Memory-Based Integral Sliding-Mode Control for T-S Fuzzy Systems With PMSM via Disturbance Observer

Stabilization analysis of fractional-order nonlinear permanent magnet synchronous motor model via interval type-2 fuzzy memory-based fault-tolerant control scheme

The main objective of this study is to improve the convergence rate performance and analyze the stability properties of the FOPMSM model considering the load-torque external disturbances and actuator faults. Due to the complex nonlinearity, the presented FONPMSM model in the d-q frame is approximated by an IT-2 T-S fuzzy modeling technique. Besides, the fuzzy memory-based FTC is designed to eliminate the typical characteristics of chaotic behaviors and stabilize the proposed nonlinear model even if load torque disturbances, actuator faults in the controller, and time delays occur. Further, by employing the fractional order-based fuzzy LKF, some sufficient conditions are carried out in terms of LMIs to guarantee the asymptotic stability conditions, and simultaneously, disturbance reduction is confirmed. And then, the desired control gain matrices are determined from solvable LMIs, which can help to enhance the system stability performance. Finally, the numerical simulation of T-S fuzzy-based FOPMSM model is given to validate the applicability and efficiency of the proposed controller.

Model predictive and compensated ADRC for permanent magnet synchronous linear motors

Traditional linear active disturbance rejection control (LADRC) may have difficulty to achieve a rapid precise disturbance rejection for a permanent magnet synchronous linear motor (PMSLM). By making use of model information, a model predictive and compensated LADRC (MPLADRC) method is proposed in this paper. In this method, a model compensated extended state observer (MESO) is designed to transform the controlled object into an established mathematical model through total disturbance compensation. Meanwhile, considering the delay problem of MESO, a phase advance module is designed to improve the estimation speed of MESO for system disturbance and state, thus the MESO can rapidly compensate various uncertainty disturbances to the controlled object in real time. The model predictive controller (MPC) is then designed based on the mathematical model, and its optimal control law is then obtained through a quadratic objective function to further suppress the disturbance unobserved by the designed MESO. The proposed method can thus realize a dual-degree-of-freedom disturbance rejection through the MESO and MPC. The simulation and experimental results validate the effectiveness of the proposed MPLADRC in rapid anti-disturbance and fast positioning for the motion control of the PMSLM.

Adaptive Neural Network Control Using Nonlinear Information Gain for Permanent Magnet Synchronous Motors

In this study, an adaptive neural network (NN) control using nonlinear information (NI) gain for permanent magnet synchronous motors (PMSMs) is proposed to improve control and estimation performance. The proposed method consists of a nonlinear controller, a three-layer NN approximator, and NI gain. The nonlinear controller is designed via a backstepping procedure for position tracking. The commutation scheme is designed to implement the PMSM control without the direct-quadrature (DQ) transform. The three-layer NN approximator is designed to estimate the unknown complex function generated by the recursive backstepping process. The NI gains are designed to enhance the control and estimation performance according to the increased tracking errors owing to the load torque and the desired position variations. All of signals in the closed-loop system guarantee the semiglobal uniformly ultimately boundness (UUB) using the Lyapunov stability theorem and the input-to-state stability (ISS) property. The performance of the proposed method was validated by experiments performed using a PMSM testbed.

Non-Fragile Observer-Based Adaptive Integral Sliding Mode Control for a Class of T-S Fuzzy Descriptor Systems With Unmeasurable Premise Variables

The issue of non-fragile observer-based adaptive integral sliding mode control for a class of Takagi–Sugeno (T-S) fuzzy descriptor systems with uncertainties and unmeasurable premise variables is investigated. General nonlinear systems are represented by nonlinear T-S fuzzy descriptor models, because premise variables depend on unmeasurable system states and fuzzy models have different derivative matrices. By introducing the system state derivative as an auxiliary state vector, original fuzzy descriptor systems are transformed into augmented systems for which system properties remain the same. First, a novel integral sliding surface, which includes estimated states of the sliding mode observer and controller gain matrices, is designed to obtain estimation error dynamics and sliding mode dynamics. Then, some sufficient linear matrix inequality (LMI) conditions for designing the observer and the controller gains are derived using the appropriate fuzzy Lyapunov functions and Lyapunov theory. This approach yields asymptotically stable sliding mode dynamics. Corresponding auxiliary variables are introduced, and the Finsler's lemma is employed to eliminate coupling of controller gain matrices, observer gain matrices, Lyapunov function matrices, and/or observer gain perturbations. An observer-based integral sliding mode control strategy is obtained to assure that reachability conditions are satisfied. Moreover, a non-fragile observer and a non-fragile adaptive controller are developed to compensate for system uncertainties and perturbations in both the observer and the controller. Finally, example results are presented to illustrate the effectiveness and merits of the proposed method.

Finite-Time L2-Gain Asynchronous Control for Continuous-Time Positive Hidden Markov Jump Systems via T-S Fuzzy Model Approach

This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L₂ performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.