Download presentation

1
**Time Response and State Transition Matrix**

Lecture 05 Analysis (I) Time Response and State Transition Matrix 5.1 State Transition Matrix 5.2 Modal decomposition --Diagonalization 5.3 Cayley-Hamilton Theorem Modern Control Systems

2
**Modern Control Systems**

The behavior of x(t) et y(t) : Homogeneous solution of x(t) Non-homogeneous solution of x(t) Modern Control Systems

3
**Modern Control Systems**

Homogeneous solution State transition matrix Modern Control Systems

4
**Modern Control Systems**

Properties Modern Control Systems

5
**Non-homogeneous solution**

Convolution Homogeneous Modern Control Systems

6
**Modern Control Systems**

Zero-input response Zero-state response Modern Control Systems

7
**Modern Control Systems**

Example 1 Ans: Modern Control Systems

8
**Modern Control Systems**

Using Maison’s gain formula Modern Control Systems

9
**Modern Control Systems**

How to find State transition matrix Methode 1: Methode 2: Methode 3: Cayley-Hamilton Theorem Modern Control Systems

10
**Modern Control Systems**

Methode 1: Modern Control Systems

11
**Modern Control Systems**

Method 2: Diagonalization Example 4.5 diagonal matrix Modern Control Systems

12
**Modern Control Systems**

Diagonalization via Coordinate Transformation Plant: Eigenvalue of A: Assume that all the eigenvalues of A are distinct, i.e. Then eigenvectors, are independent. Coordinate transformation matrix Modern Control Systems

13
**Modern Control Systems**

where Modern Control Systems

14
**Modern Control Systems**

New coordinate: (4.1) Solution of (4.1): The above expansion of x(t) is called modal decomposition. Hence, system asy. stable ⇔ all the eigenvales of A lie in LHP Modern Control Systems

15
**Modern Control Systems**

Example Find eigenvector Modern Control Systems

16
**Modern Control Systems**

(4.2) Solution of (4.1): Modern Control Systems

17
**Modern Control Systems**

In the case of A matrix is phase-variable form and Vandermonde matrix for phase-variable form Modern Control Systems

18
**Modern Control Systems**

Example: depend Modern Control Systems

19
**Modern Control Systems**

20
**Modern Control Systems**

Case 3: Jordan form Generalized eigenvectors Modern Control Systems

21
**Modern Control Systems**

Example: Modern Control Systems

22
**Modern Control Systems**

Cayley-Hamilton Theorem Method 3: Theorem: Every square matrix satisfies its char. equation. Given a square matrix A, Let f(λ) be the char. polynomial of A. Char. Equation: By Caley-Hamilton Theorem Modern Control Systems

23
**Modern Control Systems**

any Modern Control Systems

24
**Modern Control Systems**

Example: Modern Control Systems

25
**Modern Control Systems**

Example: Modern Control Systems

26
**Modern Control Systems**

27
**Modern Control Systems**

28
**Modern Control Systems**

29
**Modern Control Systems**

30
**Modern Control Systems**

31
**Modern Control Systems**

32
**Modern Control Systems**

Example: Modern Control Systems

33
**Modern Control Systems**

Example: Modern Control Systems

Similar presentations

Presentation is loading. Please wait....

OK

Advanced Operating Systems

Advanced Operating Systems

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on good communication skills Ppt on solar energy conservation Ppt on village life in india Ppt on metro rail in india Ppt on mammals and egg laying animals coloring Ppt on contact and noncontact force Ppt on energy giving food example Ppt on elections in india download song Ppt on section 188 of companies act 2013 Ppt on roman numerals