An implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems

In conventional reaching law approaches, the disturbance suppression is achieved at the cost of high-frequency chattering or increasing the complexity of algorithm such as adding a high-order disturbance compensator. This paper presents the design and analysis of a novel implicit discretization-based adaptive reaching law for discrete-time sliding mode control systems. First, the implicit Euler technique is introduced into the design of discrete reaching laws, and it is proved to be able to eliminate numerical chattering completely. By using a self-adaptive power term, the newly designed reaching law can obtain an arbitrarily small boundary layer of sliding surface, and at the different phases of sliding mode motion, the adaptive power parameter can automatically regulate its value to guarantee globally fast convergence without destroying the accuracy of sliding variable. Then, based on a predefined trajectory of sliding variable, the discrete-time sliding mode control law is developed to realize high control accuracy without additional design. Compared with previous methods, the main contribution of proposed reaching law lies in that it can acquire high-precision sliding mode motion and simultaneously eliminate numerical chattering in spite of complex uncertainties only by adjusting the adaptive power parameter. Finally, a simulation example on the piezomotor-driven linear stage is provided to verify the theoretical results.

Optimization of the New Index Reaching Law of the Active Suspension Sliding Mode Controller Based on the Cuckoo Search Algorithm

To facilitate the performance of the active suspension system, the optimization of a new reaching law of the active suspension sliding mode controller based on cuckoo algorithm is addressed in this paper. Firstly, a linear model of the active suspension system is built. Then, according to the features of the new exponential reaching law, an active sliding mode control scheme based on the new sliding mode reaching law is designed. Finally, the simulation results are separated into two stages to verify the suitability and superiority of the proposed control scenario.

Low-Speed Transient and Steady-State Performance Analysis of IPMSM for Nonlinear Speed Regulator with Effective Compensation Scheme

The speed response of the interior permanent magnet synchronous motor (IPMSM) drive at low speeds was analyzed. To eliminate the effect of external disturbance or parameter uncertainty, a nonlinear speed control loop was designed based on the sliding-mode exponential reaching law, which reduces chatter, which is the major drawback of the constant reaching law sliding-mode control technique. The proposed nonlinear speed control eliminates speed ripples at low speed under load disturbance. The problem of speed convergence at low speed is caused by electromagnetic torque ripples, which cause shaft speed oscillations that affect drive performance. The main objective of the proposed method is to change the traditional IPMSM control design by compensating with an appropriate signal along the reference current and across the output of the speed control loop. To optimize the speed tracking performance during disturbances or parametric variations, a nonlinear speed control scheme is designed that can vigorously adapt to the change in the controlled system. The comparative analysis shows that the method provides excellent transient performance (e.g., fast convergence response, less overshoot, and fast settling time) and standstill performance (e.g., reduced steady-state error) compared with conventional control methods at low speed under varying load conditions. The method is easy to implement and does not require additional computational cost. To demonstrate the effectiveness and feasibility of the design approach, a numerical analysis was conducted, and the control scheme was verified using MATLAB/Simulink considering various operating conditions.