Disturbance rejection in fuzzy systems based on two dimensional modified repetitive-control

Deep optimization design of 2D repetitive control systems with saturating actuators: An adaptive multi-population PSO algorithm

This paper presents an optimization design method for a two-dimensional (2D) modified repetitive control system (MRCS) with an anti-windup compensator. Using lifting technology, a 2D hybrid model of the MRCS considering actuator saturation is established to describe the control and learning of the repetitive control. A linear-matrix-inequality (LMI)-based sufficient condition is derived to ensure the stability of the MRCS. Two tuning parameters, the selection of which is critical to the system design, are used in the LMI to adjust the control and learning, and hence the reference-tracking performance. A new cost function, developed through time domain analysis, directly evaluates the control performance of the system without calculating control errors, thus reducing the optimization time. Based on this cost function, an adaptive multi-population particle swarm optimization algorithm is presented to select an optimal pair of tuning parameters in which multiple populations cooperatively search in non-intersecting search intervals. An anti-windup term is added between the low-pass filter and the time delay in the modified repetitive controller to mitigate the undesirable effect of actuator saturation on system performance and stability. Simulations and experiments on the speed control of a rotation control system demonstrate the validity of the approach.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.