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Lesson 4

Linear system. Lesson 4. State space approach. State equation. Dynamic equation. Output equation. State variable. State space. r- input. p- output. D. +. +. C. B. +. -. A. Inner state variables. Motivation of state space approach. +. -. +. noise. Example 1.

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Lesson 4

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  1. Linear system Lesson 4 State space approach

  2. State equation Dynamic equation Output equation State variable State space r- input p- output Linear System by Meiling CHEN

  3. D + + C B + - A Inner state variables Linear System by Meiling CHEN

  4. Motivation of state space approach + - + noise Example 1 Transfer function BIBO stable unstable Linear System by Meiling CHEN

  5. + + + -2 + - + Example 2 BIBO stable, pole-zero cancellation Linear System by Meiling CHEN

  6. then system stable State-space description Internal behavior description Linear System by Meiling CHEN

  7. Definition: The stateof a system at time is the amount of information at that together with determines uniquely the behavior of the system for 單純從 並無法決定x在 以後的運動狀況。除非知道 與 。所以 與 是這個系統過去的歷史總結。故 與 可以作為系統的狀態。 Example M Linear System by Meiling CHEN

  8. Input 對系統的歷史總結。 Example : Capacitor electric energy Example : Inductor Magnetic energy Linear System by Meiling CHEN

  9. Remark 1:狀態的選擇通常與能量有關， 例如: Position  potential energy Velocity  Kinetic energy Remark 2:狀態的選擇必需是獨立的物理量， 例如: 實際上只有一個狀態變數 Linear System by Meiling CHEN

  10. K M2 M1 B1 B3 B2 Example Linear System by Meiling CHEN

  11. Armature circuit Field circuit Example Linear System by Meiling CHEN

  12. Linear System by Meiling CHEN

  13. Dynamical equation Transfer function Laplace transform matrix Transfer function Linear System by Meiling CHEN

  14. Example MIMO system Transfer function Linear System by Meiling CHEN

  15. + + - - Remark : the choice of states is not unique. exist a mapping Linear System by Meiling CHEN

  16. Different state equation description p is nonsingular Linear System by Meiling CHEN

  17. Definition : Two dynamical systems with are said to be equivalent. The nonsingular matrix p is called an equivalence transformation. & Theorem: two equivalent dynamical system have the same transfer function. Linear System by Meiling CHEN

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