Setpoint Tracking-Error Control Design for Stabilization of Quadruple-Tank Process With Time Delay Using a Relaxing Port-Hamiltonian Formulation

Abstract

The nonlinearity of chemical processes primarily arises from strong interdependencies among state variables and the presence of time delays. This characteristic leads to complex dynamic behaviors such as non-minimum phase responses, posing significant challenges for control design. This study presents a novel control strategy that integrates Pade approximation of time delay with a tracking-error-based control law within a port-Hamiltonian (PH) framework. Specifically, the Pade approximation is employed to effectively handle the time delay by approximating exponential delay terms, thereby facilitating its incorporation into the control design and enhancing the robustness of the closed-loop system. Concurrently, the tracking-error-based feedback laws ensure the asymptotic convergence of system trajectories to the desired reference trajectories, even in the presence of non-minimum phase dynamics. The proposed methodology is illustrated through simulations on the quadruple-tank process - a benchmark nonlinear system with inherent time delays. Results demonstrate that the proposed control scheme successfully mitigates the adverse effects of time delay and achieves the closed-loop stabilization at the target equilibrium point.