Sliding mode control of coupled tanks using conditional integrators

This paper is on set point regulation of the liquid level in coupled tanks, using continuous sliding mode control (SMC) with integral action. The integrator action occurs only conditionally inside the boundary layer. This "conditional integrator" (CI) design results in improved transient performance over conventional SMC with integral action. It also retains the robustness to uncertain system parameters and disturbances that ideal SMC exhibits, but without control chattering, which is important, because chattering can cause valve wear and tear. We consider two cases: (i) a SISO system with 2 tanks, and (ii) a MIMO system of quadruple tanks. Our controller happens to be a saturated PID controller with anti-windup structure in the SISO case, and 2 decentralized PI controllers in the MIMO case. This is of particular significance because while the application of nonlinear control strategies such as feedback linearization, adaptive/neural control and nonlinear model predictive control has reached considerable maturity for process systems, industrial practice has traditionally relied on PI/PID controllers. Simulation results show that good tracking performance is achieved, in spite of disturbances and unmodeled dynamics.