The direct current (DC) motor is the core part of an electrical vehicle (EV). The unmatched perturbation of load torque is a challenging problem in the control of an EV system driven by a DC motor and hence a deep control concern is required. In this study, the proposed solution is to present two control approaches based on a backstepping control algorithm for speed trajectory tracking of EVs. The first control design is to develop the backstepping controller based on a quasi-sliding mode disturbance observer (BS-QSMDO), and the other controller is to combine the backstepping control with quasi-integral sliding mode control (BS-QISMC). In the sense of Lyapunov-based stability analysis, the ultimate boundedness of the proposed controllers has been detailedly analyzed, assessed, and evaluated in the presence of unmatched perturbation. A modified stability analysis has been presented to determine the ultimate bounds of disturbance estimation error for both controllers. The determination of ultimate bound and region-of-attraction for tracking and estimation errors is the contribution achieved by the proposed control design. The performances of the proposed controllers have been verified via computer simulations and the level of ultimate bounds for the estimation and tracking errors are the key measures for their evaluation. Compared to BS-QISMC, the results showed that a lower level of ultimate boundedness with a higher convergent rate can be reached based on BS-QSMO. However, a higher control effort can be exerted by the BS-QSMO controller as compared to BS-QISMC; and this is the price to be paid by the BS-QSMO controller to achieve lower ultimate boundedness with a faster convergence rate.

This paper proposes the use of the integral sliding mode control (ISMC) based on the barrier function to control the servo actuator system with friction. Based on the barrier function, the main features of the ISMC design were preserved, additionally, the proposed control design is done without the need to know the bound on the system model uncertainty, accordingly, the overestimation of the control gain doesn’t take place and the chattering is eliminated. Moreover, the steady-state error can be adjusted via selecting the barrier function parameter only. The simulation results demonstrate the performance of the proposed ISMC based on the barrier function where the system angle successfully follows the desired angular position with a small pre-adjusted steady-state error. Additionally, the obtained results clarify superior features compared with a traditional ISMC designed to the same actuator.

Numerous thermal practical applications utilize shell and tube heat exchanger appliances to transfer heat energy between hot and cold working fluids. Incorporating metal foam to the outer periphery of inner tube improves the heat transfer process from hot water in the tube side to cold water in the shell side and consequently improves heat exchanger performance. In this study, the integration of use of a porous material together with designing a robust adaptive controller could efficiently regulate the outlet cold water temperature to the desired value. This is achieved with respect to the time required for cold water to reach the desired temperature (settling time) and the amount of hot water volume flow during a certain time span. A barrier function-based adaptive sliding mode controller (BF-based adaptive SMC) is proposed, which requires only the information of temperature measurement of cold water. The stability of BF-based adaptive SMC is proved utilizing Lyapunov function analysis. The effectiveness of proposed controller is verified via numerical results, which showed that the proposed controller could achieve considerable accuracy of cold water temperature using suitable design parameters. In addition, the robustness of controller against variation in inlet temperature is also verified. Another improvement to performance of heat exchanger system is achieved by adding the metal foam of aluminum material on inner pipe perimeter with wide range of metal foam to outer inner pipe diameters ratio ($1\le s\le 1.8$). The results showed that the settling time is significantly reduced which enables outlet cold water to reach the required temperature faster. With respect of the case of non-adding metal foam on inner pipe outer circumference, when $s=1.2$, the settling time and hot water temperature are reduced by $1/2$ and $17.3\%$, respectively, while for $s=1.8$, they are decreased by $\le 1/20$ and $35.3\%$ correspondingly. Accordingly, the required volume flow for hot water is reduced considerably.

Robust control of non-linear systems with coupled dynamics subject to different types of disturbance is addressed in this paper. The method is applied for control and trajectory tracking of robotic manipulators. Robust trajectory tracking of the robot in the presence of payload force, friction force, and parameters uncertainty is achieved using integral sliding mode controller technique. To evaluate the proposed control system simulation has been performed using the dynamic model of Phantom Omni robot and the results of the simulation demonstrate the superiority of the proposed control system compared with the conventional sliding mode control and PD controller.

Latency in flux observation has an adverse effect on the performance of observer-based field-oriented speed control for three-phase induction motor (IM). The reduction of the convergent rate of estimation errors could improve the performance of speed-controlled IM based on flux observers. The main contribution is to design a fast convergent flux observer, which provides bounded estimation error immediately after one instant of motor startup. The proposed flux observer fused barrier function adaptive mechanism with integral sliding mode control principle to yield BFISMO. Rigorous stability analysis has been conducted to achieve global flux estimation error ultimate boundedness. Moreover, three controllers have been designed. The first control design is devoted to flux control based on a backstepping controller, while the other two controllers’ design is dedicated to rotor speed control of the motor. The speed controller is developed by combining the backstepping control with disturbance observers to estimate the unmatched load torque named quasi-sliding mode observer (QSMDO), and nonlinear disturbance observer (NLDO). Based on numerical simulations, the performance and efficacy of the proposed BFISMO have been assessed by conducting a comparison study to other observer techniques. The results showed the superiority of the proposed observer over the conventional versions.

The main drawback of the classical sliding mode observer is the chattering problem which eliminated in the present via replacing the signum function with an approximation to get approximate classical sliding mode observer. When the signum function is replaced with an approximating one, the estimation error will not go to zero anymore, but it will go to the bounded region around the origin. In this paper, the bounded region is obtained and controlled by adjusting the parameters of the proposed observer. The DC motor system suffers from a perturbation vector, and unmeasured angular acceleration is utilized as an application to a nonlinear controller based on the proposed observer.