1. Modern Control TheoryLecture 1, written by Xiaodong Zhao1 Modern Control Theory Syllabus Course Coordinator: Dr. Xiaodong Zhao – Room: Building Lab 2, south 506 – Tel: 86919131 – Email: xdzhao@hziee.edu.cn Lecture: 2 hours per week Reference Books: Xie Keming, Modern Control, Beijing University of Technology, 2000. Liu Bao, Modern Control, China Machine Press, 1997. Grading: Final Exam: 50% Midterm Exam: 20% Homework: 15% Attendance: 15% Homework: 4~6 problems per chapter ftp://210.32.34.81

2. Modern Control TheoryLecture 1, written by Xiaodong Zhao2 Enjoy your study Enjoy your life!

3. Modern Control TheoryLecture 1, written by Xiaodong Zhao3 Contents Chapter 1: State Space Description Chapter 2: Linear System Analysis Chapter 3: Controllability & Observability Chapter 4 Stability of Control System Chapter 5 State Feedback and State Observer

4. Modern Control TheoryLecture 1, written by Xiaodong Zhao4 Chapter 1: State Space Description 1.1 Basic Concepts State: is a set of numbers such that the knowledge of these numbers and the input functions will, with the equations describing the dynamics, provide the future state and output. State Variables: variables that determine the future behavior of a system when the present state and the excitation signals are known. State Vector: the column matrix consisting all n state variables State Space: the n dimensional space constructed by the state variables

5. Modern Control TheoryLecture 1, written by Xiaodong Zhao5 1.2 State Space Description State differential equation Output equation Compact notation

6. Modern Control TheoryLecture 1, written by Xiaodong Zhao6 Example 1: Consider the RLC circuit Input: Output: Energy stored in capacitor & inductor Utilizing Kirchhoff’s law: Let, we get

7. Modern Control TheoryLecture 1, written by Xiaodong Zhao7 Note that, we have Let, we get  The state variables are not a unique set, the number of state variables is equal to the number of independent energy-storage elements.

8. Modern Control TheoryLecture 1, written by Xiaodong Zhao8 Different types of description Nonlinear time variant system Nonlinear time invariant system Linear time variant system Linear time invariant system

9. Modern Control TheoryLecture 1, written by Xiaodong Zhao9 Linear time variant system block diagram Linear time variant system flow graph

10. Modern Control TheoryLecture 1, written by Xiaodong Zhao10 Simulation structure Example 2: Consider the following system

11. Modern Control TheoryLecture 1, written by Xiaodong Zhao11 1.3 State Variables Modeling Example 3: Consider the RLC circuit Inputs: Output: State variables: Utilizing Kirchhoff’s law:

12. Modern Control TheoryLecture 1, written by Xiaodong Zhao12 We can get Or in matrix form

13. Modern Control TheoryLecture 1, written by Xiaodong Zhao13 Example 4: Consider the DC motor system Inputs: armature voltage & load torque Output: angular velocity Energy stored: inductor & rotary inertia State variables: Where are constants of the DC motor

14. Modern Control TheoryLecture 1, written by Xiaodong Zhao14 We can get Or in matrix form