Robustness of the nonlinear PI control method to ignored actuator dynamics

TL;DR

This paper investigates the robustness of nonlinear PI control against ignored actuator dynamics, showing that with fast enough actuator response and appropriate gain selection, stability and regulation are achievable.

Contribution

It demonstrates that nonlinear PI control can be robust to ignored actuator dynamics when using Nussbaum function-based gains and sufficiently fast actuators.

Findings

Global boundedness and regulation achieved under specified conditions

Validation through simulation examples

Applicable to sector bounded nonlinear systems with unknown control directions

Abstract

This note examines the robustness properties of the nonlinear PI control method to ignored actuator dynamics. It is proven that global boundedness and regulation can be achieved for sector bounded nonlinear systems with unknown control directions if the actuator dynamics are sufficiently fast and the nonlinear PI control gain is chosen from a subclass of the Nussbaum function class. Simulation examples are also presented that demonstrate the validity of our arguments.