**Abstract**

This study describes an adaptive sliding mode control (ASMC) for the control of switched reluctance motor (SRM). The main objective is to minimize torque ripples with controller effort smoothness while the system is under perturbation by structured uncertainties, unknown parameters, and external disturbances. The control algorithm employs an adaptive approach to remove the need for prior knowledge within the bound of perturbations. This is suitable for tackling the chattering problem in the sliding motion of ASMC. In order to achieve control effort smoothness and more effective elimination of chattering, the algorithm then incorporates proper modifications in order to build a chattering-free robust adaptive sliding mode control (RASMC) using Lyapunov stability theory. A final advantage of the algorithm is that system stability and error convergence are guaranteed. The effectiveness of the proposed controller in improving robustness and minimizing ripples is demonstrated by numerical simulation. Experimental validation is used to demonstrate the efficiency of the proposed scheme. The results indicate that RASMC provides a superior performance with respect to speed tracking and disturbance rejection over the conventional sliding mode control (CASMC) in the face of uncertainties in model and dynamic loads.

**Keywords:** switched reluctance motor, ripple minimization, robust adaptive sliding mode control, chattering elimination, automotive application

### **1. Introduction**

The past two decades witnessed a unique interest in using switched reluctance motors fueled by their several advantages over other motors. Therefore, one can expect them to play a more crucial role in the industry in the future. The rotor of switched reluctance motor (SRM) has no winding, which gives more preference to the machine, including smaller size, lower costs, higher speeds, and high-power density and reliability [1].

Double saliency structure, inherent magnetic saturation, and time variation of parameters induce nonlinear complexity and high uncertainties in the dynamic model. Furthermore, the load torque uncertainties in many applications such as

variable payloads are inevitable. One biggest challenge in SRM drives is torque ripples. Therefore, compared with other methods like magnetic structure design to achieve minimized torque ripple performance, advanced control methods have been considered further, including model predictive control [2], fuzzy logic controller [3], internal model control [4], Lyapunov function-based robust controller [5], and H-infinity robust technique [6, 7]. Moreover, applications of nonlinear robust adaptive algorithms for SRM control have been proposed in [8, 9]. However, the sophisticated design of these methods is their disadvantage. Hence, appropriate simple nonlinear control design regarding uncertainties is necessary.

performance. For example, [31, 32] integrate HOSMC with gain adaptation techniques. RASMC, which replaces discontinuous sign function by continuous tanh function with incorporation of ASMC, is introduced in [33, 34]. Reference [35] proposed modified robust adaptive control, while the modification occurred in error

*Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor*

A robust adaptive controller by incorporating exponential function instead of discontinuous function is proposed in [36, 37]. Some changes are applied to the control law so that signals of closed-loop system would finally become uniformly bounded. This method is effective in reducing and smoothing the control effort by developing simple estimation of sliding gain despite unknown time-varying pertur-

This paper tries to employ RASMC for chattering-free speed control of SRM with high-accuracy robust tracking performance under structured uncertainties and perturbations. The proposed scheme can reject any applied unknown bounded, time-varying disturbances. Torque ripple minimization and transient response improvement are also tried to be achieved. Additionally, the presented method demonstrates control effort considerable smoothness. Asymptotic stability is retained by Lyapunov theory, and it is shown that states of the closed-loop system are bounded and asymptotically converge on zero. The validity and effectiveness of the proposed algorithm have been demonstrated by simulation and experiment. The implementation is presented using a 4KW, four-phase, DSP-based SRM drive system. The results verify the desired performance of proposed strategy by comparing

The SRM possesses a simple design with salient poles on both the rotor and stator but without windings on its rotor. Operation is based on the tendency to stand in alignment with the rotor and stator poles which yields a stable position, and consequently, the reluctance is minimized. Torque production is due to the sequential excitation of diametrically opposite stator poles by a switching algorithm [25].

*Jω*\_ ¼ *T*<sup>e</sup> � *T*<sup>L</sup> � *Bω*,

*dλ θ*ð Þ , *i dt*

where *v* is the voltage, *i* denotes the current, *λ* is the flux linkage, and *r* stands for the phase resistance. Moreover, *J* is the inertia of the motor, *B* denotes the motor load friction, *T*<sup>e</sup> is the electromagnetic torque, and *T*<sup>L</sup> shows the load torque.

In the conventional SMC, the upper bound of uncertainties is needed in controller design, whereas adaptive sliding mode method may estimate the bound of perturbations. By taking the uncertainties into account in the mechanical part of

(1)

The basic sets of electrical and mechanical differential equations are used for dynamic modeling of SRM. The motor state–space dynamic model can be

*v* ¼ *ri* þ

\_ *θ* ¼ *ω*,

**3. Conventional adaptive sliding mode control design**

SRM dynamic model (1), one can write

bations. The approach benefits from the low computational process.

dynamic definition not in switching function.

*DOI: http://dx.doi.org/10.5772/intechopen.91161*

with CASMC.

stated as

**123**

**2. The dynamic model of SRM**

Recently, designing controllers based on variable structure system and sliding mode control (SMC) thanks to its features such as simplicity, high-speed feedback control that could be easily used along with motor switching circuit, and inherent robustness against nonlinear complex uncertain dynamic systems has been the focus of many researchers. Conventional SMC (CSMC) design for torque control considering ripple reduction is used in [10–14], but these methods unfortunately suffer from the chattering phenomenon. To solve this problem, several attempts are reported for SRM control that is briefly mentioned as follows.

Ref. [15] introduced robust variable structure control causing reduced torque ripple operation. However, the magnetic saturation is neglected. Ref. [16] proposed SMC-based flux linkage controller for switched reluctance motor. Advantage of chattering reduction is achieved by using boundary layer around the switch surface. However, this method creates a finite steady-state error [17]. The idea of using continuous sliding mode function is also presented in [18]. Fuzzy discontinuous SMC for this purpose is developed in [19], but the results show that chattering exists. Ref. [20] uses a dynamic sliding mode controller in the input of the speed controller instead of sign function, but external disturbance and system uncertainties are not considered. Ref. [21] developed chattering-free nonlinear sliding mode controller; however, it focused on permanent magnet synchronous motor. Higher order sliding mode control (HOSMC) is also proposed for alleviating the chattering problem [22, 23]. For example, [24] proposed second-order sliding mode control (SOSM) with super-twisting algorithm for speed control of SRM but unfortunately it only contains simulation results. Application of second-order sliding mode control with the focus on dynamic improvement of phase currents is also proposed in [25].

The deficiency of most designed controllers based on sliding mode is a result of the requirement of prior knowledge about upper bound of uncertainties and unmodeled dynamics. In other words, the regular SMC estimates upper bound of perturbations through calculation of switching gain to compensate their undesired effect. The gain increases with higher value of upper bound and leads to chattering phenomenon and control effort intensification. This may excite high frequency, which causes problems for hardware implementing. Chattering-free approaches for design SMC are classified in two major categories: interaction with switching gain selection and dynamic modification in sliding function [26]. In the case of switching gain selection, one useful approach is adaptive-based sliding mode controls (ASMC) [27, 28].

In this paper, it is further attempted to develop a SRM drive speed control aiming to torque ripple minimization. In doing so, a robust adaptive-based scheme was applied to overcome the uncertainties of model and load torque. The main idea lies in estimation of desired switching gain to reduce chattering. To make this, there is no need to know the upper bound of uncertainties. On the other hand, control gain is tried to be maintained as small as possible that is sufficient to counteract the uncertainties. The method is used successfully in AC electric drive [29, 30].

In recent years, there is a growing concern to integrate the chattering reduction techniques for building a unified effective method to yield chattering-free *Chattering-Free Robust Adaptive Sliding Mode Speed Control for Switched Reluctance Motor DOI: http://dx.doi.org/10.5772/intechopen.91161*

performance. For example, [31, 32] integrate HOSMC with gain adaptation techniques. RASMC, which replaces discontinuous sign function by continuous tanh function with incorporation of ASMC, is introduced in [33, 34]. Reference [35] proposed modified robust adaptive control, while the modification occurred in error dynamic definition not in switching function.

A robust adaptive controller by incorporating exponential function instead of discontinuous function is proposed in [36, 37]. Some changes are applied to the control law so that signals of closed-loop system would finally become uniformly bounded. This method is effective in reducing and smoothing the control effort by developing simple estimation of sliding gain despite unknown time-varying perturbations. The approach benefits from the low computational process.

This paper tries to employ RASMC for chattering-free speed control of SRM with high-accuracy robust tracking performance under structured uncertainties and perturbations. The proposed scheme can reject any applied unknown bounded, time-varying disturbances. Torque ripple minimization and transient response improvement are also tried to be achieved. Additionally, the presented method demonstrates control effort considerable smoothness. Asymptotic stability is retained by Lyapunov theory, and it is shown that states of the closed-loop system are bounded and asymptotically converge on zero. The validity and effectiveness of the proposed algorithm have been demonstrated by simulation and experiment. The implementation is presented using a 4KW, four-phase, DSP-based SRM drive system. The results verify the desired performance of proposed strategy by comparing with CASMC.
