Design of Adaptive Periodic Event-Triggered Mechanism-Based EID with MRC Based on PSO Algorithm for T-S Fuzzy Systems

This article discusses issues with disturbance rejection and periodic signal tracking in a specific type of time-varying delay nonlinear systems. The proposed approach, known as the modified repetitive controller (MRC) scheme, utilizes an equivalent-input-disturbance (EID) estimator to enhance the system’s performance. It effectively improves the system’s ability to reject both aperiodic and periodic unknown disturbances, while also achieving accurate tracking of periodic reference signals. A T-S fuzzy model has been used to roughly represent the system nonlinearity. Additionally, a fuzzy state observer based on an adaptive periodic event-triggered mechanism (APETM-FSO) has been used to decrease data transfer, energy use, and communication resource utilization. The APETM is able to identify the occurrence of an event by surpassing a predetermined threshold with the error signal, thanks to the designed adaptive event triggering condition. Transmission of the current data only takes place when the event happens, while data can remain unchanged using a zero-order hold if the event does not occur. In addition to, controller parameters are tuned using a particle swarm optimization (PSO) approach. Hence, T-S fuzzy model-based EID, MRC, FSO-APETM, and PSO construct the overall system. In order to ensure the asymptotic stability of the entire system in the presence of unknown disturbances, the article establishes sufficient conditions using the Lyapunov–Krasovskii functional stability theory and linear matrix inequalities (LMIs). These conditions are derived to guarantee the desired stability properties of the system. To demonstrate the effectiveness and feasibility of the proposed scheme, simulation results with comparative study are presented. The proposed controller has achieved better tracking performance with less tracking error with maximum value of 0.05. In addition, the suggested APETM has minimum triggering times which is 34 as comparison with PETM which is 40 times, and hence, APETM is more effective than PETM in reducing data transmission frequency and using less communication resources overall.