Dynamic Linearizing Feedback Design for a Single-Link Manipulator under Unmatched Disturbances

Abstract

Using the output feedback linearization method, we consider the design of a servo system for a single-link manipulator, which is elastically coupled to a gearbox shaft and controlled by a sensorless DC motor. Unlike typical problem formulations, we assume significant parametric uncertainty in the controlled plant model and the presence of external, unmatched disturbances. The output (measured and controlled) variable is the angular position of the manipulator, which, during control, tracks the reference trajectory. There is no analytical description of the reference signal; only its current value is known. The design of a tracking system is based on the equivalent canonical form of the “input – output” relationship with respect to mixed variables, which are functions of state variables, external influences, and their derivatives. A combined control law has been formalized that linearizes a closed-loop virtual “input – output” system under conditions of an uncertain control multiplier. A reduced observer with piecewise linear corrective actions in the form of nested saturators has been developed. The observer is constructed on the basis of a canonical system with an uncertain input and, based on the tracking error measurements, estimates mixed variables and generalized disturbances with a given accuracy without dynamic generators of external influences and additional expansion of the state space. It is shown that observer gain coefficients tuning can be performed using a reference Hurwitz polynomial with a large stability margin. The actual gains will be many times smaller than those of a typical observer with linear correction without saturation, which generates large spikes in estimated signals and control action at the beginning of the transient process. Numerical simulation results are presented, demonstrating the performance of the tracking system and the advantages of the developed observer compared to a typical observer with linear correction without saturation.