Designing a double-loop observer to control a single-link manipulator under uncertainty

A single-link manipulator with an electrical actuator is considered, and a dynamic feedback control is designed for tracking a given reference signal of its angular position. The problem statement includes the following assumptions: the output (controlled) variable is not measured; the sensors are located only on the electrical drive; the mechanical subsystem has exogenous and parametric disturbances. Under the smooth disturbances, a discontinuous control law is formed in terms of the canonical input-output system written in the tracking error. For implementing this law, a double-loop observer with piecewise linear corrections is developed. In the first loop, the controlled variable is restored using an observer of the electrical subsystem. This variable, together with the reference signal, serves to design corrections in the second loop. The second observer is a replica of the virtual input-output system. It restores mixed variables–functions of the state variables, the exogenous actions, and their derivatives–to form the feedback law. The order of the observers in each loop is reduced by discarding the dynamics of the estimated variables, treated as bounded perturbations in the observation problem. A tuning procedure is proposed that allows estimating the unmeasured endogenous and exogenous signals with a required accuracy in a given time under an additive parasitic signal in the corrections. The simulation results are presented.