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

This paper introduces a simple and effective method for selecting the maximum feedback gains in PD-type 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 closed-loop system with high stability and a dynamic response with near-minimum settling time. Our approach is unique in that it simultaneously possesses: (1) a model of real-world performance-limiting factors (i.e., filtering and delay), (2) the ability to meet performance and stability criteria, and (3) the simplicity of a single closed-form expression. A central focus of our approach is the characterization of system stability through exhaustive searches of the feedback parameter space. Using this search-based 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 closed-form 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 real-world actuators with widely differing system properties and show that our method successfully produces the maximum achievable nonoscillating impedance response.