1. Analysis of Control Systems in State Space
2009 Lecture Side
January 2009
Lecture by
Suradet Tantrairatn
Instructor and Researcher
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
Month 200X

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
Month 200X

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
Month 200X

5. Solving the time-invariant state equation (3)
Aerospace
Engineering
2009 Subject Name Aircraft Materials
Month 200X

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
Month 200X

7. Laplace Transform Approach to the Solution of Homogeneous State Equation (2)
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

8. State - Transition Matrix
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

9. Example Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

10. Exercise 1 Find x1(t) , x2(t) The initial condition Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

11. Exercise 1 (Solution) Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

12. Solution of Nonhomogeneous State Equation
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

13. Solution of Nonhomogeneous State Equation (2)
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

14. Solution of Nonhomogeneous State Equation (3)
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

15. Example 2 Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

16. Exercise 2 Find x1(t) , x2(t) The initial condition Input is Unit Step
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

17. Exercise 2 (Solution) Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

18. Matrix Exponential eAt
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

19. Matrix Exponential eAt
Method 1 : Solution
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

20. Example 3 Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

21. Example 3 Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

22. Matrix Exponential eAt
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

23. Matrix Exponential eAt
Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

24. Example 4 Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

25. Exercise 4 ( โดยการหา state-transition matrix ใช้ทั้ง 3 วิธี) Control
Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

26. Exercise 4 Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X

27. Laplace Transform Control Engineering
2009 Subject Name Automotive Automatic Control
Month 200X