Abstract
It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous-time systems with time delay and relative degree two. This paper analyzes the asymptotic behavior of zero dynamics for the sampled-data models corresponding to the continuous-time systems mentioned above, and further gives an approximate expression of the zero dynamics in the form of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zero dynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideas presented here generalize well-known results from the delay-free control system to time-delay case.
Highlights
It is well known that unstable zero dynamics limit the control performance that can be achieved
As you can see in these table and figures, (17) gives good approximation and the sampling zero dynamics can lie inside the unit circle for a sufficiently small sampling period by satisfying condition (36)
This paper analyzes the asymptotic behavior of zero dynamics for a discrete-time system when a continuous-time system with a time delay is explicitly discretized in the case of a zero-order hold (ZOH) and relative degree two
Summary
It is well known that unstable zero dynamics limit the control performance that can be achieved. More research for discrete zero dynamics has been shown in the past decade, and these known results present the asymptotic characterization of zero dynamics for the discretized systems without time delay [8–15]. It is important to investigate the asymptotic properties of zero dynamics in the sampled-data models corresponding to the continuous-time plants with time delay for the digital control system design. When the relative degree of a continuoustime transfer function with time delay is two, discrete zero dynamics, especially sampling zero dynamics, are located just on the unit circle, that is, in the marginal case of the stability when the sampling period tends to zero.
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