Feedback Controller Design for the Four-Tank Process using Dissipative Hamiltonian Realization

Abstract

This paper considers the problem of stabilizing the quadruple-tank process using an approximate dissipative Hamiltonian realization. The proposed approach consists in canceling by feedback the deviation of the system from a Hamiltonian system. First, we obtain a characteristic one-form for the system by taking the interior product of a non vanishing two-form with respect to the controlled vector field. We then construct a homotopy operator on a star-shaped region centered at a desired equilibrium point. The dynamics of the system is then decomposed into an exact part and an anti-exact one. The exact part is generated by a potential, hence stability of this part is guaranteed using the generating potential as a Lyapunov function. The stabilizing feedback controller is designed by canceling the anti-exact part of the characteristic one-form. Application of the resulting controller is illustrated by numerical simulations.