A Closed Form Solution for Selecting Maximum Critically Damped Actuator Impedance Parameters

Abstract

This paper introduces a simple and effective method for selecting the maximum feedback gains in PDtype controllers applied to actuators where feedback delay and derivative signal filtering are present. The method provides the maximum feedback parameters that satisfy a phase margin criteria, producing a closedloop system with high stability and a dynamic response with nearminimum settling time. Our approach is unique in that it simultaneously possesses: (1) a model of realworld performancelimiting factors (i.e., filtering and delay), (2) the ability to meet performance and stability criteria, and (3) the simplicity of a single closedform expression. A central focus of our approach is the characterization of system stability through exhaustive searches of the feedback parameter space. Using this searchbased method, we locate a set of maximum feedback parameters based on a phase margin criteria. We then fit continuous equations to this data and obtain a closedform expression which matches the sampled data to within 2–4% error for the majority of the parameter space. We apply our feedback parameter selection method to two realworld actuators with widely differing system properties and show that our method successfully produces the maximum achievable nonoscillating impedance response.