0 \text{ if } V = 0 \\ \\ \text{Upshift} & \begin{cases} N\_{11} \left( 1^{\text{st}} \text{ gear} \right) \text{if } 0 < V \le V\_{\text{u1}} \\ N\_{12} \left( 2^{\text{nd}} \text{ gear} \right) \text{if } V\_{\text{u1}} < V \le V\_{\text{u2}} \\ N\_{13} \left( 3^{\text{rd}} \text{ gear} \right) \text{if } V\_{\text{u2}} < V \le V\_{\text{u3}} \\ N\_{14} \left( 4^{\text{th}} \text{ gear} \right) \text{if } V\_{\text{u3}} < V \le V\_{\text{u4}} \\ N\_{15} \left( 5^{\text{th}} \text{ gear} \right) \text{if } V > V\_{\text{u4}} \\ N\_{11} \left( 1^{\text{st}} \text{ gear} \right) \text{if } V\_{\text{d1}} < V \le V\_{\text{d2}} \\ N\_{12} \left( 2^{\text{nd}} \text{ gear} \right) \text{if } V\_{\text{d1}} < V \le V\_{\text{d2}} \\ N\_{13} \left( 3^{\text{rd}} \text{ gear} \right) \text{if } V\_{\text{d2}} < V \le V\_{\text{d4}} \\ N\_{14} \left( 4^{\text{th}} \text{ gear} \right) \text{if } V > V\_{\text{d1}} \end{cases} \tag{29}$$

#### **3. Optimization**

As mentioned before, the hybridization kit is composed of two in-wheel electric motors assembled directly in the vehicle rear wheels and powered by a lead-acid battery. The main objective of this study is, focusing on a local drive cycle (Campinas, Brazil), to define the best configuration for the battery and electric motors and also the power split control and gear shifting strategy associated with each proposed configuration. To do that, a multi-objective optimization problem is formulated and solved by means of the interactive adaptive-weight genetic algorithm (i−AWGA) proposed by Gen, Cheng and Lin [62]. The i−AWGA technique performs a wide search for the best solution, and it is not limited to false minimums, as occurs in some other optimization techniques. Moreover, this method was applied in several previous works, regarding vehicle multi-objective optimization [32–34,59], reaching satisfactory results.

#### *3.1. Problem Formulation*

The first optimization criterion *f*1(**X**) is the minimization of the total fuel consumption *FT* (Equation (23)) that represents the ICE fuel consumption and the conversion of the battery charge cost in hypothetical fuel (Equation (22)).

The second optimization criterion *f*2(**X**) is the minimization of the engine carbon monoxide (*CO* (g/km)), nitrogen oxide (*NOx* (g/km)) and hydrocarbon (*HC* (g/km)) emissions. These emissions are combined in a single parameter named emission factor *EF* [32,33]. The *EF* value is defined by the adaptive-weight technique [62] according to Equation (30) as a function of the maximum and minimum values of each gas emission presented in the solution database.

$$E\_F(\mathbf{X}) = \frac{CO(\mathbf{X}) - CO\_{\text{min}}}{CO\_{\text{max}} - CO\_{\text{min}}} + \frac{NOx(\mathbf{X}) - NOx\_{\text{min}}}{NOx\_{\text{max}} - NOx\_{\text{min}}} + \frac{HC(\mathbf{X}) - HC\_{\text{min}}}{HC\_{\text{max}} - HC\_{\text{min}}} \tag{30}$$

Finally, the third optimization criterion *f*3(**X**) is the minimization of the battery mass *Mbat* that represents the majority of the extra weight added by the hybridization kit to the vehicle and reduces the available space in the vehicle trunk where it is meant be assembled.

Therefore, the optimization criteria are:

$$f\_1(\mathbf{X}) = \min\left(F\_T(\mathbf{X})\right) \tag{31}$$

$$f\_2(\mathbf{X}) = \min\left(E\_F(\mathbf{X})\right) \tag{32}$$

$$f\_3(\mathbf{X}) = \min\left(M\_{\text{bat}}(\mathbf{X})\right) \tag{33}$$

subjected to the constraints *C* presented in Equation (34).

$$\mathcal{C} = \begin{cases} 20 \text{ Ah} \le B\_{\mathcal{C}} \le 150 \text{ Ah} \\ 5\% \le P\_{\mathcal{E}} \le 95\% \\ 250 \text{ rpm} \le \omega\_{\mathcal{T}\mathcal{L}} \le 150 \text{ rpm} \\ 10 \text{ Nm} \le T\_{\text{max}} \le 200 \text{ Nm} \\ V\_{u1} < V\_{u2} < V\_{u3} < V\_{u4} \\ 1 \text{ km/h} \le V\_{\mathcal{D}} \le 10 \text{ km/h} \\ \omega\_{\text{min}} \le \omega\_{\mathcal{E}} \le \omega\_{\text{max}} \\ R \ge 0.9997 \\ \mathcal{C}0 \le 40.53 \text{ g/km} \\ \mathcal{N}0 \ge \mathcal{G}.08 \text{ g/km} \\ HC \le 7.64 \text{ g/km} \end{cases} \tag{34}$$

Besides the EMs and battery parameters used to narrow the optimization process, some extra constraints were included to ensure the correct behavior of the vehicle. The first one is the ICE operation range, which cannot be below the idle speed (*ωmin* ≈ 84 rad/s) and cannot overcome the maximum allowed speed (*ωmax* ≈ 680 rad/s).

The final constraints are included to avoid any configuration that presents poor acceleration performance caused by the fuel consumption minimization, and to prevent configurations that increase the tailpipe emissions due to the ICE warm-up delay. To be considered viable, the PHEV configuration cannot generate more CO, NOx and HC emissions than the conventional vehicle. Moreover, the vehicle performance is evaluated as the correlation coefficient *R* calculated by the Equation (35) [30,63] in which the simulated speed profile *Vs* is compared to the standard driving cycle *Vcs* in discrete time steps of 0.1 s, and the analyzed PHEV must reach at least the same performance of the conventional vehicle *R* = 0.9997, using a standard gear shifting strategy proposed by its manufacturer [64].

$$R = \sqrt{\frac{\left(\sum \left(V\_{cs} - \vec{V}\_c\right) \left(V\_s - \vec{V}\right)\right)^2}{\sum \left(V\_{cs} - \vec{V}\_c\right)^2 \sum \left(V\_s - \vec{V}\right)^2}}\tag{35}$$

#### *3.2. Genetic Algorithm*

The optimization starts with the definition of chromosomes **X** (Equation (36)) that constrain the design variables of a specific potential solution.

$$\mathbf{X} = \begin{bmatrix} B\_{\mathbb{C}} & P\_E & \omega\_{T\mathbb{C}} & T\_{\text{max}} & \mathbf{V}\_{\mathbf{s}\text{shift}} \end{bmatrix} \tag{36}$$

The initial solution database is composed of randomly defined chromosomes (considering the constrains *C*) that are simulated and included in the population if they reach the minimum required performance.

#### 3.2.1. Selection, Crossover and Mutation

Once an initial solutions population is developed, the results are classified by the i−AWGA technique (Equation (37)), which compares the current result of each optimization criterion *fk*(**X**) with the maximum *f max k* and minimum *f min k* values of the analyzed criterion presented in the population. Moreover, a penalty value *Pp* = 0 is added to the dominated solutions, aiming to decrease their probability of reproduction. On the other hand, the non-dominated solutions (Pareto frontier) receive *Pp* = 1 value, which increases their fitness value Ft(**X**), improving their selection probability as a function of the sum of all *Ft*(**X**) values according to the population size *PM* as shown by Equation (38).

$$Ft(\mathbf{X}) = \sum\_{k=1}^{3} \frac{f\_k^{\max} - f\_k(\mathbf{X})}{f\_k^{\max} - f\_k^{\min}} + P\_p(\mathbf{X}) \tag{37}$$

$$S\_P(\mathbf{X}) = \frac{Ft(\mathbf{X})}{\sum\_{X=1}^{PM} Ft(\mathbf{X})} \tag{38}$$

The crossover process starts with the selection of two members of the population, which are named Member 1 (*M*1) and Member 2 (*M*2). The values of the design variables of these selected chromosomes are then randomly combined, generating a new chromosome denominated **Xcr** which is simulated. It is included in the population if it respects the constraints *C* and if the minimum performance criteria are reached.

To provide diversity among the values of the design variables present in the population, the mutation process randomly changes some of the chromosomes values of the selected members and of the crossover chromosome **Xcr**, generating three new chromosomes **Xmt1**, **Xmt2** and **Xmtc** that are evaluated by the constrains *C*. Table 3 shows the mutation rules according to the operator 0 ≤ *Mut* ≤ 1 defined by the MatlabTMfunction *rand*.

**Table 3.** Mutation operator.

#### 3.2.2. Population Control and Convergence Criterion

The initial population is composed of 100 members (randomly generated chromosomes), which are combined by the crossover and mutation operators. The addition of new solutions increases the population size until it reaches a limit value *Plim* = 200. Once the population limit is reached, the worst solutions (higher Pareto ranking) are eliminated from the population. If a population composed of exclusively non-dominated solutions (Pareto frontier) reaches *Plim*, the limit is increased *Plim* = *Plim* + 100 to avoid the elimination of the whole population.

The convergence is defined by the stagnation of the evolution process, which is characterized by the repetition of the Pareto frontier [33,59,65] for over 20 generations of 80 new simulated solutions (crossover and mutation).

Figure 7 shows the optimization flowchart according to the applied method.

**Figure 7.** Optimization flowchart.

#### **4. Results and Discussion**

After the convergence of the algorithm, the Pareto frontiers of non-dominated solutions are defined as optimum configurations with different compromise among the optimization criteria. Among these solutions, some of them are selected to be analyzed: the minimum energy cost solution min *f*1 and the minimum emissions min *f*2, the minimum battery min *f*3. Moreover, the min *f*1 solution presents the best trade-off (max *Ft* value) among the analyzed criteria.

However, the min *f*1 (best trade-off) and min *f*2 present large batteries (up to ≈144 kg), representing the advantages of the electric powertrain system against the combustion one. On the other hand, the minimum battery min *f*3 solution was able to save fuel, but the tailpipe emissions were close to the ones of the conventional vehicle. In addition to these solutions, the Pareto frontier presents several other optimum solutions, and two of them were selected based on the decrease of the battery mass (criterion *f*3). These extra solutions were named *To f f*1.5 (making *Ft*(*f*3) 50% more valuable: 1.5 × *Ft*(*f*3)) and *To f f*2 (making *Ft*(*f*3) 100% more valuable: 2 × *Ft*(*f*3)), increasing the importance of the *Ft* value related to the battery mass minimization, selecting the lighter hybridization kit configurations.

Table 4 shows the results of the selected configurations and their respective chromosomes. Moreover, Figure 8 shows the Pareto frontier and highlights the selected configurations.

**Table 4.** Optimized chromosomes and results.

*Vehicles* **2020**, *2*

**Figure 8.** Optimized solutions.

#### *4.1. Standard Vehicle*

The standard solution to be compared to the optimized PHEV configurations is the conventional vehicle configuration propelled only by the ICE and using a standard gear shifting strategy proposed by the vehicle manufacturer [64]. Figure 9 shows the ICE running time for each operation point (torque/speed), where it is possible to observe that the ICE presents several points close to the idle/low-speed regime, which is a characteristic of the Campinas driving cycle (Figure 2). The standard gear shifting strategy is shown in Figure 9; it represents the higher speed section of the cycle.

**Figure 9.** Conventional (internal combustion engine (ICE)) vehicle results.

As it can be seen in Figure 8c and Table 4, the conventional vehicle fuel consumption and resulting emissions are fully dominated by the optimum PHEV configurations.

#### *4.2. Minimum Battery Size Solution* min *f*3

The minimum battery size solution focuses on minimizing the EMs and battery, resulting in a more compact hybridization kit, with a 24.14 kg battery and low power EMs responsible only for 8.22% of the vehicle power demand. This configuration allows for the upshifting anticipation (Figure 10c) compared to the standard shifting procedure, which saves fuel by moving the ICE operation point to a low-speed/high-torque [32,33], as can be observed in Figure 10a. The EMs operation is presented in Figure 10b where it is possible to observe that in the majority of the time, the electric driving system is used only as a supplementary propelling system, which ensures the vehicle performance even with the upshifting anticipation, and decreases the ICE torque, saving fuel.

**Figure 10.** Minimum battery size configuration powertrain behavior.

This configuration was able to reduce the equivalent fuel consumption (*FT*) by 3.8%, and present tailpipe emissions close to the standard vehicle results (−3.03% *CO*, −2.3% *NOx* and −1.57% *HC*), as is shown in Table 4.

#### *4.3. Minimum Emissions Solution* min *f*2

The minimum emission PHEV configuration(min *f*2) presents a high level of electrification of the vehicle propelling system, in which the EMs are responsible for 55.4% of the power demand. Therefore, the EMs present high torque, as shown in Figure 11b, in which it is possible to observe that these EMs operate at maximum torque for a large amount of time. Moreover, these high torque EMs also expressively decrease the ICE required torque (Figure 11a), associated with the upshifting anticipation (Figure 11c), keeping the ICE running under ≈ 2700 rpm.

**Figure 11.** Minimum emissions configuration powertrain behavior.

On the other hand, this configuration needs a large battery of ≈144 kg to ensure the availability of the electric propelling system during the 42 km of the analyzed driving cycle. Due to the mentioned minimization of the ICE using, it was possible to save 1.22 L of fuel, compared to the conventional vehicle, which represents 21.74% economy regarding the overall cost to perform the desired path. Due to the heavy use of the electric drivetrain system, this PHEV configuration results in −33.88% *CO*, −35.36% *NOx* and −18.19% *HC*.

Regarding the cost relation between fuel and electricity, the presented results have shown a favorable scenario for vehicle electrification. However, the use of large batteries may lead to other issues, such as a higher cost of the aftermarket hybridization kit, difficulty of assembling the battery in the vehicle and possible interference in vehicle handling [34].

#### *4.4. Minimum Cost Solution* min *f*1 *(Best Trade-Off)*

Regarding the optimized scenario, the minimum cost solution min *f*1, which represents the minimum equivalent fuel consumption (*FT*) among the Pareto frontier is rated as the best-compromised solution (higher fitness value *Ft*). This PHEV configuration presents EMs that provide up to 105 Nm, which act similarly to the min *f*2 EMs, keeping the ICE running at a low speed and torque regime, which together, lead to fuel economy. The electric propelling system is responsible to fulfill 66.20% of the power demand, which results in a high concentration of EM operation points close to the maximum torque curve, as shown in Figure 12b. This configuration was able to decrease the cost to perform the

driving cycle in 22.55% and generate −28.4% *CO*, −33.55% *NOx* and −19.11% *HC*—fewer emissions compared to the conventional vehicle.

**Figure 12.** Minimum cost solution powertrain behavior.

Besides the satisfactory reached results regarding cost end emissions of the min *f*1 configuration, this aftermarket hybridization kit needs a 137 kg battery, which implies in the same issues listed before regarding large batteries. Therefore, the configurations *To f f*1.5 and *To f f*2 analyzed below, are included to represent some alternative hybridization kits composed of lighter batteries and EMs, which can be more suitable in cases in which a lower powertrain electrification degree is desired.

#### *4.5. Trade-Off Considering* 1.5 × *Ft*(*f*3)*: The To f f*1.5

The first of the selected trade-off solutions was defined by assigning 50% more weight to the battery mass minimization at Equation (37) that determines the fitness *Ft* value, used to classify the population. This configuration is powered by a ≈ 90 kg battery and EMs able to perform up to 83 Nm, which operates the majority of the time at maximum torque regime, as shown in Figure 13b. Moreover, the power split control (*PE*) was defined as 37.17% due to the lower EMs torque capacity compared to the min *f*1 and min *f*2 PHEV configurations. Similarly to the previously mentioned configurations, the *To f f*1.5 keeps the ICE running at low torque and speed, which enables 950 mL fuel-saving and an equivalent fuel consumption 18.75% lower compared to the conventional vehicle. Furthermore, the *To f f*1.5 solution also enhanced the ICE emissions, by decreasing 23.78% of the *CO*, 17.76% *NOx* and 11.12% *HC*.

**Figure 13.** Trade-off configuration (1.5 × *Ft*(*f*3)) powertrain behavior.

#### *4.6. Trade-Off Considering* 2 × *Ft*(*f*3)*: The To f f*2

Finally, the trade-off solution considering the *Ft* calculated with 2 × *Ft*(*f*3), results in a PHEV configuration with 42.55 kg battery and EMs with 43.48 Nm torque capacity. This configuration decreases the equivalent fuel consumption in 14.13% and the emissions in 0.86% *CO*, 5.59% *NOx* and 4.58% *HC*. The ICE and EMs operation points and the gear shifting strategy are presented in Figure 14.

**Figure 14.** *Cont.*

**Figure 14.** Trade-off configuration (2 × *Ft*(*f*3)) powertrain behavior.

The *To f f*2 solution, in the same way as the minimum battery size PHEV configuration (min(*f*3)), represents a lower powertrain electrification degree. Even with the lower gains in terms of energy consumption, these configurations may become good alternatives to provide cheaper hybridization kits due to their smaller batteries and electric motors, in addition to their lower interference in the vehicle weight distribution and drivability.

#### **5. Conclusions**

In this paper, an aftermarket hybridization kit that converts a vehicle originally driven by a combustion engine into a PHEV was proposed. An optimization problem was formulated, aiming to decrease the overall cost (regarding fuel consumption and battery charging) to perform a local driving cycle, attenuating the tailpipe emissions and reducing the battery mass, which leads to a low price hybridization kit. Some design variables were taken into account; they could change the capacity and the weight of the batteries, the power and the torque of the EMs, the gear shifting strategy and the PMC strategy. Considering the needs of the customer, the optimization of the kit was suitable to a local driving cycle, reflecting the real service loads that it would face.

After the driving cycle was set, an optimization process was conducted by means of the i−AWGA, which was able to find out a Pareto frontier of optimum configurations of the kit. Some of these solutions could be selected, such as the ones that further reduced the travel cost or emissions, resulting in vehicles with a high degree of electrification. These solutions were suitable for customers who were prone to adding more weight to their vehicles and buying a kit with a higher purchase price (due to the cost of large battery packs).

On the other hand, an optimum configuration with the minor battery weight could be found, which would result in a minor purchase price and would be less effective at reducing travel costs and emissions. If battery size was used as a rule, it would be possible to find other optimum solutions in the Pareto frontier to significantly reduce the wanted index but with a non-extravagant additional weight of the kit.

Furthermore, the optimization algorithm led to another aftermarket hybridization kit configuration which presented good trade-off among the optimization criteria. Each of these optimum configurations presented improvements in the overall energy cost (fuel and electricity) and engine emissions according to the applied electrification degree resulting from the assembled electric motors and battery.

Finally, the presented results have shown that it is possible to obtain expressive enhancements by converting a conventional vehicle propelled only by a combustion engine into a PREV. However, this study is only theoretical, and some other steps are necessary to ensure the feasibility of the proposed concept.

Our future work will guide the decisions among all the Pareto solutions. A study regarding the aftermarket hybridization kit cost, the purchase price and the consumer acceptation will contribute to define the kit setup for a certain local. Regarding the emissions, the electric energy mix and the kit material, manufacture and disposal must be taken into account in future analyses to ensure environmental gains. Moreover, the effectiveness of the hybridization kits should be evaluated under a set of different driving

scenarios, to ensure the robustness of the designed devices. Finally, the real-time control for vehicle power management control also needs to be developed, aiming to make the hybridization kit feasible.

**Author Contributions:** Conceptualization, J.J.E. and F.G.D.; methodology, J.J.E. and L.C.d.A.e.S.; software, J.J.E.; formal analysis, J.J.E. and F.M.S.; writing—original draft preparation, J.J.E., F.M.S. and F.C.C.; writing—review and editing, F.M.S., L.C.d.A.e.S. and F.C.C.; visualization, J.J.E.; F.M.S. and F.C.C.; supervision, F.G.D. and L.C.d.A.e.S.; project administration, F.G.D. and L.C.d.A.e.S. All authors have read and agreed to the published version of the manuscript.

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

**Acknowledgments:** The authors wish to thank the State of São Paulo Research Foundation (FAPESP), Federal Technological University of Paraná—UTFPR, Ponta Grossa and the University of Campinas (UNICAMP) for financial support and scholarships.

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

#### **References**

c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).


*3.4.1 Microscopy view*

The textile fibers, particularly the natural ones, have typical longitudinal and cross-sectional shapes and therefore can be identified by viewing them under the optical microscope. This technique cannot be used very successfully in the case of man-made fibers, except for a few because their cross-sections can be modified during production. Typical cross-sectional and longitudinal shapes of some of the fibers are given in the following **Tables 4** and **5**.

#### **Table 4.**

*Microscopic appearances of the natural fibers.*

#### **Table 5.**

*Microscopic appearances of the man-made fibers.*

*Basic Functional Application for Natural Fibers and Types DOI: http://dx.doi.org/10.5772/intechopen.102998*


**1.4 Factors affecting packaging interaction**

The shelf life of packaged food is dependent on numerous factors such as the intrinsic nature of the food, e.g. acidity (pH), water activity (aw), nutrient content, occurrence of antimicrobial compounds, redox potential, respiration rate and biological structure, and extrinsic factors, e.g. temperature, relative humidity (RH) and the surrounding gaseous composition. These factors will directly influence the chemical, biochemical, physical and microbiological spoilage mechanisms of individual food products and their achievable shelf lives. By carefully considering all of these factors, it is possible to evaluate existing and developing active packaging technologies and apply them for maintaining the quality and extending the shelf life of different food products.


*4.3. [18F]NaF Production*

The 2-mL solution of [18F]F<sup>−</sup> in enriched water was manually applied to a preconditioned Sep-Pak Light QMA cartridge (WAT023525, Waters, Zellik, Belgium). The QMA was rinsed with 3 mL of water and [18F]NaF was eluted with 300 μL of 0.9% NaCl solution (typically 5 GBq is eluted). The eluate was diluted with water to obtain a 10 MBq/μL solution.