上海交通大学：《现代控制理论》课程教学资源（讲稿）Chapter 2 Mathematic Description of Systems

Chapter 2 12 Example:RLC circuit 2 state variables: capacitor voltage,vc inductor current,i T多房

12 Example: RLC circuit R L C 2 state variables: • capacitor voltage, vC • inductor current, iL Chapter 2

Chapter 2 13 Example:RLC circuit 2 circuit equations: diyvc 0=C di

13 Example: RLC circuit 2 circuit equations: 1 0 L C C L C di L v dt dv C i v dt R     R L C Chapter 2

Chapter 2 14 Example:RLC circuit 2 circuit equations:2 State equations: diLvc dt 0=C 1 dt 《】

14 Example: RLC circuit 2 circuit equations: 2 State equations: 1 1 1 L C C L C di v dt L dv i v dt C R           1 0 L C C L C di L v dt dv C i v dt R     Chapter 2

Chapter 2 15 What are "State Equations"? A set of 1st-order differential equations ontrol Theory Describe instantaneous change in state SJTU

15 What are “State Equations”? • A set of 1st-order differential equations • Describe instantaneous change in state Chapter 2

Chapter 2 16 Example:Differential Equ. 3rd-order ODE 3 state variables W=y Sntrol Tyeo 岁+3)+3)+y=u w2= w3= SJTU W1=w2 3 state equations W2=w3 m3=-州1-3w2-3w3+u

16 Example: Differential Equ. • 3rd-order ODE y y y y u     3 3 1 2 3 w y w y w y    3 state variables 1 2 2 3 3 1 2 3 3 3 w w w w w w w w u        3 state equations Chapter 2