Designing a Robust Memory State Feedback Controller Leveraging LMI on DC Motor Under Time Delays and Norm-Bounded Disturbances

This paper investigates the performance of a predictor-based  H_∞controller applied to a first-order DC motor system under significant input-time delays. Alongside the proposed predictor-based H_∞ controller, an LQR controller has been implemented to serve as a benchmark for effectively comparing and evaluating the performance of the proposed method. This study specifically focuses on scenarios involving time delays exceeding one second and external disturbances such as constant, sinusoidal, and stochastic disruptions. The proposed controller employs a robust memory-state feedback mechanism to ensure closed-loop stability and minimize the impact of disturbances. Using Linear Matrix Inequality (LMI) conditions, the controller compensates for input delays of up to five seconds while guaranteeing disturbance attenuation. A delay-dependent Lyapunov stability analysis is conducted to validate the proposed approach. Comprehensive simulation results and evaluations based on key performance metrics, such as settling time and overshoot, indicate that the predictor-based H_∞  controller outperforms both the open-loop configuration and the LQR controller. Notably, the proposed approach achieves a reduced overshoot, a faster transient response, and superior disturbance attenuation compared to the LQR method. Furthermore, this controller significantly enhances the overall system robustness and control precision in scenarios with prolonged delays. The predictor-based H_∞ controller suggests an innovative solution for mitigating the effects of long input delays in DC motor systems, thereby overcoming a pivotal challenge in robust control.