포화 구동기를 갖는 선형 시스템의 계획 이득 H∞ 제어 = Gain scheduled H∞ control of linear systems with saturating actuators

다국어 초록 (Multilingual Abstract)

The majority of control theories is focused on linear systems, and one usually designs a control system based on these linear control theories. However, in practical applications, we frequently encounter many atypical linear terms : modeling error, disturbance, non-linearity of actuators, and time-delay in the state and so on. In general, if not considered appropriately, these atypical linear terms are frequently causative of system performance degradation and instability of control systems. The reality is that, in most cases, these terms are ignored when we design a control system, because of difficulty and/or complexity in handling these terms.
In this dissertation, we are interested in the design of control for linear systems with atypical linear terms, specially actuator saturation and time-delay in state. The dissertation consists of five sections.
In section I, motivation, background and goal of research are described.
In section II, preliminary works that are relevant to this thesis subject are presented. And major lemmas are outlined.
In section III, the design of control for linear system with saturating actuators is presented based on the concept of gain scheduling (GS) method. The basic idea of GS method is to adopt an appropriate control gain according to the staying region of states: a smaller region of states permits a larger control gain, and vice versa. This idea comes from the fact that a larger control gain gives a better performance when it is well-designed. The sub-region of states is obtained by dividing the reachable set sequently. The control gains of GS method are obtained by minimizing the gain at each sub-region while satisfying the actuator capacity. The obtained result is expressed in the form of linear matrix inequality(LMI), and the usefulness of this GS method is shown by examples compared to the static control.
In section IV, the design of gain scheduled control for time-delayed linear systems with saturating actuators is addressed. Here, the time-delay is a time-varying and its magnitude and time-derivative are bounded. Based on two Lyapunov-Krasovskii functionals(LKF), we derive a result expressed in the form of LMI. The usefulness of this result is shown by examples compared to the previous results.
Finally, in section V, the concluding remarks are presented.

목차 (Table of Contents)

• Ⅰ. 서 론 1
• 1.1 연구 배경 및 목적 1
• 1.2 연구 방법 7
• 1.3 논문 구성 8
• Ⅱ. 예비 결과 10
• 2.1 제어 및 Lyapunov의 안정성 정리 10
• 2.2 포화 구동기를 갖는 시스템 18
• 2.3 시간 지연 선형 시스템 21
• 2.4 선형 행렬 부등식 34
• Ⅲ. 포화 구동기를 갖는 선형 시스템의 계획 이득 제어기 설계 40
• 3.1 포화 구동기를 갖는 선형 시스템 40
• 3.2 문제 기술 및 예비 결과 43
• 3.3 주요 결과 50
• 3.3.1 상수-이득 제어기 설계 50
• 3.3.2 계획-이득 제어기 설계 56
• 3.4 수치 예제 60
• Ⅳ. 포화 구동기를 갖는 시간 지연 선형 시스템의 계획 이득 제어기 설계 70
• 4.1 포화 구동기를 갖는 시간 지연 선형 시스템 70
• 4.2 문제 기술 및 예비 결과 72
• 4.3 주요 결과 81
• 4.3.1 상수-이득 제어기 설계 81
• 4.3.2 계획-이득 제어기 설계 91
• 4.4 수치 예제 95
• Ⅴ. 결 론 100
• 참고문헌 102