Robust PI Passivity-based Control of Nonlinear Systems: Application to Port-Hamiltonian Systems and Temperature Regulation

TL;DR

This paper presents a passivity-based method for designing globally stable PI controllers for certain nonlinear systems, including port-Hamiltonian systems and thermal processes, using minimal system information.

Contribution

It identifies a class of nonlinear systems where a globally stable PI controller can be designed with limited knowledge, leveraging passivity theory.

Findings

Successfully designed a globally stable PI controller for port-Hamiltonian systems.

Extended the control approach to thermal processes.

Discussed challenges in adaptive PI controller design.

Abstract

This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated coordinates. The construction of the PI is done invoking passivity theory. The difficulties encountered in the design of adaptive PI controllers with the existing theoretical tools are also discussed. As an illustration of the theory, we consider port--Hamiltonian systems and a class of thermal processes.