*3.3. Stabilization and Release of Leaf Essential Oil Microcapsules*

The constituents of common essential oils from aroma plants are small molecular weight and highly volatile. The encapsulation of limonene would influence its properties, such as evaporation, stabilization and controlled release, by different encapsulation methods and selected materials. The retention of limonene in extruded starch (nonencapsulation) was quite low (8.0%) compared with that of limonene microencapsulated with β-cyclodextrin (92.2%) [20].

Using the accelerated dry-heat aging test to evaluate the stability and release of leaf essential oil microcapsules. Figure 3 shows the weight losses of β-cyclodextrin (β-CD), linalool-chemotype leaf essential oil (LL oil), and leaf oil microcapsules (β-CD/LL oil) at 105 ◦C during the accelerated aging period. The weight loss of β-CD was very slight (less than 0.5%) after 8 days of the accelerated aging test; it indicated that β-CD was thermostable at 105 ◦C. Trotta et al. (2000) investigated the thermal behavior of β-CD; the decomposition temperature of β-cyclodextrin was 250 ◦C by using the thermogravimetric analysis (TGA) [39]. Weight losses of linalool-chemotype leaf essential oil was 99.1% after

30 min at 105 ◦C (data not shown in Figure 2); leaf essential oil exhibited highly volatile in the high-temperature environment. Weight losses of leaf essential oil microcapsules were 6.73%, 9.33%, 12.14%, and 13.40% after 1, 2, 4, and 8 days of the aging test, respectively. Results revealed that microencapsulation with β-cyclodextrin slowed down the release/emission of leaf essential oil in the dry-heat aging test and improved the thermal stabilization of linalool-chemotype leaf essential oil. min at 105 °C (data not shown in Figure 2); leaf essential oil exhibited highly volatile in the high-temperature environment. Weight losses of leaf essential oil microcapsules were 6.73%, 9.33%, 12.14%, and 13.40% after 1, 2, 4, and 8 days of the aging test, respectively. Results revealed that microencapsulation with β-cyclodextrin slowed down the release/emission of leaf essential oil in the dry-heat aging test and improved the thermal stabilization of linalool-chemotype leaf essential oil.

As for the ethanol/water ratio, the highest yield of microcapsule was 98.1% under the 1:5 ratio of ethanol to water. There was no statistically significant difference in the microcapsule yields between the solvent ratio of 1:3 and 1:5 (*p* < 0.05). Using the optimal reaction conditions, the yield of linalool-chemotype leaf essential oil microencapsulated with β-

The constituents of common essential oils from aroma plants are small molecular weight and highly volatile. The encapsulation of limonene would influence its properties, such as evaporation, stabilization and controlled release, by different encapsulation methods and selected materials. The retention of limonene in extruded starch (non-encapsulation) was quite low (8.0%) compared with that of limonene microencapsulated with β-

Using the accelerated dry-heat aging test to evaluate the stability and release of leaf essential oil microcapsules. Figure 3 shows the weight losses of β-cyclodextrin (β-CD), linalool-chemotype leaf essential oil (LL oil), and leaf oil microcapsules (β-CD/LL oil) at 105 °C during the accelerated aging period. The weight loss of β-CD was very slight (less than 0.5%) after 8 days of the accelerated aging test; it indicated that β-CD was thermostable at 105 °C. Trotta et al. (2000) investigated the thermal behavior of β-CD; the decomposition temperature of β-cyclodextrin was 250 °C by using the thermogravimetric analysis (TGA) [39]. Weight losses of linalool-chemotype leaf essential oil was 99.1% after 30

*Molecules* **2021**, *26*, x FOR PEER REVIEW 6 of 8

*3.3. Stabilization and Release of Leaf Essential Oil Microcapsules*

cyclodextrin was 96.5%.

cyclodextrin (92.2%) [20].

**Figure 3.** Changes in weight loss of leaf essential oil microcapsules during the dry-heat aging period. β-CD: β-cyclodextrin; LL oil: *C. osmophloeum* leaf oil; β-CD/LL oil: leaf oil microcapsules; different letters (a–e) in the figure refer to the statistically significant difference at the level of *p* < 0.05 according to the Scheffé's test. **Figure 3.** Changes in weight loss of leaf essential oil microcapsules during the dry-heat aging period. β-CD: β-cyclodextrin; LL oil: *C. osmophloeum* leaf oil; β-CD/LL oil: leaf oil microcapsules; different letters (a–e) in the figure refer to the statistically significant difference at the level of *p* < 0.05 according to the Scheffé's test.


**2. Measuring tests**

Using road construction experience with Royal Road Product (RRP235Special), as an innovative method for the first time, the layers underneath the sleeper have been replaced with the clayey subgrade stabilized with RRP235special. To investigate reaction against applied forces, a series of static and dynamic lab and field experiments such as maximum compaction test, California bearing ratio, unconfined compressive strength, Brazilian indirect tensile test, direct shear strength, uniaxial cyclic tests, and single tie push test (STPT) are needed. All the tests were done using the international codes according to **Table 1**.

The samples were made in different RRP235special dosages according to **Table 2**.

### **Table 1.**

*Table of tests.*

**Table 2.** *Dosage of RRP235special in different samples.* *Developing a Novel Superstructure System for the Ballasted Railways Using RRP235special... DOI: http://dx.doi.org/10.5772/intechopen.111470*


*Article* **Path-Following Control Method for Surface Ships Based on a New Guidance Algorithm**

**Zhanshuo Zhang 1, Yuhan Zhao 1, Guang Zhao 2, Hongbo Wang 1,\* and Yi Zhao 1,\***

**Abstract:** A new type of path-following method has been developed to steer marine surface vehicles along desired paths. Path-following is achieved by a new hyperbolic guidance law for straight-line paths and a backstepping control law for curved paths. An optimal controller has been improved for heading control, based on linear quadratic regulator (LQR) theory with nonlinear feedback control techniques. The control algorithm performance is validated by simulation and comparison against the requirements of International Standard IEC62065. Deviations are within the allowable range of the standard. In addition, the experimental results show that the proposed method has higher control accuracy.

**Keywords:** ship motion control; path-following; guidance algorithm; nonlinear feedback

**Citation:** Zhang, Z.; Zhao, Y.; Zhao, G.; Wang, H.; Zhao, Y. Path-Following Control Method for Surface Ships Based on a New Guidance Algorithm. *J. Mar. Sci. Eng.* **2021**, *9*, 166. https://doi.org/10.3390/jmse9020166

Academic Editor: Jakub Montewka Received: 27 December 2020 Accepted: 1 February 2021 Published: 6 February 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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 (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

Autopilot is the main equipment for ship motion control; it controls the ship's course without the participation of the helmsman [1]. On autopilot, the ship follows the target route automatically, which can effectively reduce ship operating costs [2]. This paper presents a new method for ship track control. The goal of the control system is to follow a preset route with good anti-interference ability [3]. Path-following control systems for marine vehicles are usually constructed as three independent blocks: guidance, navigation and control [4]. Guidance is the action or the system that continuously computes the reference position, velocity and acceleration of the vehicle to be used by the control system [5]. Navigation is the action or the system that directs the vehicle, by which the position, course and traveled distance is determined. The control system determines the necessary forces and moments to achieve a certain objective.

Line of sight (LOS) is the most commonly used guidance algorithm. This algorithm was first applied to track control of surface ships by Mcgookin and Fossen and has been widely studied [6–9]. The advantage of the LOS guidance algorithm is that it controls the ship's motion by imitating the behavior of the helmsman to eliminate track deviation from the planned route. However, there are some defects in the LOS guidance algorithm. When the distance between the next target waypoint on the target route and the current position of the ship is large, a large track deviation will be produced when the ship tracks the planned route through the guidance algorithm, in addition, the convergence speed of the algorithm is also very slow. In response to this problem, an integral LOS (ILOS) has been proposed and extensively analyzed. Fossen and Lekkas [10] proposed an ILOS based on adaptive control theory that can compensate for drift forces effectively.

Stability analysis is an important topic for navigation and control systems used in autonomous marine vehicles. Proportional-integral-derivative (PID) controllers or proportional derivative controllers are usually used in ship autopilot design [11,12]. In recent

years, improved PID control algorithms have emerged. For example, steering parameters for normal adaptable PID autopilots have been developed during the last decade [13,14]. Dlabac et al. [15] presented a particle swarm optimization (PSO)-based PID controller for ship course-keeping. Recently, nonlinear controllers for autopilot motion control of marine vessels have been reported. Oh and Sun [16] presented a model predictive control for path following of underactuated surface vessels. Guerrero et al. [17] employed an adaptive high- order sliding mode controller for trajectory tracking of autonomous underwater vehicles. Designs based on neural networks [18,19], pole placement technique (PPT) [20], fuzzy logic [21], extended state observer technique (ESO) [22] and some other methods are also used. Wang et al. [23] presented a heading control algorithm based on an H-infinite optimization algorithm to counteract the influence of waves and ensure that ships can turn steadily in rough seas. Sun et al. [24] proposed a feedback linearization optimal heading control algorithm to effectively control a ship's course. Veremey et al. [25] proposed a new approach for the compensative transformation of reference dynamic output controllers. Du et al. [26,27] used adaptive robust nonlinear control to adjust a ship's course and track. Xiang et al. [28] improved the fuzzy logic method and tested it on underwater ships and marine surface vehicles. Xu et al. [29] proposed a vector field guidance law to follow the ship's trajectory. Although most of these methods have good results, there is no standard to verify the control effect of their experiments and the ship model they use is no comprehensive consideration for each type of ship, which cannot effectively verify the results. Liu et al. [30] proposed a nonlinear robust control algorithm based on Backstepping method to control ship straight-path tracking. However, there is no curve path tracking method in this study. Zhao et al. [31] based on Serret-Frenet frame transformation develop a tracking error model and the backstepping controller compensates the nonlinearity of the container ship. Xu et al. [32] proposed an adaptive backstepping controller for pathfollowing control of an underactuated ship based on a nonlinear steering model, which can achieve the effect of path control. But the shortcoming in both two is, they present pretty few control scenarios of the researches to verify the reliability of the algorithm, moreover, the scene of track control is too simple.

This paper presents a new path-following control law. The main innovation of this paper is to propose hyperbolic guidance law and apply it to straight-line path-following control. This design improves the convergence of the straight-line path-following control. For curved path-following in the transition between two adjacent straight-line paths, this paper improved a reverse stepping method to calculate heading rate commands to make the system globally asymptotically stable. Compared with the previous research, the extended state observer (ESO) for the controller model is established to estimate and compensate the state in this paper, which can improve the anti-interference ability of the ship in the path following. In the presence of sea current interference, also gives a correction formula. In this paper, linear quadratic regulator (LQR) and nonlinear feedback control are combined to improve the traditional LQR heading controller to improve the control accuracy of heading and yaw rate of the ship. Finally, the track control effect of three different types of ships is verified in simulations and the control effect is evaluated according to International Standard IEC62065 [33].

Section 2 establishes a mathematical model, including ship motion simulation and control and identifies controller parameters. Section 3 describes the design of the heading controller. Section 4 introduces the new guidance algorithm. Section 5 presents analysis of simulation results. Finally, Section 6 contains the conclusions.

#### **2. Mathematical Model of Ship Motion**

#### *2.1. Process Plant Model*

We describe the ship motion model in five basic compositions, with three degrees of freedom, shown in Figure 1. The model is derived from Newton's laws of motion using linear equations to relate hydrodynamic forces to the respective motions in the horizontal plane. The equations are as follows [4]:

$$\left[m\left[\dot{u} - \upsilon r - x\_{\mathcal{S}}r^2 - y\_{\mathcal{S}}\dot{r}\right] = X\_{\prime} \tag{1}$$

$$m\left[\dot{v} + \mu r - y\_{\mathcal{J}}r^2 + x\_{\mathcal{J}}\dot{r}\right] = \mathcal{Y}\_{\prime} \tag{2}$$

$$I\_z \dot{r} + m \left[ \mathbf{x}\_{\mathcal{S}} \left( \dot{v} + ur \right) - y\_{\mathcal{S}} \left( \dot{u} - vr \right) \right] = N\_\prime \tag{3}$$

where *X*, *Y* and *N* denote external forces and moment, while *xg*, *yg*, *zg* describe the location of the center of gravity. *u*,*v* and *r* denote surge velocity, sway velocity and yaw angular velocity, respectively, . *u*, . *v* and . *r* are their derivatives. *Iz* is the yaw moment of inertia, *m* is the total mass of ship. It is common to let the body frame coordinate origin coincide with the center of gravity; thus, the equations can be rewritten as:

$$m\left(\dot{u} - vr\right) = X\_\prime \tag{4}$$

$$m(\dot{v} + \mu r) = Y\_\prime \tag{5}$$

$$I\_z \dot{r} = N.\tag{6}$$

**Figure 1.** Ship motion mathematical model.

The hydrodynamic force *X* is linearized and is assumed to be proportional to the ship linear velocity, *u* in surge. Let *Ru* denote the linear coefficient of hydrodynamic resistance to forward motion and *Xthrust* denote the thrust provided by the propeller. Thus Equation (4) becomes:

$$m(\dot{u} - vr) = X\_{thrust} - R\_{\text{\textquotedblleft}tr} \,\text{u}.\tag{7}$$

Let *τu* denote the time constant of the linear surge response model, *Ku* denote the coefficient of thrust, *u*max denote maximum forward speed, and *X*max denote maximum thrust:

$$\begin{aligned} \tau\_u &= m/R\_{u\prime} \\ \mu\_{\text{max}} &= X\_{\text{max}}/R\_{u\prime} \\ K\_u &= \mu\_{\text{max}}/\tau\_u. \end{aligned} \tag{8}$$

Substituting Equation (8) into Equation (7) yields:

$$
\dot{\mu} = K\_{\mu} X^{\prime} + vr - u/\tau\_{\mu}. \tag{9}
$$

In the same way, for sway response model let *τv* = *m*/*Rv* denote the linear coefficient of hydrodynamic resistance to sway motion, then Equation (5) becomes:

$$
\dot{\upsilon} = -\iota r - \upsilon/\tau\_{\upsilon}.\tag{10}
$$

For the yaw response model, Equation (6) becomes:

$$I\_z \dot{r} = K\_r \left(\delta\_a K\_\mu X' \tau\_\mu / L + \mathcal{W} \right) + \gamma L R\_v (\upsilon - \gamma L r) - R\_r r\_\prime \tag{11}$$

where *Kr* is a constant of proportionality, *γ* is the yaw stability factor, *L* is the length of the ship, *δa* is the real rudder deflection, *Rv* is the linear coefficient of hydrodynamic resistance to lateral motion, *Rr* is the linear coefficient of hydrodynamic resistance to yaw and *τr* = *Iz*/*Rr* denotes the time constant of the yaw response model. Simplifying by relating the moment of inertia to the mass and length as a uniformly dense rod to its mass and length, then the moment of inertia can be obtained as *Iz* = *mL*2/12. *KrW* is the turning moment imparted by wave disturbance, *K r* is the normalized coefficient of rudder moment, which can be expressed as *K r* = *Krδ*max/*Iz*.

The wave interference model established in this paper consists of a series of square half wave waves. The duration *T* and height *H* of each half wave are random numbers related to the Bretschneider wave spectrum [34]. Finally, a square wave interference signal is generated by the wave model, in which the calculation methods of the duration *T* and the wave height *H* are as follows:

$$\begin{cases} \quad T = 0.5T\_0(\text{ss}) \times (1 + 0.5Rand\_b) \\\ H = H\_0(\text{ss}) \times (1 + H\_r \times Rand\_b) \times A\_a \end{cases} \tag{12}$$

where *Randb* denotes a random number among [−1, 1]. A value of 0.5 for *Hr* is recommended, while *Aa* has alternating sign (i.e., ±1) to describe wave direction, *ss* means the sea state level, *T*0(*ss*) and *H*0(*ss*) are the natural period and significant wave height under sea state *ss*, respectively. The range of values is shown in Table 1.

**Table 1.** The value of natural period and meaningful wave height under different sea conditions.

Referring to the modeling method of wave interference in IEC62065, this paper ignores the influence of wave interference on ship surge motion and sway motion, only adds the wave interference torque of ship's yaw motion to the mathematical model of ship's motion. Rewrite ship yaw Equation (11) as:

$$\dot{r} = K\_{r}^{\prime} \frac{K\_{\rm u} X^{\prime} \tau\_{\rm u}}{L} \cdot \delta\_{\rm u}^{\prime} + \frac{12 \gamma (\upsilon - \gamma L r) \tau\_{r}}{L \tau\_{\upsilon}} - \frac{r}{\tau\_{r}} + 0.01 K\_{r}^{\prime} S\_{f} H\_{\prime} \tag{13}$$

where *δa* is the normalized rudder position obtained by *δ a* = *δa*/*δa*max, *Sf* is a Scaling Factor. A value of 20 for the Scaling Factor is recommended.

#### *2.2. Control Plant Model*

We simplify the process plant model described in the previous section to design the autopilot control algorithm. The simplified model contains only the main physical properties of the process. Notomo [35] proposed a linearized model for ship steering equations, which is given by a simple transfer function between *r* and *δ*.

$$\frac{r}{\delta}(\mathbf{s}) = \frac{\mathbf{K}}{(\mathbf{1} + \mathbf{T}\mathbf{s})'} \tag{14}$$

where *T* and *K* are the time constant and gain constant, respectively. Neglecting the roll and pitch modes (*φ* = *θ* = 0), such that:

.

$$
\psi = r \tag{15}
$$

finally yields:

$$\frac{\psi}{\delta}(\mathbf{s}) = \frac{\mathbf{K}}{\mathbf{s}(1+T\mathbf{s})},\tag{16}$$

where *ψ* is the heading angle.

The time domain form of Equation (16) is:

$$T\ddot{\psi} + \dot{\psi} = \mathcal{K}\delta.\tag{17}$$

Notomo's first order model is usually written as:

$$T\dot{r} + r = K\delta.\tag{18}$$

When the straight motion of the ship is unstable or critical stable, nonlinear maneuvering models should be used. A nonlinear term can be added in Equation (18); thus, Notomo's nonlinear first order model can be obtained as:

$$
\dot{T}\dot{r} + r = K(\delta + \mathcal{K}\_v v). \tag{19}
$$

This is the commonly used control plant model for the design of the steering autopilot, in which *Kv* is the coefficient of the nonlinear term.

#### *2.3. Controller Parameter Identification*

In the above-mentioned control model, some parameters cannot be obtained directly but need to be obtained by system parameter identification. In control applications, the controller performance is bound to the assumptions and approximations of the model. To obtain the corresponding controller parameters more accurately, we apply the forgetting factor least square algorithm to Notomo's nonlinear first order model to identify the ship motion model.

The Recursive Least Square (RLS) algorithm with exponential forgetting is given as follows [36]:

$$
\hat{\theta}(k) = \hat{\theta}(k-1) + Q(k) \left[ y(k) - \Phi^T(k) \hat{\theta}(k-1) \right], \tag{20}
$$

$$Q(k) = P(k-1)\Phi(k)\left[\lambda I + \Phi^T(k)P(k-1)\Phi(k)\right]^{-1},\tag{21}$$

$$P(k) = \frac{1}{\lambda} \left[ I - \mathcal{Q}(k) \Phi^T(k) \right] P(k-1), \tag{22}$$

where the forgetting factor value of *λ* is 0.98 < *λ* < 0.995, Φ(*k*) is the data vector and ˆ *θ*(*k*) is the estimated value of the parameter vector. *Q*(*k*) and *P*(*k*) are the intermediate variable help us get ˆ *θ*(*k*) we want.

Next, referring to the ship motion simulation model, substituting control Equation (19) into ship motion Equation (13), the values of *T*, *K* and *Kv* are obtained as follows:

$$\begin{cases} \quad T = \frac{\frac{\tau\_v \tau\_r}{\tau\_v + 12\tau\_r \gamma^2}}{\frac{T K\_r \prime u\_{\text{max}} X'}{L \mathcal{L}\_{\text{max}}}}, \\\quad K\_v = \frac{12\gamma T}{K L \tau\_v}. \end{cases} \tag{2.3}$$

To facilitate the identification calculation, Equations (11) and (13) are rewritten in the following form:

$$\begin{cases} \ Y\_0 = \theta\_0 X\_0 + \theta\_1 X\_1\\ \ Y\_1 = \theta\_2 X\_2 \end{cases} \tag{24}$$

where

$$\begin{cases} \ Y\_0 = \dot{r} - \frac{12\gamma}{L\tau\_v} \upsilon\_{\mathcal{U}} + \frac{12\gamma^2}{\tau\_v} r \\\ Y\_1 = \dot{\upsilon}\_{\mathcal{K}} + \iota\_{\mathcal{K}} r \end{cases} , \tag{25}$$

$$\begin{cases} X\_0 = \frac{U}{L} \delta'\_{\, \, a} \\ \quad X\_1 = r \\ \quad X\_2 = v\_w \end{cases} \tag{26}$$

$$\begin{cases} \begin{array}{c} \theta\_0 = \frac{KL}{T\Pi} \\ \theta\_1 = -\frac{1}{T} + \frac{12\gamma^2}{\tau\_v} \\ \theta\_2 = -\frac{1}{\tau\_v} \end{array} . \end{cases} \tag{27}$$

According to the recursive formula of the forgetting factor least squares identification algorithm in Equations (20)–(22), the corresponding identification results *θ*0, *θ*1 and *θ*2 can be obtained. Through *θ*0, *θ*1 and *θ*2, the three controller parameters *T*ˆ, *K*ˆ and *K*ˆ *v* of the nonlinear first-order Notomo model can be solved:

$$\begin{cases} \begin{array}{l} \Upsilon = \frac{1}{-\delta\_1 + \frac{12\gamma^2}{\pi\_v}},\\ \hat{\mathcal{K}} = \frac{\frac{\partial\_0}{\partial\_r} \hat{T} \hat{U}}{L},\\ \hat{\mathcal{K}}\_v = \frac{12\gamma^2}{L\mathcal{K}\tau\_v}. \end{array} \end{cases} \tag{28}$$

#### **3. Optimal Heading Controller**

This section describes the design of the optimal heading controller. The main goal is to calculate the controller parameters in terms of the Notomo constants obtained by the identification algorithm in the previous section and introduce them in the LQR controller law. Then, nonlinear feedback is added to improve LQR controller to achieve nonlinear control and better control accuracy. In addition, to filter out the influence of sea wave interference on the acquisition of ship heading signal, an extended state observer (ESO) is added to this design to obtain the estimated value of the low-frequency heading signal. Thus, the controller can obtain accurate and fast course control.

#### *3.1. LQR Controller*

Assume that the heading signal *ψ* can be obtained by a compass and the yaw rate *r* can be obtained by a rate gyro or by a state observer. Notomo's first order model in Equation (18) can be written as the state space form:

$$
\dot{X} = AX + Bu\_{c\prime} \tag{29}
$$

where *X* = (*r*, *ψ*, *δ*) *T* is the state vector and *uc* is the controller input, which denotes the desired rudder rate. *A* and *B* are the coefficient matrixes with:

$$A = \begin{pmatrix} -1/T & 0 & K/T \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix},\tag{30}$$

$$B = \begin{pmatrix} 0 & 0 & 1 \end{pmatrix}^T,\tag{31}$$

*Xd* = (*rd*, *ψd*, *δ*) *T* denotes the objective state vector. The goal of the controller design is to converge the state *X* to the objective *Xd*:

$$\lim\_{t \to \infty} X = X\_{d\prime} \tag{32}$$

*X*1 denotes the error vector:

$$
\widetilde{X} = X - X\_d = \begin{pmatrix} \widetilde{r} \,\widetilde{\psi} \,\delta \end{pmatrix}^T,\tag{33}
$$

where 1*r* = *r* − *rd*, *ψ*1 = *ψ* − *ψd*. The control performance specification can be measured in terms of:

$$J = \int\_0^\infty \left( \tilde{X}^T Q X + \mu\_c^{-T} R \mu\_c \right) dt\_\prime \tag{34}$$

where *Q* is a 3-dimensional diagonal matrix, in which diagonal elements are the weighting factors. *R* is the weighting factor of the input. The LQR problem is to find the optimal control *uc*(*t*) such that *J* in Equation (34) is minimized,

$$\mu\_{\varepsilon} = -R^{-1}B^{T}P\hat{X}\_{\prime} \tag{35}$$

where *P* is the positive defined solution of the Riccati Equation [37]:

$$A^T P + PA - PBR^{-1}B^T P + Q = 0\tag{36}$$

Let

$$\left( (k\_1, k\_2, k\_3)^T = -R^{-1} B^T P \right) \tag{37}$$

where *k*1, *k*2 and *k*3 are the controller gains obtained by the LQR law. Thus, the representation of the controller can be written as:

$$\delta\_{LQR} = \int\_0^t \left( k\_1 \widetilde{r} + k\_2 \widetilde{\Psi} + k\_3 \delta \right) d\tau. \tag{38}$$

#### *3.2. Feedback Nonlinearization Compensation*

In the controller design here, a nonlinear feedback term is added in the control law for compensating the nonlinear maneuvering of the ship. Notomo's nonlinear first order model can be rewritten as:

$$T\dot{r} + r = K(\delta + K\_v v). \tag{39}$$

Comparing with the linear controller law obtained in the previous section, the following equation can be obtained:

$$
\delta\_{LQR} = \delta\_{com} + \mathcal{K}\_{\mathcal{V}} \upsilon\_{\prime} \tag{40}
$$

where *δcom* is the command rudder angle, *Kvv* can be treated as the feedback term, such that:

$$
\delta\_{\rm com} = \delta\_{\rm LQR} - \delta\_{\rm FLJ} \tag{41}
$$

with *δFL* = *Kvv* and the value of *Kv* is obtained from the identification algorithm in the previous section.

#### *3.3. Extended State Observer*

Both surface ships and underwater vehicles need state observers to process signal data from sensors and navigation equipment. The observer in this paper is designed in terms of the nonlinear ship model and the wave disturbance model. The nonlinear ship model and the wave disturbance model are as follows:

$$\begin{cases} \begin{aligned} \dot{T}\dot{r} + r &= \mathcal{K}(\delta - \delta\_{\text{ll}} + \mathcal{K}\_{\text{U}} \upsilon) + \omega\_{\text{V}} \\ \ddot{\Psi}\_{\omega} + 2\xi\omega\_{0}\dot{\Psi}\_{\omega} + \omega\_{0}^{2}\psi\_{\omega} &= \omega\_{\omega} \end{aligned} \tag{42}$$

where *δn* is the rudder offset, *ωr* and *ωω* are the zero-mean Gaussian measurement white noise; *ψω* represents the first-order wave-induced motion, and *ς* is the relative damping ratio, conventionally assigned a value of 0.075. *ω*0 is the wave frequency.

Based on Equation (42), the state space equation of the extended state observer is:

$$
\dot{\hat{X}} = A\hat{X} + B\Gamma + G(Y - C\hat{X}),
\tag{43}
$$

where *X*ˆ denotes the estimation of the state, *X*ˆ = ˆ *δn*,*r*ˆ, *ψ*, ˆ *ξω*, *ψ*ˆ*ω T* and . ˆ *ξω* = *ψ*ˆ*ω*. Γ is the input of the model and Γ = *δ* + *Kvv*; *G* is the gain matrix; ˆ *δn* is the estimation of the rudder offset; *Y* is the heading signal obtained by the compass with *Y* = *ψ* + *ψω*.*A*, *B* and *C* are the coefficient matrixes with:

*A* =

$$
\begin{pmatrix}
0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
0 & 0 & 0 & -\omega\_0^2 & -2\zeta\omega\_0 \\
\end{pmatrix},\tag{44}
$$

$$
B = \begin{pmatrix} 0 \\ \frac{K}{T} \\ 0 \\ 0 \\ 0 \end{pmatrix},\tag{45}
$$

$$
C = \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \\ 1 \end{pmatrix}.\tag{46}
$$

The error of the state vector can be denoted as *E* = *X*ˆ − *X*, of which the differential equation is: .

$$
\dot{E} = (A - G\mathbb{C})E.\tag{47}
$$

To keep the asymptotic stability of the error vector, the solution of Equation (47) should be *E*(*t*) = *E*0*e*−*kt*, where *E*0 is the initial error value and *k* is a scale factor. Thus, all of the eigenvalues of the matrix (*A* − *GC*) have negative real parts. The gain matrix *G* can be found by pole placement in terms of the eigenvalues. In this case, the eigenvector of the matrix (*A* − *GC*) is chosen as: *P* = (*P*0, *P*1, *P*2, *P*3, *P*4) = (1.5/*T*, 1.5/*T*, 1.5/*T*, 15*ςω*0, 15*ςω*0) and the gain matrix can be obtained by using the MATLAB function.

#### **4. Guidance Law**

Systems for guidance consist of a waypoint generator with human interface. A new hyperbolic guidance method for straight-line path-following control is presented in this paper. A Lyapunov function analysis [38] is used to prove the stability of this method. For curve guidance, based on the Lyapunov stability function, this paper presents a reverse stepping method to calculate heading rate command and make the system globally asymptotically stable, with a correction formula for current interference.

#### *4.1. Error Coordinates*

Consider a straight-line path implicitly defined by two waypoints *pk* = (*xk*, *yk*) *T* ∈ *R*2 and *pk*+1 = (*xk*+1, *yk*+1) *T* ∈ *R*2, respectively. Also, consider the position of the ship denoted by the point *pt* = (*xt*, *yt*) *T* ∈ *R*2. Then the direction of the path can be defined as:

$$\mathfrak{a}\_{k} := \mathfrak{a}\text{tan}2(\mathfrak{x}\_{k+1} - \mathfrak{x}\_{k'}\mathcal{Y}\_{k+1} - \mathfrak{y}\_{k}).\tag{48}$$

Fossen [4] gives the formula to calculate the cross-track error:

$$\vec{P}(t) = -[\mathbf{x}\_t - \mathbf{x}\_k]\cos(\mathfrak{a}\_k) + [\underline{y}\_t - \underline{y}\_k]\sin(\mathfrak{a}\_k). \tag{49}$$

The calculation of the cross-track error in the transition curved path between two adjacent straight-line paths is complicated. Figure 2 shows two adjacent straight-line paths described by the waypoints *pk*,*pk*+1 and *pk*+2. *Rk*+1 is the radius of the transition curve and the cross-track error of the transition curved path can be obtained by:

**Figure 2.** The transition curved path.

First, determine the direction of the curved path (clockwise or counterclockwise). Based on Equation (48), the direction *αk* of the straight-line path *pk pk*+1 and the direction *αk*+1 of the straight-line path *pk*+1 *pk*+2 can be calculated. Then the direction of the curved path is:

$$F\_{k+1} = \text{sign}(\sin(a\_{k+1} - a\_k));\tag{50}$$

here, *Fk*+1 denotes the direction of the curved path, a positive sign means clockwise and a negative sign means counterclockwise.

Second, determine the center point of the curved path. The angle between the two adjacent straight-line paths can be obtained in terms of the direction *αk*, *αk*+1 and *Fk*+1.

$$
\gamma\_{k+1} = \pi - F\_{k+1}(\mathfrak{a}\_{k+1} - \mathfrak{a}\_k). \tag{51}
$$

Then the distance between the center point and the waypoint *pk*+1 can be determined in terms of the angle *γk*+1 and the radius *Rk*+1.

$$D\_{k+1} = R\_{k+1} / \sin\left(\frac{\gamma\_{k+1}}{2}\right). \tag{52}$$

The angle between the vector from the center point *Ok*+1 to the waypoint *pk*+1 and North can be obtained in terms of the angle *γk*+1, the direction *Fk*+1 and *αk*.

$$
\mathfrak{a}\_{\mathcal{O}\_{k+1}} = \mathfrak{a}\_k - F\_{k+1} \gamma\_{k+1}.\tag{53}
$$

Based on the waypoint *pk*+1, the direction *αOk*+1 and the distance *Dk*+1 from the center point *Ok*+1 to the waypoint *pk*+1, the coordinate *POk*+1 = *xOk*+1 , *yOk*+1 of the center point *Ok*+1 can be determined:

$$\mathcal{p}\_{O\_{k+1}} = \mathcal{p}\_{k+1} - R\_{k+1} \binom{\sin \mathfrak{a}\_{O\_{k+1}}}{\cos \mathfrak{a}\_{O\_{k+1}}} \,. \tag{54}$$

Finally, the cross-track error can be calculated by:

$$\vec{P}(t) = F\_{k+1} \| \boldsymbol{p}\_t - \boldsymbol{p}\_{O\_{k+1}} \| \, -\boldsymbol{R}\_{k+1}.\tag{55}$$

The course angle command is the direction of the vector tangential to the point on the path that is closest to the vehicle. The course angle command can be calculated by:

$$\dot{\chi}(t) = \chi(t) - atan2\left(\mathbf{x}(t) - \mathbf{x}\_{O\_{k+1}}, y(t) - y\_{O\_{k+1}}\right) + \frac{\pi}{2}F\_{k+1}\tag{56}$$

here, *χ*(*t*) is the current course.

#### *4.2. Straight-Line Path Guidance*

The main goal of straight-line path-following control is to eliminate cross-track and heading errors. Hyperbolic guidance will achieve a more rapid convergence of pathfollowing maneuvering because of its smoothing and transition properties. Thus, a hyperbolic guidance methodology is adopted with a hyperbolic tangent function. As shown in Figure 3, the curve OC denotes a hyperbola, of which the asymptote is the straight-line path. The hyperbola equation is:

$$y = R\_c \frac{e^{k\_c x} - e^{-k\_c x}}{e^{k\_c x} + e^{-k\_c x}},\tag{57}$$

where *Rc* denotes the distance between the origin *O* and the straight-line and *P*1(*t*) is the distance from the ship to the planned route at time *t* with *Rc* > *P*1(*t*).

**Figure 3.** The hyperbolic guidance law.

Then, the position of the ship *pt* can be denoted by *x*0, *Rc* − *P*1(*t*) and the angle *ζ* shown in Figure 3 can be calculated by:

$$\mathcal{Z}(t) = \text{sign}\left(\widetilde{P}(t)\right) \arctan\left[k\_c \left(2\left|\widetilde{P}(t)\right| - \frac{\widetilde{P}(t)^2}{R\_c}\right)\right],\tag{58}$$

where *kc* is a constant coefficient with *kc* > 0, denoting the rate of approach to the straightline path.

Then the course command can be obtained by:

$$\chi\_c = a\_k + \zeta(t) = a\_k + \text{sign}\left(\check{P}(t)\right)\text{arctan}\left[k\_c\left(2\left|\check{P}(t)\right| - \frac{\check{P}(t)^2}{R\_c}\right)\right],\tag{59}$$

where *χc* is the command course and *αk* is initial heading angle.

#### *4.3. Curved Path Guidance*

For curved path following, a kinematic controller generates the desired states for motion control. The control method can be designed using a dynamic model of the ship by specifying a reference frame that moves along the path. A Serret-Frenet reference frame [39] is usually chosen. Figure 4 shows an inertia reference frame {*i*} = (*xi*, *yi*, *zi*), a body-fixed reference frame {*s*} = (*xs*, *ys*, *zs*) and a Serret-Frenet frame {*m*} = (*xm*, *ym*, *zm*). The origin *Om* of {*m*} is attached to the point on the path that is closest to the vehicle. R denotes the radius of the curved path.

**Figure 4.** Path-following: reference frame.

The notation *Hc a*/*b* is adopted in this paper, where {*a*}, {*b*} and {*c*} denote the three different frames and *H* denotes the coordinate of {*a*} in frame {*b*} relative to {*c*}. Such that:

$$r\_{\mathbf{m}/i}^i + r\_{\mathbf{s}/m}^i = r\_{\mathbf{s}/i\prime}^i \tag{60}$$

where *r* denotes the distance vector.

Time differentiation of Equation (60) yields:

$$
\upsilon\_{m/i}^i + \frac{d}{dt}\upsilon\_{s/m}^i = \upsilon\_{s/i\prime}^i \tag{61}
$$

where *v* denotes the speed vector. And *d dtri s*/*m* can be obtained by:

$$\frac{d}{dt}r\_{\text{s}/m}^i = R\_m^i \omega\_{m/i}^i \times r\_{\text{s}/m}^m + R\_m^i \upsilon\_{\text{s}/m}^m \tag{62}$$

where *Ri m* denotes the transformation matrix from {*m*} to {*i*} and *ωi m*/*i* = 0, 0, − . *α T* denotes the rotation vector between the {*m*} and {*i*} frames.

Substituting Equation (62) into Equation (61) and multiplying by *Ri m* on both sides of the equation, yields:

$$
\boldsymbol{v}\_{m/i}^{m} + \boldsymbol{\omega}\_{m/i}^{l} \times \boldsymbol{r}\_{s/m}^{m} + \boldsymbol{v}\_{s/m}^{m} = \boldsymbol{R}\_{s}^{m} \boldsymbol{v}\_{s/i}^{s}.\tag{63}
$$

Then the kinematic equations can be obtained:

$$\begin{cases} \dot{\vec{P}} = -\omega \sin \tilde{\chi} \\ \dot{\vec{\alpha}} = \frac{\mu \cos \tilde{\chi}}{R + FP} \end{cases} \tag{64}$$

where *P*1 is the position deviation, *χ*1 is the course deviation, *α* is the planned course and *F* indicates the direction of the transition curve. *F* = 1 means turning clockwise, *F* = −1 means turning counterclockwise.

Thus, goal of the curved path-following controller is to calculate the yaw rate commands, forcing the ship to approach the curved path. This paper presents a reverse stepping calculation method based on the Lyapunov function to obtain the yaw rate commands.

First, calculate the course commands. Consider the Lyapunov function candidate as follows:

$$V\_1 = \frac{1}{2}\widehat{P}^2.\tag{65}$$

Time differentiation of Equation (65) yields:

$$
\dot{V}\_1 = -\widetilde{P}\mu\sin(\chi-\kappa).\tag{66}
$$

To satisfy global asymptotic stability (GAS), it is necessary to guarantee that *V*1 < 0 as *P*1 = 0 and . *V*1 = 0 as *P*1 = 0. Thus, the following equation is adopted:

$$
\dot{V}\_1 = -k\_1 \hat{P}^2 \le 0,\tag{67}
$$

where *k*1 is the scaling factor, with *k*1 > 0.

Based on Equation (65) and Equation (66), the course commands can be calculated by:

$$\chi\_{\varepsilon} = \alpha + \arcsin\left(\frac{k\_1 \bar{P}}{\mu}\right). \tag{68}$$

Equation (68) suggests that the course command *χc* will approach the path direction *α* to eliminate the course error *χ*1, as the cross-track error is decreasing. However, the path direction *α* is varying with ship motion during the curved path-following control. Thus, it is necessary to calculate the yaw rate commands. Consider the Lyapunov function candidate:

$$V\_2 = \frac{1}{2}\tilde{\chi}^2,\tag{69}$$

with *χ*1 = *χ* − *χc*. Time differentiation of Equation (69) yields:

$$\dot{V}\_2 = (\chi - \chi\_c) \left( \dot{\chi} - \dot{\alpha} - \frac{\dot{\tilde{P}}}{\sqrt{\left(u/k\_1\right)^2 - \tilde{P}^2}} \right). \tag{70}$$

To satisfy GAS, it is necessary to guarantee that . *V*2 < 0 as *χ* = *χc* and . *V*2 = 0 as *χ* = *χc*. Thus, the following equation is adopted:

$$
\dot{V}\_2 = -k\_2 \hat{\chi}^2,\tag{71}
$$

where *k*2 is the scaling factor, with *k*2 > 0.

Based on Equations (64), (68), (70) and (71), the course commands can be calculated by:

$$\dot{\chi}\_c = \frac{u \cos \tilde{\chi}}{R + F\tilde{P}} - \frac{-u \sin \tilde{\chi}}{\sqrt{\left(u/k\_1\right)^2 - \tilde{P}^2}} - k\_2 \tilde{\chi}\_\prime \tag{72}$$

where . *χc* is the derivative of *χc*, indicating the command track angular rate. We neglect the varying of the drift angle *β*, thus the varying rate course command can be treated as the yaw rate command, approximately. However, this does not fit in the presence of wave disturbance. In the presence of sea current interference, the yaw rate commands need to be adjusted as:

$$
\sigma\_c = \dot{\chi}\_c \frac{u\_\%}{u\_\% - u\_f \cos(\varphi\_\% - \varphi\_f)} \,\prime \tag{73}
$$

where *rc* denotes the yaw rate command, *ug* denotes the ship speed over the ground, with direction *ϕg* and *uf* is the current speed through water, with direction *ϕf* .

Figure 5 is the three-layer control structure of ship track control proposed in this paper. The track control module calculates the current planned navigation section of the ship according to the current ship position information and environmental interference information and calculates the track deviation and heading deviation, then modifies the planned heading angle according to the deviation information, calculates the command heading angle and sends it to the heading control module. According to the current compass signal, rudder angle signal and yaw speed signal, the course control module calculates the course deviation after comparing with the command heading and calculates the command rudder angle through the course control algorithm.

**Figure 5.** Basic composition of track control system.

Finally, the rudder angle control layer drives the rudder to make the actual rudder angle consistent with the command rudder angle, so as to realize the track control of the ship.

Figure 6 shows the path-following control overall flow chart:

**Figure 6.** Path-following control flow chart.

#### **5. Simulation Results**

International Standard IEC62065 is used to test the performance of the path-following control algorithm presented in this paper. Based on the standard, three classes of ship are adopted: class A fast ferry, class B container and class C tanker. See Table 2 for details.

**Table 2.** Parameters for three ships.

The heading controller parameters are given in Table 3:

**Table 3.** Heading controller parameters.

The ships' initial states for the three test scenarios are as follows:

Ship A:(u0, v0, r0, ψ0) = (15.4 m/s, 0 m/s, 0 rad/s, 0 deg);

Ship B:(u0, v0, r0, ψ0) = (12.9 m/s, 0 m/s, 0 rad/s, 0 deg);

Ship C:(u0, v0, r0, ψ0) = (5.1 m/s, 0 m/s, 0 rad/s, 65 deg);

In control applications, it is important to validate the controller experimentally, this paper takes ship class B as the simulation object and the ship parameters are shown in Table 2. The step steering signal is selected as the input signal and the rotation experiment is used as the experimental method of controller parameter identification. The trajectory is shown in Figure 7 and the simulation data is shown in Table 4.

**Table 4.** Simulation data of class B ship rotation experiment.

It can be seen from the experimental results that the control model established in this paper meets the ship's turning characteristics and the established model is reliable.

Secondly, the course control algorithms of the three types of ships in Table 2 are verified. For ship class A, the initial speed of the ship is 15.4m/s, the command thrust is 0.67, under sea state 3 and the command heading angle is 30 degrees. As for ship class B,

the initial speed is 12.9 m/s, the command thrust is 0.8, under sea state 3 and the command heading angle is 30 degrees. For ship class C, the initial speed of the ship is 5.1m/s, the command thrust is 1, under sea state 3 and the command heading angle is 30 degrees. Figures 8–10 shows that the improved LQR control algorithm in this paper is compared with the traditional LQR algorithm and the simulation experimental chart of course control is obtained. The simulation data is shown in Table 5.

**Figure 7.** Testing results for ship class B in rotation experiment.

**Figure 8.** Comparative experiment of course control for ship class A: (**a**) The course angle changes with time; (**b**) The actual rudder angle changes with time.

**Figure 9.** Comparative experiment of course control for ship class B: (**a**) The course angle changes with time; (**b**) The actual rudder angle changes with time.

**Figure 10.** Comparative experiment of course control for ship class C: (**a**) The course angle changes with time; (**b**) The actual rudder angle changes with time.

**Table 5.** The results of the heading control test.

Based on the above experimental results, the following conclusions can be drawn: the improved algorithm combining LQR with feedback nonlinearization control can achieve the function of ship course control, the overshoot, control accuracy and corresponding time are better than the traditional LQR control method. In addition, by adding a state observer can ensure that the ship can sail according to the expected instructions under sea state 3 without frequent steering.

There are three test scenarios used to evaluate performance of the path-following controller. Details of the scenarios are given in Tables 6–8.

**Table 6.** The parameters of the track for ship class A.

**Table 7.** Parameters of the track for ship class B.

**Table 8.** Parameters of the track for ship class C.

Results of testing the three classes of ship are shown in Figures 11–13. WPTs in the figure are waypoints.

**Figure 11.** Testing results for ship class A: (**a**) Ship trajectory; (**b**) Observation index: rudder angle, track deviation and heading deviation.

**Figure 12.** Testing results for ship class B: (**a**) Ship trajectory; (**b**) Observation index: rudder angle, track deviation and heading deviation.

**Figure 13.** Testing results for ship class C: (**a**) Ship trajectory; (**b**) Observation index: rudder angle, track deviation and heading deviation.

From Figure 11, we can see that ship class A has a maximum cross-track error of 24.8 m and the maximum course error 11.3◦, which satisfies the requirements set by IEC62065 of setting the course deviation limit to 25◦ and the cross-track deviation to 100 m. The experimental results show that this algorithm has the advantage of less steering time.

Results for ship class B are shown in Figure 12, with a maximum cross-track error of 22 m and maximum course error of 1.6◦, which satisfies the requirements of setting the course deviation limit to 15◦ and the cross-track deviation to 60 m.

Results for ship class C are shown in Figure 13, where the experimental environment is under rough sea state 5, with maximum cross-track error of 27.24 m and maximum

course error of 3.9◦, which satisfies the requirements of setting the course deviation limit to 15◦ and the cross-track deviation to 100 m.

Tests of ship class B in the presence of wave disturbance and a simulated current of 5 kn are also performed. The results are shown in Figure 14.

**Figure 14.** Testing results for ship class B in the presence of disturbance: rudder angle, track deviation and heading deviation.

As shown in Figure 14, in the presence of sea state 3 and a simulated current of 5 kn, 30◦N and the other requirements for test are the same as those for ship class B listed earlier, the results for ship class B satisfy the IEC62065 requirements with maximum cross-track error of 30.1 m and maximum course error of 3.96◦. The experimental result shows that the proposed algorithm has demonstrated good robustness.

To further verify the control effect of the proposed algorithm, additional comparative experiments have been done. For ship class B, the traditional and adaptive PID control algorithms were used for track control, as shown in Figure 15. The experimental results are also compared with traditional LQR controller and the improved LQR control algorithm with nonlinear feedback term proposed in this paper and the track deviations are shown in Figure 16. Specific data are in Table 9. It can be seen from the experimental results that the traditional LQR control method has better tracking effect in the tracking task of direct sail or low speed tracking simple curve. However, it is difficult to guarantee the tracking accuracy in tracking complex task path. The maximum deviation under traditional PID controller, adaptive PID controller, traditional LQR controller and improved LQR controller are as follows: 176.9 m, 48.51 m, 23.32m and 22 m. In terms of stability, the traditional LQR controller performs poorly. And for the improved LQR controller, the deviation is around 0 for more than 3000 s. The performance of the control method proposed in this paper is significantly better than that of the other three control methods.

**Figure 15.** Navigation route for ship class B under different control methods: (**a**) traditional proportional-integral-derivative (PID) control law; (**b**) adaptive PID control law.

**Figure 16.** Testing results for ship class B under different control methods.

**Table 9.** Experimental result for comparison of different control algorithms.

#### **6. Conclusions**

A new practical guidance and control algorithm for marine vehicles is introduced in this paper. The main innovation is the hyperbolic guidance law used in straight-line path-following control. For curved path-following in the transition between two adjacent straight-line paths, this paper improves the reverse stepping method for the controller to calculate heading rate command to make the system globally asymptotically stable, with a correction formula for sea current interference. Traditional LQR and feedback nonlinear control are combined to improve the accuracy of course control. Different types of ships are verified in this paper, simulation results based on the International Standard IEC62065 are included to demonstrate system performance. The algorithms satisfy the IEC62065 testing requirements. Three additional experiments verified that the control method has good robustness and good control effect.

**Author Contributions:** Conceptualization, Z.Z. and H.W.; methodology, Z.Z.; software, Z.Z.; validation, Z.Z., H.W., Y.Z. (Yuhan Zhao) and G.Z.; formal analysis, Z.Z.; investigation, Z.Z.; resources, Z.Z.; data curation, Y.Z. (Yuhan Zhao) and G.Z.; writing—original draft preparation, Z.Z.; writing—review and editing, Z.Z.; visualization, Z.Z.; supervision, H.W. and Y.Z. (Yi Zhao); project administration, H.W. and Y.Z. (Yi Zhao); funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by the Russian Foundation for Basic Research (RFBR) (No. 20-07-00531).

**Institutional Review Board Statement:** "Not applicable" for studies not involving humans or animals.

**Informed Consent Statement:** "Not applicable" for studies not involving humans.

**Data Availability Statement:** Data sharing not applicable. No new data were created or analyzed in this study. Data sharing is not applicable to this article.

**Acknowledgments:** The authors are grateful to the anonymous reviewers for their valuable comments and suggestions that helped improve the quality of this manuscript.

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

#### **References**


Preface

The interest in flexible electronics is on the rise as it brings an added functionality and es‐ thetic value in the unconventional interfaces, such as biomonitoring systems, wearables, flexible textiles, paper-based technologies, and many other curves of soft schemes, for which traditional electronics are not suitable. The demand in new flexible platforms turns to a pur‐ suit for functional materials and technologies commonly compatible with a low tempera‐ ture, high-throughput processing, and novel methods for device integration. New device design leads to an immense field from fundamental research to the new technologies and engineering methods bringing advanced functionality. A wide range of functional materials involving nanoparticles, composites, semiconductor and metallic nanowires, carbon nano‐ materials, polymers, conductive inks, and different hybrid structures are particularly inter‐ esting. Printing technologies have been demonstrated to be highly efficient and compatible with many flexible substrates; furthermore, surface preparation methods play an important role for the fabrication of electronic devices. This book brings a comprehensive overview on the most important technology development in the field of flexible electronics. The interest in flexible electronics is on rise as it brings an added functionality and thetic value in the unconventional interfaces, such as biomonitoring systems, suitable. in platforms suit for functional materials and technologies commonly compatible with a low ture, high-throughput processing, and novel methods for device integration. New design leads to an immense field from fundamental research to the new technologies involving nanoparticles, composites, semiconductor and metallic nanowires, carbon materials, polymers, conductive inks, and different structures are particularly esting. Printing have been demonstrated to be flexible substrates; furthermore, surface preparation play an

> **Simas Rackauskas** University of Turin Turin, Italy

**Chapter 1**

**Provisional chapter**

**Surface Modification of Polyimide Films for Inkjet-**

**Surface Modification of Polyimide Films for**

**Inkjet-Printing of Flexible Electronic Devices**

DOI: 10.5772/intechopen.76450

Kapton polyimide films are one of the most commonly used flexible and robust substrates for flexible electronic devices due to their excellent thermal, chemical, mechanical, and electrical properties. However, such films feature an inert and highly hydrophobic surface that inhibits the deposition of functional materials with water-based fluids (solutions, suspensions, inkjet inks, *etc*.), which raise the need for their surface modification to reduce their inherent surface inertness and/or hydrophobicity in order to allow for the fabrication of electronic devices on the substrates. Traditional Kapton surface modification approaches use harsh conditions that not only cause environmental and safety problems but also compromise the structural integrity and the properties of the substrates. This chapter focuses on two recently-developed mild and environmentally friendly wet chemical approaches for surface modification of Kapton HN films. Unlike the traditional methods that target the polyimide matrix of Kapton films, these two methods target the slip additive embedded in the polyimide matrix. The surface modified Kapton films resulted from these two methods allowed for not only great printability of both waterand organic solvent-based inks (thus facilitating the full-inkjet-printing of entire flexible electronic devices) but also strong adhesion between the inkjet-printed traces and the

**Keywords:** surface modification, Kapton, polyimide, flexible electronic devices, sensors,

Kapton HN films, which are well known to be made of polyimide polymer, are one of the most commonly used substrates for flexible electronics due to their excellent physical and

> © 2016 The Author(s). Licensee InTech. 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.

© 2018 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.

**Printing of Flexible Electronic Devices**

Yunnan Fang and Manos M. Tentzeris

Yunnan Fang and Manos M. Tentzeris

http://dx.doi.org/10.5772/intechopen.76450

**Abstract**

substrate films.

inkjet-printing

**1. Introduction**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Surface Modification of Polyimide Films for Inkjet-Printing of Flexible Electronic Devices Surface Modification of Polyimide Films for Inkjet-Printing of Flexible Electronic Devices**

DOI: 10.5772/intechopen.76450

Yunnan Fang and Manos M. Tentzeris Yunnan Fang and Manos M. Tentzeris

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.76450

#### **Abstract**

Kapton polyimide films are one of the most commonly used flexible and robust substrates for flexible electronic devices due to their excellent thermal, chemical, mechanical, and electrical properties. However, such films feature an inert and highly hydrophobic surface that inhibits the deposition of functional materials with water-based fluids (solutions, suspensions, inkjet inks, *etc*.), which raise the need for their surface modification to reduce their inherent surface inertness and/or hydrophobicity in order to allow for the fabrication of electronic devices on the substrates. Traditional Kapton surface modification approaches use harsh conditions that not only cause environmental and safety problems but also compromise the structural integrity and the properties of the substrates. This chapter focuses on two recently-developed mild and environmentally friendly wet chemical approaches for surface modification of Kapton HN films. Unlike the traditional methods that target the polyimide matrix of Kapton films, these two methods target the slip additive embedded in the polyimide matrix. The surface modified Kapton films resulted from these two methods allowed for not only great printability of both waterand organic solvent-based inks (thus facilitating the full-inkjet-printing of entire flexible electronic devices) but also strong adhesion between the inkjet-printed traces and the substrate films. printability

**Keywords:** surface modification, Kapton, polyimide, flexible electronic devices, sensors, inkjet-printing


**Acknowledgements**

AMLW is supported by an Australian Government Research Training Program Stipend and MAJ was supported by an MS Research Australia/NHMRC Research Betty Cuthbert Fellowship. Project funds were obtained from Multiple Sclerosis Research Australia (MSRA), Lions' club, Australia, and Australian Health Research Alliance-Women's Health Research Translation Network (WHRTN).


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Dynamic Yarn Behavior on Airjet Looms. *Textile Res. J.*, Vol. 75, No. 10, (Oct 1,

Yarn Behavior on Air-jet Looms. *Textile Res. J.*, Vol. 79, No. 18, (Nov 13, 2009),

Composite material, also called composite, a solid material that results when two or more different substances, each with its own characteristics, are combined to create a new substance whose properties are superior to those of the original components in a specific application (Encyclopædia Britannica, 2011). Because the objective in manufacturing component is to produce a stiff and a strong material with a low density, these materials have found place in many application fields such as land transportation, marine, construction, aerospace and medical. There are two constituents in a composite material which are the reinforcement and matrix phases. From the matrix point of view, composites can be divided into three main categories; polymer, metal and ceramic matrix composites (Zhang, 2003). Based on the reinforcement mechanism, composites can be separated as particle reinforced (large particle, dispersion strengthened), fibre reinforced (continuous (aligned), and short fibres (aligned or random)) and structural composites (laminates, sandwich). Fibre reinforced composites have been first introduced in exterior parts of Corvette in 1953. Today, fibre reinforced composites are used in many application fields.

Textile structural composites usually consist of stacked layers known as 2D laminates, exhibit better in-plane strength and stiffness properties compared to those of metals and ceramics (Bilisik, 2010, 2011; Mohamed&Bogdanovich, 2009). However, the application of 2D laminates in some critical structures in aircraft and automobiles has also been restricted by their inferior impact damage resistance and low through thickness mechanical properties when compared against the traditional aerospace and automotive materials such as aluminium alloys and steel (Mouritz et al., 1999). These structures have low out-of plane properties because of the lack of third direction reinforcements which will result in low delamination resistances (Chou, 1992). In order to improve interlaminar properties of the 2D laminates, three dimensional (3D) textile preforms have been developed by using different manufacturing techniques like weaving, knitting, braiding, stitching, and non-woven manufacturing. Among these manufacturing techniques, sewing and 3D weaving are the promising technologies which address the shortcomings of the stack-reinforced composites (Padaki et al., 2010). Since manufacturing technology has a direct effect on the fibre orientation and fibre volume fraction of the preform, the properties of the end product will vary depending on the production and end-use requirements (Peters, 1998).

Although 3D woven preforms have been used for approximately forty years in different application fields, there is not a common understanding and definition of these fabrics

6. A non-woven, non-interlaced 3D fabric forming process designed to connect three orthogonal sets of yarns together with no interlacing (weaving), interloping (knitting), or intertwining (braiding). The fabric is held together by a special binding

However Soden and Hill added a new category as 4A to Khokar's classification for the fabrics that could be placed between categories 4 and 5 where the conventional 2D weaving process uses three sets of yarns to produce *an interlaced 3D fabric* with yarns in the warp,

Regardless of the types of machines used, weaving technology is capable of constructing 3D fabrics with many different geometrical shapes. Chen studied the configurations and geometries of the 3D woven fabrics and classified 3D woven fabrics into four different

> Compound structure, with regular or tapered geometry

Uneven surfaces, even surfaces, and tunnels on different level in multi-directions

Tubular nodes and solid nodes

Multilayer Spherical shells and open box shells

In 3D woven fabrics, generally multilayer, angle interlock and orthogonal weave architectures are the most widely used weave structures. While multilayer and angle interlock weave structures can be produced with conventional 2D weaving machines especially with shuttle looms, orthogonal weave architecture needs a special designed 3D weaving machine to be produced. Orthogonal weave structures consist of three sets of yarns that are perpendicular to each other (X, Y and Z coordinates). In this particular 3D woven fabric formation process, Z yarns interconnect all individual warp- and fill-directional yarns and thus solidify the fabric (Bogdanovich, 2007). Mechanical and structural properties of the composites having orthogonal weave architectures with various binding weaves and different numbers of layers were investigated (Chen&Zanini, 1997 as cited in

 Since straight yarns exist in the orthogonal structures, tensile stiffness and strength properties of these structures are well regardless of type of binding weave. However, tensile stiffness and strength values of these weave structures are directly proportional

weft and through-the-thickness directions (Soden&Hill, 1998).

Multilayer Orthogonal Angle Interlock

Multilayer Orthogonal Angle Interlock

Table 1. 3D textile structures and weave architectures (Chen, 2011).

Behera&Mishra, 2008). The results of the investigation are as follows:

Hollow Multilayer

Shell Single layer

**2.3 Weave structures and properties**

with the number of layers.

categories, as listed in Table 1 (Chen, 2007 as cited in Chen et al., 2011).

**Structure Architecture Shape**

process.

Solid

Nodal

which make them difficult to comprehend. Therefore, this chapter attempts to make a detailed overview of 3D woven fabrics, basic structure of 3D woven fabrics, definitions and classifications of 3D woven fabrics in comparison with 2D woven fabrics.


*Edited by Miroslav Blumenberg*

The word melanin refers to dark natural pigments produced by the oxidative degradation of tyrosine, catalyzed by tyrosinase, and polymerized into insoluble granular substance. The main function of melanin is to protect from harmful agents, primarily UV radiation, but also from oxidation, heavy metals, etc. In this volume, chapters deal with production of melanin in human oral mucosa (Liviu et al.), the regulation of melanin action (Cecile et al.), production and potential technological application of fungal melanins (Pombiero-Sponchiado et al.) and an innovative method for measuring melanin in various samples (Zdybel et al.). In conclusion, this volume presents various biological and industrial aspects of melanin production, uses and analysis.

ISBN 978-953-51-2979-0

Melanin

Photo by dimarik / iStock

## Melanin

*Edited by Miroslav Blumenberg*


**Author details**

Sarah Hooper1 \* and Sybill Amelon2

1 Ross University School of Veterinary Medicine, Basseterre, Saint Kitts

2 USDA Forest Service Northern Research Stations, Columbia, USA

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 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.

*Pesticide Exposure Risks to Chiropteran Species and the Impacts on Emerging Zoonotic Diseases DOI: http://dx.doi.org/10.5772/intechopen.100643*