Additive Mixed Sensitivity Design of PID Controllers for Continuous-Time System with Uncertain Time-Delay

Abstract

This paper presents an algorithm for all achievable coefficients of Proportional Integral Derivative (PID) controllers in an integral-derivative plane that stabilizes and satisfies additive mixed sensitivity constraint with an uncertain time delay for a continuous-time system. This algorithm solves the singularity problem of designing PID controllers in the integral and derivative plane and estimates achievable ranges of proportional gain of the PID controllers. A numerical cascaded ball and beam with unity feedback control of an SRV-DC motor and uncertain communication time delays in the system process demonstrate the application of this methodology. In this application, the additive weight bounds the additive errors for the cascaded ball and beam and the closed-loop SRV-DC motor system transfer function with the internal communication time delays