High Performance Tracking Optimal Linear Matrix Inequality-Fractional-order PI for MIMO Processes

The simple design, tuning, and quick implementation of the PI family of controllers influence single-input, single-output (SISO) process control applications. However, with the industrial revolution, many industrial processes are now designed as multiple-input multi-output (MIMO) systems. The conventional controllers in this process produce suboptimal performance due to the system’s non-linear, interacting, and dynamic nature. A linear matrix inequality-based fractional-order PI (LMIFPI) controller is proposed to address and overcome the quadruple-tank system’s (QTS) interaction behaviour. In addition, the simulated annealing (SA) optimization algorithm is employed to determine the controller parameters using the integral square error (ISE) as the desired objective function. Experimental results indicate that the proposed controller achieved an almost 33.1652% faster settling time, a 7.651% reduction in overshoot, and a nearly 1.7% quicker rise time performance.