Robust output regulation for Timoshenko beam equation with two inputs and two outputs

In this article, we consider two-dimensional robust output tracking for a Timoshenko beam equation where the disturbances and references are produced by a finite-dimensional exosystem. This requires at least two controls from basic output regulation theory of linear systems. The observer-based error feedback control approach is adopted in investigation through the following steps: (a) for the plant with no systematic uncertainties, choose a set of disturbances and references to obtain a nominal system; (b) for the nominal system, design an observer to realize 2-copy of the exosystem; (c) find a feedforward control for nominal system; and (d) allocate proportionally the states in feedforward control by those of the observer to obtain an observer based error feedback control also for nominal system. Since the control contains a 2-copy of the exo-system and the states of the observer are proportionally allocated in control, the problem is significantly different from SISO cases. The error feedback control is then proved to be bounded and also robust to systematic uncertainties and all disturbances and references produced from the exo-system. The numerical simulations validate the theoretical results.

Automated summary

This article discusses two-dimensional robust output tracking for a Timoshenko beam equation using an observer-based error feedback control approach to handle disturbances and references produced by an external exosystem. By following certain steps, the control problem is addressed and theoretical results are validated through numerical simulations.