Transient response improvement of feedback control systems using hybrid reference control

Abstract

By means of the internal model principle, an approach to improve the performance of a stabilised closed-loop continuous time linear system based on manipulation of the reference signal is developed. A change in the reference signal is equivalent to implementing an instantaneous change via the choice of a decision vector in the state of the reference signal model, and the analysis of the proposed approach called hybrid reference control (HRC) system is then shown to be equivalent to the analysis of a linear impulsive dynamical system. Conditions for asymptotic stability and convergence of the output tracking error for a HRC system are expressed in term of conditions on the decision vectors. Conditions are then derived which guarantee that the HRC system leads to an improved transient performance compared to a conventional closed-loop control system. In particular, it is shown how decision vectors are chosen so that a HRC system results in a deadbeat response.

Keywords:

• hybrid systems
• deadbeat response
• linear impulsive systems
• internal model principle
• impulsive controllability
• Lyapunov stability