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Analysis of Control Systems in State Space

2009 Lecture Side. January 2009. Lecture by. Analysis of Control Systems in State Space. Chapter Eleven week2. Control Engineering. Review Exercise. จงแปลง Transfer Function ให้อยู่ในรูปบัญญัติ ( Controllable และ Jordan Canonical Form ) ?. Control Engineering.

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Analysis of Control Systems in State Space

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  1. 2009 Lecture Side January 2009 Lecture by Analysis of Control Systems in State Space Chapter Eleven week2 Control Engineering

  2. Review Exercise จงแปลง Transfer Function ให้อยู่ในรูปบัญญัติ ( Controllable และ Jordan Canonical Form ) ? Control Engineering 2009 Subject Name Automotive Automatic Control

  3. Solving the time-invariant state equation review the solution of the scalar differential equation by assume a solution x(t) of the form Als; t = 0 : Aerospace Engineering 2009 Subject Name Aircraft Materials

  4. Solving the time-invariant state equation (2) now solve the vector-matrix differential equation assume that the solution in the form of vector power series in t, also, Aerospace Engineering 2009 Subject Name Aircraft Materials

  5. Solving the time-invariant state equation (3) t = 0; Aerospace Engineering 2009 Subject Name Aircraft Materials

  6. Laplace Transform Approach to the Solution of Homogeneous State Equation Take Laplace transform Take inverse Laplace transform Control Engineering 2009 Subject Name Automotive Automatic Control

  7. Laplace Transform Approach to the Solution of Homogeneous State Equation (2) Control Engineering 2009 Subject Name Automotive Automatic Control

  8. State - Transition Matrix Control Engineering 2009 Subject Name Automotive Automatic Control

  9. Example Control Engineering 2009 Subject Name Automotive Automatic Control

  10. Exercise 1 Find x1(t) , x2(t) The initial condition Control Engineering 2009 Subject Name Automotive Automatic Control

  11. Exercise 1 (Solution) Control Engineering 2009 Subject Name Automotive Automatic Control

  12. Solution of Nonhomogeneous State Equation Control Engineering 2009 Subject Name Automotive Automatic Control

  13. Solution of Nonhomogeneous State Equation (2) Control Engineering 2009 Subject Name Automotive Automatic Control

  14. Solution of Nonhomogeneous State Equation (3) Control Engineering 2009 Subject Name Automotive Automatic Control

  15. Example 2 Control Engineering 2009 Subject Name Automotive Automatic Control

  16. Exercise 2 Find x1(t) , x2(t) The initial condition Input is Unit Step Control Engineering 2009 Subject Name Automotive Automatic Control

  17. Exercise 2 (Solution) Control Engineering 2009 Subject Name Automotive Automatic Control

  18. Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control

  19. Matrix Exponential eAt Method 1 : Solution Control Engineering 2009 Subject Name Automotive Automatic Control

  20. Example 3 Control Engineering 2009 Subject Name Automotive Automatic Control

  21. Example 3 Control Engineering 2009 Subject Name Automotive Automatic Control

  22. Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control

  23. Matrix Exponential eAt Control Engineering 2009 Subject Name Automotive Automatic Control

  24. Example 4 Control Engineering 2009 Subject Name Automotive Automatic Control

  25. Exercise 4 ( โดยการหา state-transition matrix ใช้ทั้ง 3 วิธี) Control Engineering 2009 Subject Name Automotive Automatic Control

  26. Exercise 4 Control Engineering 2009 Subject Name Automotive Automatic Control

  27. Laplace Transform Control Engineering 2009 Subject Name Automotive Automatic Control

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