On Global Regulatability of Robot Manipulators by Classical PID

Abstract

This paper studies a class of uncertain multi-input multi-output (MIMO) nonlinear systems using extended PID (EPID) control. We focus on systems possessing a well-defined vector relative degree whose components may vary across channels, a setting that received limited attention in the existing literature on PID-type control. We develop a channel-wise EPID controller, where each control input is constructed from the proportional, integral, and derivative terms of the corresponding tracking error, and the highest derivative order is selected according to the relative degree of that channel. Under suitable growth conditions on the unknown nonlinearities, we construct an admissible set of EPID parameters specified by prescribed initial-state bounds, the uncertainties and the reference signal. We show that any parameter choice from this set guarantees semiglobal stability of the closed-loop system and achieves the desired setpoint regulation. These results indicate that the EPID parameters can be designed independently for each channel, justifying the common engineering practice of channel-by-channel tuning in strongly coupled and uncertain MIMO systems, including flight control systems.