Multi-objective optimal synthesis of robust control systems for plants exhibiting non-minimum phase and integrating...

The classical controller design methods, often lead to sub-optimal performance, especially when implemented for plants exhibiting complex dynamics like integrals, non-minimum phase zeros, time-delays, etc.; and the controllers synthesised using classical methods can result in poor time domain characteristics, and limited robustness. Thus, it is essential to formulate the controller synthesis methods that improve stability, dynamic performance, and robustness. Proposed design explores the synthesis of optimal and robust controllers by posing the controller synthesis as a multi-objective optimization problem; wherein objectives of peak sensitivity, minimization of integral square error and control effort, along with phase margin penalty and delay margins are considered while formulating the objective function; followed by solving it by multi-objective genetic algorithm. Following the synthesis, a set of Pareto-optimal solutions is generated; to identify the ideal controller from these solutions, K-Means clustering is applied along with the determination of the utopia point for controller selection. The work is implemented for four systems like (a) integrating system, (b) position control of DC motor, (c) non-minimum phase hydropower system and (d) coupled tank systems. The proposed controller demonstrates significant quantitative improvement of performance metrics across all systems when compared to conventional methods. Additionally, Monte Carlo simulations for the robustness analysis are included to establish the superiority of the proposed method over the conventional.