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Lecture 02

Lecture 02. State space approach. Control system analysis and design. Step1: Modeling By physical laws By identification methods Step2: Analysis Stability, controllability and observability Step3: Control law design Classical, modern and post-modern control Step4: Analysis

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Lecture 02

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  1. Lecture 02 State space approach

  2. Control system analysis and design • Step1: Modeling • By physical laws • By identification methods • Step2: Analysis • Stability, controllability and observability • Step3: Control law design • Classical, modern and post-modern control • Step4: Analysis • Step5: Simulation • Matlab, Fortran, simulink etc…. • Step6: Implement Nonlinear Systems by Meiling CHEN 2009

  3. Dynamic system descriptions: • Differential equation : time-domain approach • Linear/Nonlinear systems • Transfer function : frequency-domain approach • Linear systems • Dynamic equation: state space approach • Linear/Nonlinear systems • Describing function : frequency-domain approach • Nonlinear systems Nonlinear Systems by Meiling CHEN 2009

  4. LTI systems: State equation Dynamic equation Output equation State variable State space r- input p- output Nonlinear Systems by Meiling CHEN 2009

  5. D + + C B + - A Inner state variables Nonlinear Systems by Meiling CHEN 2009

  6. Motivation of state space approach + - + noise Example 1 Transfer function BIBO stable unstable Nonlinear Systems by Meiling CHEN 2009

  7. + + + -2 + - + Example 2 BIBO stable, pole-zero cancellation Nonlinear Systems by Meiling CHEN 2009

  8. system stable State-space description Internal behavior description Nonlinear Systems by Meiling CHEN 2009

  9. 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 Nonlinear Systems by Meiling CHEN 2009

  10. Input 對系統的歷史總結。 Example : Capacitor electric energy Example : Inductor Magnetic energy Nonlinear Systems by Meiling CHEN 2009

  11. 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 Nonlinear Systems by Meiling CHEN 2009

  12. K M2 M1 B1 B3 B2 Example Nonlinear Systems by Meiling CHEN 2009

  13. Armature circuit Field circuit Example Nonlinear Systems by Meiling CHEN 2009

  14. Nonlinear Systems by Meiling CHEN 2009

  15. Dynamical equation Transfer function Laplace transform matrix Transfer function Nonlinear Systems by Meiling CHEN 2009

  16. Example MIMO system Transfer function Nonlinear Systems by Meiling CHEN 2009

  17. + + - - Remark : the choice of states is not unique. exist a mapping Nonlinear Systems by Meiling CHEN 2009

  18. The solution of LTI system Non-homogeneous solution Forced responses Homogeneous solution Natural responses Nonlinear Systems by Meiling CHEN 2009

  19. Nonlinear systems: LTI Dynamic equation Nonlinear Dynamic equation Nonlinear Systems by Meiling CHEN 2009

  20. m Nonlinear system example: Pendulum equation Nonlinear Systems by Meiling CHEN 2009

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