線性多變數系統之塊解耦控制

Abstract

本論文針對線性多變數系統之單位回授控制架構，於塊解耦控制的目標下，探討塊解耦控制器存在之條件，並設計塊解耦控制器的參數化解及塊解耦前置補償器。在既有文獻上提到，若受控系統的不穩定極點與零點是不相同的假設下，此單位回授控制系統一定存在塊解耦控制器。因此本論文提出若受控系統擁有相同的不穩定極點與零點發生時，如何判定塊解耦控制器存在。若受控系統的相同不穩定極點與零點是單一的情況下，存在塊解耦控制器的判定是相當容易驗證。若受控系統沒有相同的不穩定極點與零點時，本論文設計了受控系統所有塊解耦控制器的參數化解。塊解耦控制器的另一種設計方法，是先設計塊解耦前置補償器，再設計每個塊組的回授控制器。塊解耦前置補償器與受控系統串接後的新系統是塊對角化系統，且塊解耦前置補償器與受控系統間不能發生不穩定極點及零點相消的狀況。因為塊解耦前置補償器把受控系統分解成數個維數較小的子系統，能使大維數穩定控制器的複雜度減少。本論文除了利用塊解耦控制器的參數化解，用來設計塊解耦控制的最佳加權靈敏函數的問題，並利用塊解耦前置補償器來分析塊解耦控制的代價。

In this thesis, we consider the unity-feedback configuration for the linear multivariable systems. We discuss the conditions for existence of block decoupling controllers and design the parameterization of all block decoupling controllers and propose block decoupling precompensators. Under the assumption of the plant without unstable pole-zero coincidence, the literature proposed that the unity-feedback system exists a block decoupling controller. Thus, we propose how to judge the existence of block decoupling controllers under the plant with unstable pole-zero coincidences. If the plant has simple unstable pole-zero coincidences, it is easy to verify that the plant exists a block decoupling controller. In our dissertation, we design the parameterization of all block decoupling controllers under the assumption of the plant without unstable pole-zero coincidence. Another method to design block decoupling controllers is to first design a block decoupling precompensator, then design the feedback controllers for each of the block channel. The cascade connection of the block decoupling precompensator and the plant is block diagonal, and there is no unstable pole-zero cancellation between the precompensator and the plant. Since the block decoupling precompensator separate the plant into several smaller dimension subplants, it will reduce the complexity to design large dimension stabilizable controllers. We use the parameterization of block decoupling controllers to design optimal weighted sensitivity function problems and use the block decoupling precompensator to analyze the cost of block decoupling. 2. Preliminary 2.1 System Configuration and Basic Definitions 2.2 Coprime Factorizations 3. Necessary and Sufficient Conditions for Existence of Block Decoupling Controller 3.1 Simple C+-Coincidence 3.2 Second Order C+-Coincidence 4. Parameterizations of Block Decoupling and Decoupling Controllers 4.1 Block Decoupling Case 4.2 Decoupling Case 5. Block Decoupling and Decoupling Precompensators 5.1 Design Block Decoupling Precompensators 5.2 Design Decoupling Precompensators 6. Rectangular Plant Case 6.1 Block Decoupling Controllers Designs for Rectangular Plants 6.2 Block Decoupling Precompensators Design for Rectangular Plants 7. Optimal Block Decoupling Controller Design 7.1 Optimal Decoupling and Cost of Decoupling 7.2 Optimal Block Decoupling and Cost of Block Decoupling 8. Concluding Remarks