A linear matric inequality based multi-loop PI control design for coupled multivariable liquid level system.

This paper presents design and development of an optimal robust PI controller based on linear matrix inequalities for a typical industrial process control system. In this method, the design problem has been transformed into a state feedback controller design problem for an augmented uncertainty MIMO system. In this work, a dynamic decoupler is designed to handle loop interaction.  The control problem is then solved for the obtained decoupled subsystem by employing a constraint optimization approach, ensuring compliance with a defined LQ cost objective function. Simulation results verify the efficacy of the proposed controller, presenting its effectiveness in achieving both set-point accuracy and disturbance attenuation. Furthermore, the study employs disk margin analysis to ascertain safe ranges for gain and phase margin.