Abstract
In this paper, the dynamic output feedback control problem of discrete-time singularly perturbed systems is considered based on the reduced-order technique. We first show that a proper but not strictly proper dynamic output feedback controller designed for the reduced-order model generally is not a stabilizing compensator for the original system, even though the fast subsystem is stable. To obtain the robustness of the dynamic output feedback controller, an auxiliary system is designed. Based on this, the design of the dynamic output feedback for the reduced-order subsystem is reduced to the simultaneous design of a static output feedback controller for the fast subsystem and a strictly proper dynamic output feedback controller for the auxiliary system, respectively. Based on the obtained results, we confirm that it is possible to generate the robustness for the proposed dynamic output feedback control. Thus, the restriction on the strict properness can be alleviated. Finally, a realistic practical example for the nuclear reactor model is provided to show the effectiveness of the obtained theoretical results.
Highlights
The problem of controller design for singularly perturbed systems has attracted the attention of many researchers for many years [1,2,3,4]
Due to the great development of information technique, the design of the feedback controller for discrete-time singularly perturbed systems has been investigated by many studies, and some important results have been obtained despite being in much fewer numbers than the continuous case [5,6,7,8,9,10,11,12,13,14,15]
In contrast to the Riccati approach, the linear matrix inequality (LMI) that arise in a system and control theory can be formulated as convex optimization problems that are amenable to compute a solution and can be solved effectively
Summary
The problem of controller design for singularly perturbed systems has attracted the attention of many researchers for many years [1,2,3,4]. We focus on the problem of designing a proper but not strictly proper dynamic output feedback controller for a class of fast sampling discrete-time singularly perturbed systems using the reduced-order model. Where x1 ∈ Rn1 and x2 ∈ Rn2 (n1 + n2 = n) denote the state vectors of the slow and fast dynamics, respectively; u ∈ Rq is the control input; y ∈ Rp is the output; the small parameter ε > 0 is positive; all matrices in system (1)-(2) are constant matrices with appropriate dimensions It is shown in [6] that this model can be obtained by the discrete-time analogue for a continuous system under the fast sampling rate. We will investigate a non-strictly proper dynamic output feedback controller for system (1)-(2)
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call