A two-degree-of-freedom modified Smith predictor for teaching-friendly control of unstable systems with time delay

This paper presents a two-degree-of-freedom modified Smith predictor scheme designed to control unstable second-order processes with time delay, aimed at simplifying control tuning for educational and practical applications. The proposed control structure consists of a PID controller, a PD controller, and a lead/lag filter. The PID controller handles set-point tracking, whereas both controllers impact disturbance rejection. Each controller is designed using the pole placement approach, offering a tuning parameter to balance performance and robustness. In addition, a low-pass filter enhances the set-point response by reducing noise and preventing high-frequency oscillations. The control objectives are appropriate set-point tracking and disturbance rejection, smooth control actions, and enhanced robustness against model uncertainties. Although optimizing all conflicting objectives simultaneously is inherently challenging due to the multi-objective nature of the problem, the proposed approach effectively balances performance and robustness, demonstrating a well-rounded and practical solution. Simulation results confirm that the proposed control technique significantly outperforms recent methods in terms of performance-robustness trade-off. Future research will explore industrial applications, extend the approach to higher-order unstable systems with time delay, and investigate adaptive control and machine learning techniques for real-time tuning. The development of user-friendly software tools and analysis of energy efficiency and applicability to multivariable systems will also be examined.