MIMO Control of an Interacting Two-Tank System: A Comparative Study of PID and MPC via Chirp-Based Frequency-Domain System Identification

Abstract

Effective control of interacting multiple-input-multiple-output (MIMO) systems is critical in many industrial applications since stable flow and level regulation affect process safety and efficiency. A commonly encountered challenge in such systems is the coupling between inputs and outputs, which complicates controller design and tuning. This study addresses the control of an interacting two-tank system by comparing the performance of conventional Proportional-Integral-Derivative (PID) controllers with Model Predictive Control (MPC). The main objective of the study is to evaluate the suitability and effectiveness of MPC in managing coupled dynamics, actuator constraints, and setpoint tracking, in contrast to classical PID controllers. The system was identified using frequency-domain techniques, where chirp signals were injected into each input, and the resulting output responses were processed using the Discrete Fourier Transform (DFT) to estimate transfer function models. PID controllers were designed using the root locus method, while MPC was implemented based on a discrete-time state-space model. Simulation results showed that while PID controllers performed acceptably in single-loop configurations, they suffered from excessive overshoot (up to 187%) and a prolonged settling time of 53 seconds when applied to the full MIMO system, despite exhibiting 0 steady-state error. More importantly, the actuator produced an impractically high flowrate of 2.7×10⁴ L/min. In contrast, MPC achieved faster settling times (under 23 seconds) and eliminated overshoot entirely (0%). Also, it limited its actuator output to a feasible flowrate of 25 L/min. These findings suggest that MPC provides a more robust and practical solution for controlling interacting MIMO systems.