This paper presents a disturbance observer-based integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. Firstly, a linear state feedback control law for the slow subsystem of the SPS is designed, and the fast subsystem is established. Secondly, a disturbance observer and an ISMC incorporating the disturbance estimate are constructed. The gain of ISMC is obtained by applying the H∞ control theory, and the resulting ISMC can effectively attenuate the mismatched disturbances. Finally, the proposed method is applied to an electric system, which illustrates the effectiveness and feasibility. The proposed design methods are based on the reduced-order subsystems and thus free of the high dimensionality and possible numerical ill-conditioned problems.

In this paper, a novel adaptive-gain sliding mode observer (SMO) is designed for sensorless control of permanent magnet linear synchronous motors (PMLSMs). By the proposed adaptive-gain algorithm, the gain can dynamically adapt to a changing operation condition of the PMLSMs and reach an appropriate value in finite time. Stability of the SMO is proved by using Lyapunov stability theory. Compared with the traditional SMO, the adaptive-gain SMO can improve the control precision, especially when the operation condition is not invariant. Simulation results are given to show the advantages of the proposed method.

This paper addresses the problems of passivity-based integral sliding mode control (ISMC) and ε-bound estimation for uncertain singularly perturbed systems (SPSs) with disturbances. Firstly, a singular perturbation parameter ε-dependent integral sliding surface is constructed with the reachability condition satisfied. Then, by passivity theory, a set of ε-independent linear matrix inequalities (LMIs) are derived to design the ISMC gain, such that the closed-loop SPSs are passive and internally exponentially stable. Furthermore, an ε-bound estimation method is proposed, such that the passivity and internally exponential stability are preserved for any ε less than or equal to the ε-bound. Compared with the existing methods, the proposed approaches are less conservative because they are derived by a more general storage function and free of equality constraints. Finally, the advantages and effectiveness of the proposed methods are demonstrated by simulation results.

Combining the feedback of predictive function control and the feedforward of extended state observer, a composite control strategy is proposed for the permanent magnet linear synchronous motor (PMLSM). The mathematical model of the PMLSM vector control system is established based on the basic structure and operation mechanism of PMLSM. Then, a speed regulator based on predictive function control (PFC) is designed to improve the speed tracking performance of the PMLSM drive system. The state and disturbance of the PMLSM system estimated by the extended state observer (ESO) transferred to the PMLSM drive system, and the robustness of the drive system will be improved. Comparative simulation and experiment results show that the proposed method has better speed tracking performance and disturbance rejection property.

This study addresses the problems of passivity analysis and disturbance observer‐based adaptive integral sliding mode control (ISMC) for uncertain singularly perturbed systems (SPSs) with input non‐linearity. Firstly, the passivity condition enabling system exponentially stable is presented in terms of linear matrix inequalities (LMIs). Secondly, a singular perturbation parameter ‐dependent disturbance observer is constructed, and the estimate is incorporated in the design of the adaptive ISMC with the reachability condition guaranteed. Then, a set of LMIs are obtained to determine the controller gain of the ISMC, and an ‐bound estimation approach is derived, such that the closed‐loop SPSs are passive and exponentially stable. Compared with the existing results, the proposed approaches have less conservatism because of adopting a more general storage function, which leads to a superior transient performance and a bigger ‐bound. Finally, the advantages and effectiveness of the proposed methods are demonstrated by three examples.