A Linear Quadratic Regulator for Liquid Level Control of Quadruple-Tank System
摘要
Owing to its nonlinear and multivariable characteristics, the quadruple-tank system is a key testbed for advanced control strategies. This paper proposes an optimized liquid-level control approach that combines linear quadratic regulator (LQR) and proportional-integral (PI) control. The system is modeled using mass conservation and Bernoulli’s principle, then linearized around the equilibrium point to derive the state-space form. An LQR controller is designed for improved dynamic response, whereas a PI controller ensures zero steady-state error and more decisive disturbance rejection. The continuous-time model is discretised to meet engineering requirements, and the performance of forward Euler, backward Euler, and Tustin methods is evaluated under various sampling times, with the Tustin method demonstrating superior stability even at larger intervals, highlighting its potential for resource-constrained industrial applications. Simulation results show that the proposed LQR+PI strategy offers fast response, high steady-state accuracy, and strong resistance to integral saturation, providing both theoretical and practical guidance for efficient quadruple-tank control.