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 17 2.3 Linear State Variable Model Ax+Bu change in LINEAR combination state of presentstate andinput ·x:state vector(or simply“state") A:system matrix (or state matrix) 。B:input matrix heory

17 2.3 Linear State Variable Model   of presentstate andinput LINEAR combination state change in x  Ax Bu • x: state vector (or simply “state”) • A: system matrix (or state matrix) • B: input matrix Chapter 2

Chapter 2 18 Example:Differential Equation 3rd-order ODE 岁+3)+3少+y=u W=y 。State variable model W2 =j w3= 所7 0 0 0 3 1

18 Example: Differential Equation • 3rd-order ODE • State variable model y y y y u     3 3 1 1 2 2 3 3 0 1 0 0 0 0 1 0 1 3 3 1 w w w w u w w                                              1 2 3 w y w y w y    Chapter 2

Chapter 2 19 Example:Mass-spring-damper ·2nd-order model 。2 state equations 21=X M+Bx+Kx=F 22=X K M

19 Example: Mass-spring-damper • 2nd-order model • 2 state equations 1 2 z x z x  Mx Bx Kx F     1 1 2 2 0 1 0 1 z z F z z K B M M M                                         Chapter 2