Digital modeling and control of multiple time-delayed systems via SVD

Abstract

Delays by controller-to-actuator and sensor-to-controller deteriorate control performance and could destabilize the overall system. In this paper, a new approximated discretization method and digital design for control systems with multiple delays is proposed. Based on a procedure for the generation of impulse response data, the multiple fractional/integer time-delayed continuous-time system is transformed to a discrete-time model with multiple integer time delays. To implement the digital modeling, the singular value decomposition (SVD) of a Hankel matrix together with a energy loss level is employed to obtain an extended discrete-time state space model. Then, the extended discrete-time state space model of the control system is reformulated as an integer time-delayed discrete-time system by computing its observable canonical form. The proposed method can closely approximate the step response of the original continuous time-delayed control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate the effectiveness of the developed method. © 2011 Springer-Verlag.