**3.2 Cascade control system**

The procedures have more than one variable or factor at the output. That should be controlled is well known as a term multivariable or MIMO processes. Interactions usually exist or occasionally do not exist between the control loops of multivariable processes, which is famed by problems in control when compared with the Single Input/Single Output (SISO) control processes. Lead–lag compensators are utilized to provide a combines performance involving both lead and lag compensator and utilized as another phase following PI and PID controllers which allow the machine to have stabilized functionality [5, 6, 12, 26]. PI controller was utilized to control the guide axis current. This sort of control procedure is shown in **Figure 7**. The disadvantages of the type of control an ambiguity of control engineers' power SISO PID controller, flexibility for both interaction adjudication and compare it with overall multivariable control it is a couple of strong tools for its layout [6–9]. Therefore, there is one easy method to tune a multi-loop PID controller by tuning each loop one by induvial work, and completely discarding the loop connections and that is carried out by the (i) loop of cascade controller for the plant move. Then re-tuning all the loops together so the general system has stable functionality and supplies a suitable load disturbance response [5, 6, 12, 26–29].

#### **3.3 Double-led compensation**

The lead compensators are used to give advance phase margin, used in this chapter as a second stage after PID controller, and used to control quadrature axis current double-lead compensators to make the system have advanced stabilized performance because it is considered a cascaded lead compensator [6, 7–12]. The double lead compensator gives double of the phase advance that a simple lead compensator that gives. The double lead compensator mathematical description can be given in (Eq. (20)). The lead compensator is utilized to control the quadrature axis present of this SynRM.

$$\mathbf{G}\_{pd}(\mathbf{s}) = K\_p \frac{\left(\mathbf{1} + \mathbb{A}\boldsymbol{\zeta}\_{\boldsymbol{\alpha}\_\mathbf{s}}\right)^2}{\left(\mathbf{1} + \mathbb{A}\boldsymbol{\zeta}\_{\boldsymbol{\alpha}\_\mathbf{p}}\right)^2} \tag{20}$$

**Figure 7.** *Cascade controller block diagram.*

### **3.4 Practical swam optimization tuning PID controller parameter**

The Particle Swarm Optimization (PSO) is a public rely on computational approaches that the primary concept came in the simulation of social behavior "social-psychological methods" fish instruction, bird flocking and swarm concept. PSO was initially designed and evolved by Eberhart and Kennedy [4, 6, 12] This concept was designed to be effective in solving problems exhibiting non-linearity and non-differentiability. The scheme is obtained from research on swarms such as fish Instruction and bird flocking. Accommodation to the results of research for a flock of birds finds that bird's food by flocking (not by everyone). Instead of using the evolutionary proses such as mutation and crossover that been used for algorithm manipulation. In the PSO algorithm, none of these presses are used, the dynamics of the population simulates a "fish flocks" attitude, where sociably sharing of information takes a major part of work and individuals can profit from discovering and former experience of all the other escorts during the food searching process [4]. The fitness function is cast to maximize the constraints domain or to minimize the preference constraints. The most common performance criteria that depend on the error criterion are Integrated Absolute Error (IAE), Integrated of Time Weight Square Error (ITSE) and integrated of Square Error (ISE) which can be calculated analytically in the frequency domain. The criteria selection depends on the system and the controller [5, 6, 12–16]. In this chapter the fitness functions are used depend on the ISE criterion and the overshoot Mpcriterion as seen on (Eqs. (21)–(24)).

$$\text{Fitness function} = \min \left( \text{ISE} \right) + \min(M\_p) \tag{21}$$

**Figure 8.** *The PSO algorithm steps.*

$$\text{ISE} = \int \mathbf{e}^2(\mathbf{t})d\mathbf{t} \tag{22}$$

$$\mathbf{M}\_{\rm p} = \max\left(\mathbf{n}\right) - \left(\mathbf{n}\_{\rm ref}\right) \tag{23}$$

$$\mathbf{e}(\mathbf{i}) = \mathbf{D}(\mathbf{i}) - \mathbf{y}(\mathbf{i}) \tag{24}$$

The við Þt and xið Þt updating for each particle in the swarm are done depending on (Eqs. (25) and (26)). Then starting the main loop and the fitness function are calculated to update the positions of particles. If the new value is better than the quondam Ibest, the new value is set to Ibest . In the same way, gbest value is also updated like the Ibest. The velocity of each agent can be updated by (Eq. (25)).

$$\mathbf{v\_i^{k+1}} = \mathbf{w} \ast \mathbf{v\_i^k} + \mathbf{c\_1} \ast \mathbf{R\_1} \ast \left(\mathbf{lbest\_i} - \mathbf{x\_i^k}\right) + \mathbf{c\_2} \ast \mathbf{R\_2} \ast \left(\mathbf{gbest\_i} - \mathbf{x\_i^k}\right) \tag{25}$$

Moreover, the current position can be updated by (Eq. (26)):

$$\mathbf{x\_i^{k+1} = x\_i^k + v\_i^{k+1}} \tag{26}$$

$$\mathbf{w} = \mathbf{w}\_{\text{max}} - \frac{(\mathbf{w}\_{\text{max}} - \mathbf{w}\_{\text{min}})}{\text{iter}\_{\text{max}}} \tag{27}$$

The diagram below explains the order of PSO processes and steps that were adopted and implemented in this design as expend in **Figure 8**.

#### **4. The design of the propulsion EV system**

The proposed system is called the Multi-Converter/Multi-Machine System (MCMMS) which consists of two SynRM that drive the two rear wheels of PEV [6, 7, 12, 13]. The linear speed of the vehicle is controlled by an EDC which gives the reference speed for each driving wheel which depends on the driver reference speed and the steering angle. Different road conditions have been applied by the Drive cycle topology to test the stability of the EV under the EDC controller. The SynRM speed is controlled by using a PID controller and the PSO algorithm has been used as an optimization technique to find the optimal PID parameter to enhance the drive system performance [2–4, 24]. The VSSVI has been used to transform the DC voltage source to three-stage AC voltage [1, 2]. The EV system has tested implemented in the Matlab/Simulink environment. Moreover, the mechanical load that reflects the street state of the vehicle each one of these elements has been displayed in **Figure 9**. Which shows a succinct description to the suggested system the two-wheel driveway process is perceptible to everyone to grantee the equilibrium of the EV on various road state [1–12].

The inner construction system for this type of EV has controlled by an EDC system that ensures the robustness of the motor vehicle [1–5]. In addition, the propulsion electric vehicle system process has referred to as a MCMMS [18, 22]. Moreover, the pure-electric-vehicle is much simplified and like the traditional mechanical vehicle in the work way, because of slipping issues from the curvature or slope "inclined" angle roads [16, 17, 23].

#### **4.1 The electronic differential controller (EDC)**

The EDC is an electronic device that guarantees deliver a maximum value of the torque and control both driving wheels, so each wheel may turn at different speed

**Figure 9.** *Propulsion system control of the EV.*

rates in virtually any curve or precisely the exact same rate of speed in the right line road. According to the road condition and especially the steering angle control of the vehicle, the electric power is distributed by EDC to each electric motor [4, 9–12, 27]. In addition, the most critical beholding in the plan of the EVs will be to make sure that the EV is secure when cornering' and under slippery road' conditions [9, 14, 15]. **Figure 10** shows the EV structure pushed at a curve road. The calculation of the speed rate of the vehicle is a task of EDC work, also is based mostly on; the driver, vehicle dimension and street condition. The linear speed rate as well as the steering angle that has awarded by the driver, which implies that both inputs regarded as the input reference to the EV system [9, 17–20, 27–30].

At the beginning of the vehicle's turn in the curve road, the driver utilizes the curve steering angle to the steering wheel to drive and control the vehicle. In this case, the EDC reacted quickly and calculate the benchmark speed of each wheel ought to be operating that appropriately and synchronous to ensure the equilibrium of the EV functionality within the curve street by increasing the speed rate of an outer motor and diminishing the speed rate of the Internal motor [4, 12, 17]. The mathematical model of this EDC signifies via (Eqs. (28) and (29)).

$$\mathbf{V}\_{\rm L} = \alpha\_{\rm v} \left( \mathbf{R} + \frac{\mathbf{d}\_{\rm o}}{2} \right) \tag{28}$$

$$\mathbf{V\_R} = \alpha\_\mathbf{v} \left( \mathbf{R} - \frac{\mathbf{d\_o}}{2} \right) \tag{29}$$

The curve road can be determined as (Eq. (30)).

$$\mathbf{R} = \frac{\mathbf{L}\_{\text{eq}}}{\tan \delta} \tag{30}$$

Moreover, the angular speed rate in a curve road for both wheels can obtain by the following in (Eqs. (31) and (32)) bellow:

$$\alpha\_{\rm L} = \frac{\mathbf{L\_{\rm 0}} + \frac{\mathbf{d\_{\rm 0}}}{2} \tan \delta}{\mathbf{L\_{\rm 0}}} \alpha\_{\rm v} \tag{31}$$

**Figure 10.** *The input and output of the EDC on the curve road.*

$$\alpha\_{\rm R} = \frac{\mathcal{L}\_{\rm 0} - \frac{\mathcal{d}\_{\rm u}}{2} \tan \delta}{\mathcal{L}\_{\rm 0}} \alpha\_{\rm v} \tag{32}$$

The difference in Rate between both of them (the left and right wheels) could be write as (Eq. (33)) bellow:

$$
\Delta \mathbf{o} = \mathbf{o}\_{\mathrm{L}} - \mathbf{o}\_{\mathrm{R}} = \frac{\mathbf{d}\_{\mathrm{o}} \cdot \tan \delta}{\mathbf{L}\_{\mathrm{o}}} \mathbf{o}\_{\mathrm{v}} \tag{33}
$$

Besides, the mention of the speed rate for both Wheel engine can be described as (Eqs. (34) and (35)) bellow:

$$
\alpha\_{Lr} = \alpha\_{\rm v} + \frac{\Delta \alpha}{2} \tag{34}
$$

$$
\alpha\_{\text{Rr}} = \alpha\_{\text{v}} - \frac{\Delta \alpha}{2} \tag{35}
$$

The Terms of the angle (δ) condition in both of straight or curve road are:


**Figure 11.** *The effective forces of the EV in an inclined road.*

#### **4.2 The resistive forces of EV**

Typically, the EV regarded as a succession of heaps that described by numerous forces mainly or resistive torque. Anyway, the forces may include three components, which will be the rolling resistance, the aerodynamic resistance along with also the pitch "incline" resistance [4]. The forces acting in an EV moving across a likely road is displayed in **Figure 11**.

The resistive forces which influenced on the EV are described as seen on (Eq. (36)). And the effective rolling resistance can be described as seen on (Eq. (37)) [31].

$$\mathbf{T\_r = T\_{aero} + T\_{slope} + T\_{time}} \tag{36}$$

$$\mathbf{T\_{tree}} = \mathbf{m} \mathbf{g} \mathbf{f\_r} \tag{37}$$

The force of the aerodynamic resistance can be explained in (Eq. (38)):

$$\mathbf{T\_{aero}} = \mathbf{1}/2 \mathbf{\hat{p}\_{air}} \mathbf{A\_{f}C\_{d}V^{2}} \tag{38}$$

Moreover, the force of the slope "incline" resistance describes in (Eq. (39)):

$$\mathbf{T\_{slope}} = \mathbf{m} \mathbf{g} \sin \mathfrak{h} \tag{39}$$

#### **5. Simulation and results**

#### **5.1 Simulation and results of cascade-PI and lead-lag-controller**

A single cascade controller with several control loops has been used in industrial processes. Since it provides an advantage in terms of ease of execution and the

ability to manually set the parameter of this managed kind. Furthermore, as compared to overall multivariable control, which has a few robust tools for its architecture, this control category has a high demand for interaction versatility modification. In this case, a system engineering team manually tunes the SISO for the PID controller to complete the control loop for this form of control. Even so, there is a single basic strategy for tuning a multi-loop PID control, which is to tune control loops step by step while refusing loop interaction completely. Furthermore, the install switch operation has been carried out by setting the I loop of the PID control. The machine would have steady functionality and a suitable load disruption response if the full loops are re-tuned together. To restrain the quadrature-axis (q) that exists in the SynRM, the lead–lag compensator was proposed.

Simultaneously, the procedure is depended on **Figure 6** that represents the SynRM cascaded control system. **Figure 12** explains the simulation for the cascaded PI controller model with the lead–lag compensator. **Table 3** reveals the cascaded controller parameters value of the cascaded controller system that has utilized by a strategy known as "trial and error". The **Figures 13**–**18** reveals the SynRM speed rate and torque due to different working condition.
