WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 13, 2014
Asymptotic Properties of Zero Dynamics of Multivariable Sampled-Data Models with Time Delay
Authors: , , ,
Abstract: It is well-known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limit the achievable control performance when controlling a system. When a continuous-time multivariable system with at least one of relative degrees greater than two is discretized in the case of the time delay and a zero-order hold (ZOH) assumption, at least one zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods. Thus, attention is here focused on continuous-time multivariable systems with time delay, and some of the relative degrees are one and the rest are two. This paper investigates the asymptotic properties of zero dynamics for the sampled-data models corresponding to the continuous-time multivariable systems mentioned above, and further derives an approximate expression of the zero dynamics in the form of a power series expansion up to the first order term of sampling period. Meanwhile, the condition for obtaining stable zero dynamics for sufficiently small sampling periods is also presented. The ideas presented here generalize well-known results from the delay-free multivariable control system to the time-delay case.
Search Articles
Keywords: Discrete-time model, Zero dynamics, Zero-order hold, Time discretization, Taylor method, Time delay, Asymptotic properties, Stability conditions
Pages: 23-32
WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 13, 2014, Art. #3