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研究生：	彭瀛全 Peng, Ying-Chuan
論文名稱：	具輸入飽和之奇異非線性隨機混合系統狀態空間自調式控制 State-Space Self-Tuning Control for Singular Nonlinear Stochastic Hybrid Systems Containing Saturating Actuators
指導教授：	蔡聖鴻 Tsai, S. H. Jason
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2003
畢業學年度：	91
語文別：	英文
論文頁數：	84
中文關鍵詞：	狀態空間自調式控制、混沌系統、奇異系統、輸入飽和、穩態觀測器
外文關鍵詞：	Chaotic system, Singular system, Steady state observer, Input saturation, State-space selftuning control
相關次數：	點閱：85 下載：5
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一種對具輸入飽和連續時間奇異非線性自調式的最佳追蹤控制器設計方法在本論文中首次被提出。其中系統參數未知，存在脈衝模點，有可量測的雜訊，決定性的雜訊和不可得知的狀態。奇異非線性系統存在不穩定的脈衝模點，和系統輸出變化快速的非線性混沌特性，會使控制變得複雜許多。首先，為奇異非線性隨機狀態空間自調式控制建構以ARMA基礎的模型，來估測系統的狀態，並設計最佳追蹤控制器，且證明對決定性雜訊仍具良好的追蹤特性。再者，在不改變已存在的系統架構下，利用附加迴路來改善由實際限制條件下的輸入飽和現象。最後，用離線參數判別所得之擴增型常數系統矩陣來當作穩態觀測器，設計具輸入飽和限制之最佳追蹤控制器，並證明此設計的穩定性。另外，在每章節的最後將分別以例子來說明所提出之控制器的效能。

A state-space self-tuning control scheme for adaptive digital control of continuous-time singular nonlinear stochastic systems, which have unknown system parameters, measurement noises, deterministic noises, and inaccessible system states is first proposed in this thesis. The singular nonlinear system is mixed with chaos and singular system in unstable impulsive mode; therefore, it is more challenging for control. First, an adjustable auto-regressive moving average (ARMA)-based noise model with estimated states is constructed for state-space self-tuning control of singular nonlinear stochastic systems, then the optimal tracker is proposed. Under this proposed optimal tracker, the stability can also be shown for the hybrid system with the deterministic noise. Next, the conditioning dual-rate digital redesign scheme is developed, which contains a conditioning fast sampling rate digital controller for reducing the bump-transfer effects and a slow sampling rate digital redesign optimal tracker. Finally, a steady-state observer is based on some reasonable initial values for the system identification. As a result, it can be used to design an optimal tracker with saturation actuators. Illustrative examples are given to demonstrate the effectiveness of design methodologies.

Chinese Abstract…………………………………………………………………. I
Abstract…………………………………………………………………………... II
List of Figures…………………………………………………..………………... VI
Chapter
1	Introduction
1.1Introduction…………………………………………............. 1-1
1.2	Organization of the thesis……………………………………………. 1-5
2	State-Space Self-Tuning Control for Singular Nonlinear Stochastic Hybrid Systems Containing Deterministic Noise…………………………. 2-1
2.1	The Prediction-Based Digital Method.……………………………….. 2-1
2.1.1	 Analog quadratic tracker………………………………………. 2-2
2.1.2	 Derivation of the prediction-based digital controller…………2-2
2.1.3	 Derivation of the prediction-based digital observer…………..2-6
2.2	ARMAX Models for Multivariable Singular Nonlinear Stochastic Systems………………………………………………………………….2-7
2.3	State-Space Innovation Models for Singular Nonlinear Stochastic Systems………………………………………………………………...2-12
2.3.1	Continuous-time system versus discrete-time    system…………………………………………………………...2-12
2.3.2	Preliminary structures of discrete-time state-space     self-tuners……………………………………………………….2-14
2.4	Hybrid State-Space Self-Tuner for Singular Nonlinear Stochastic System…………………………………………………………………2-18
2.5	An Illustrative Example……………………………….........................2-23
3	State-Space Self-Tuning Control for Singular Nonlinear Stochastic Hybrid Systems Containing Saturating Actuators………………………..3-1
3.1	Introduction…………………………………………………………….3-1
3.2	The Prediction-Based Digital Redesign Dual-Rate Conditioning-Transfer Method……………………………………….3-4
3.2.1	Derivation of the prediction-based slow-rate digital      controller.......................................................................................3-4
3.2.2	Digitally Redesigned Fast-Rate Bump-less-Transfer   Tracker………………………………………………………….3-7
3.3	Hybrid State-Space Self-Tuner for Singular Nonlinear Stochastic System containing saturating actuators………………………………3-11
3.3.1	Dual-rate self-tuning with saturating actuators…..………….3-11
3.3.2	New self-tuning-base dual rate steady state observer ………..3-15
3.4	An Illustrative Example………………………………………………..3-17
4	Conclusions………………………………………………………………….4-1

List of Figures
Figure
2.1	(a) Original analog system with analog controller
(b) Digital control system……………………………………………………...2-5
2.2	Structure of the hybrid state-space self-tuning control ……………………….2-21
2.3	(a) The deterministic singular nonlinear system, plotted in the             space with simulation time 10 sec………………………………………… 2-26
(b) The deterministic singular system, plotted in the   space with simulation time 10 sec……………………………………………………..2-26
(c) Time domain response deterministic singular nonlinear system…………...2-26
(d) Deterministic noise input  …………………………………………...2-26
2.4	(a) The desired reference  , a periodic orbit embedded within the deterministic chaotic attractor of Chen’s system cascade singular system, plotted in the   and   space………………………..2-27
(b) The deterministic singular cascade chaotic of Chen’s system time series of the desired reference orbit  ……………………………..…………2-27
2.5	The sampling and holding period  with proper initial conditions
(a)	Trajectories of  and , , plotted in   space……………………………………………………………………..2-32
(b)	Trajectories of  and , , plotted in   space……………………………………………………………………..2-32
(c)	(d) (e) (f) (g) (h)Time series of    and , ……………2-32
(i)  Time series of  ………………………………………….2-33
2.6  The sampling and holding period  with proper initial conditions
(a)	Trajectories of  and , , plotted in   
space…………………………………………………………………...2-34
(b)	Trajectories of  and , , plotted in   
space…………………………………………………………………...2-34
(c)	(e) (f) (g) (h)Time series of    and , ……………..2-34
(i )  Time series of  ………………………………………..2-35
2.7	The sampling and holding period  with proper initial conditions
(a)	Trajectories of  and ,  , plotted in   space…………………………………………………………………...2-36
(b)	Trajectories of  and ,  , plotted in   space…………………………………………………………………...2-36
(c)	(e) (f) (g) (h)Time series of    and , …………….. 2-36
(i)   Time series of  ……………………………………….2-37
3.1	Linear conditioning from  ………………………………………...3-3
3.2	Internal model control (IMC)………………………………………………..3-3
3.3	(a) Original analog system with analog controller………………………….. 3-5
(b) Digital control system…………………………………………………..3-5
3.4	The control law of wind-up system, where   represents the upper bound of linear region of the actuator……………………………………….3-6
3.5	Desired digitally redesigned sampled-data system………………………….3-10
3.6	A fictional system……………………………………………………………3-10
3.7	(a) Structure of the hybrid state-space self-tuning control…………………..3-13
(b) Dual-rate state space self-tuning control with input saturation actuator………………………………………………………………………3-14
3.8	Dual-rate self-tuning control with input saturation actuator self-tuning-base dual rate steady state Kalman Filter…………………………………………3-17
3.9	 (a) The deterministic singular nonlinear system, plotted in the     space with simulation time 10 sec…………………………………………3-20
(b)The deterministic singular system, plotted in the   space with simulation time 10 sec……………………………………………...3-20
(c) Time domain response deterministic singular nonlinear system………...3-20
(d) Deterministic noise input  ………………………………………..3-20
3.10	 (a) The desired reference  , a periodic orbit embedded within the deterministic chaotic attractor of Chen’s system cascade singular system, plotted in the   and  space………………3-21
(b) The deterministic singular cascade chaotic of Chen’s system time series of the desired reference orbit  ……………………………………...3-21
3.11	The sampling and holding period  with proper initial conditions with input saturation actuator.
(a) Trajectories of  and  , , plotted in   space……………………………………………………………………..3-24
(b) Trajectories of  and  , , plotted in  space…………………………………………………………3-24
(c)(d) (e) (f) (g) (h)Time series of    and , ……………3-24
(i) Time series of   with input saturation actuator…………………...3-24
(j) Time series of   with input saturation actuator…………3-25
3.12	Self-tuning-Base Dual Rate Steady state Kalman Filter with the sampling and holding period  with proper initial conditions and input saturation actuator.
(a)	Trajectories of   and  ,  , plotted in   space……………………………………………………………………..3-26
(b)	Trajectories of  and  ,  , plotted in   space……………………………………………………………………..3-26
(c)	(d) (e) (f) (g) (h)Time series of   and  , …………...3-26
(i) Time series of   with input saturation actuator……………………3-27
(j) Time series of   with input saturation actuator………….	3-27
                                    

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