離散時間線性時延系統之可控制性與可觀察性分析及軌跡追蹤控制器設計

On the Controllability and Observability of Discrete-time Linear Time-delay Systems and Trajectory Tracking Controller Design

劉淵銘(Yuan-Ming Liu)

指導教授 ： 馮蟻剛

國立臺灣大學/電機資訊學院/電機工程學研究所/博士(2013年)

https://doi.org/10.6342/NTU.2013.02977

摘要

本論文主要針對離散時間線性時延系統之可控制性與可觀察性分析及軌跡追蹤控制器設計。首先，對於同時具有多個狀態延遲及輸入延遲之離散時間線性時延系統提出較完整的可控制性及可觀察性定義，此新定義考慮了時延系統的完整狀態概念，且可用於判斷極點置放控制器及估測器的存在性。基於此新定義，本論文推導出用於判別系統的可控制性與可觀察性之充分必要準則，此準則除可判別系統的可控制性與可觀察性，更可分析出不可控制系統或不可觀察系統之不可控制極點及不可觀察極點，用於進一步判斷系統的可穩定性及可觀測性。本論文更對所提出之可控制性與可觀察性探討其之間之對偶性。另外，本論文亦對具輸入延遲系統發展預估式強健軌跡追蹤控制器，主要採用基於模型之預估式動態回授線性化控制器，並應用於具時變延遲及隨機資料封包遺失之網路控制系統軌跡追蹤控制，以及採用基於估測器之預估式動態回授線性化控制器，並應用於具非時變輸入延遲系統之軌跡追蹤控制。此二類預估式強健控制器能有效的補償系統動態及輸入延遲，使系統之追蹤誤差達到漸近穩定，並對有界時變參數不確定性具備一定之強健性。

關鍵字

時間延遲 ； 可控制性 ； 可觀察性 ； 網路控制系統 ； 預估控制 ； 強健軌跡追蹤

並列摘要

This dissertation studies 1) the controllability and observability of discrete-time linear time-delay systems and 2) the predictive tracking control of a class of discrete-time linear systems with an input delay. In the first part, focus is on the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observa- bility, which imply the stabilizability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. In the second part, the robust trajectory tracking control problem of discrete-time networked control systems with time-varying input delay and a time-invariant input delay are handled, based on model-based predictor and observer-based predictor, respectively. The dynamic predictive feedback linearization controller is adopted to compensate the system dynamics and input delay, so that the system output can perfectly track the desired trajectory when uncertainties are absent. Tracking errors caused by the time-varying parameter uncertainties are suppressed as much as possible. Finally, the usefulness and effectiveness of the results from both parts are illustrated by numerical examples.

並列關鍵字

time-delay ； controllability ； observability ； networked control systems ； predictive control ； robust tracking

參考文獻

[1] E.-K. Boukas and Z.-K. Liu, Deterministic and Stochastic Time Delay Systems, Birkhauser, Boston, 2002.

[4] G.-S. Park, H.-L. Choi, and J.-T. Lim, “On stability of linear time-delay systems with multiple delays”, International Journal of Systems Science, Vol. 39, no. 8, pp. 839-852, 2008.

[5] H. Shao, “New delay-dependent stability criteria for systems with interval delay”, Automatica, Vol. 45, no. 3, pp. 744-749, 2009.

[6] W. Zhang, M.S. Branicky, and S.M. Philips, “Stability of networked control systems”, IEEE Control Syst. Mag., Vol, 21, no. 1, pp. 84-99, 2001.

[7] W.-A. Zhang, L. Yu and S. Yin, “A switched system approach to control of networked control systems with time-varying delays”, J. Franklin Institute, Vol. 348, no. 2, pp. 165-178, 2011.