Control toolbox in Matlab: General Creating linear models. System - - PDF document

• Dr. –Ing. W. Wang, Dept. of Automatic Control,

SJTU Automatic Control System 1

what is Matlab? Matlab — stands for matrix laboratory

MATLAB is a software or a high-performance language for technical computing, developed by MathWorks Ltd. in USA.

Introduction to Matlab

Not required for final examination

Control toolbox in Matlab:

General Data extraction. Conversions. Model dynamics. Time-domain analysis LQR/LQG design. Time delays. Overloaded arithmetic operations. Matrix equation solvers. Creating linear models. System interconnections. Frequency-domain analysis. Classical design. Pole placement. State-space models. Model dimensions and characteristics. Demonstrations.

• Dr. –Ing. W. Wang, Dept. of Automatic Control,

SJTU Automatic Control System 2

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (

1 1 1 1 1 1 1 1

t r b dt t dr b dt t r d b dt t r d b t c a dt t dc a dt t c d a dt t c d a

m m m m m m n n n n n n

+ + + + = + + + +

− − − − − −

L L

Models of control systems in Matlab

) ( ) ( ) (

1 1 1 1 1 1

s G a s a s a a b s b s b s b s R s C

n n n m m m m

= + + + + + + + + =

− − − −

L L ) ( ) ( ) (

1 1 1 1 1 1

s G a s a s a a b s b s b s b s R s C

n n n m m m m

= + + + + + + + + =

− − − −

L L

num = [bm, bm-1, …,b1, b0] den = [an, an-1, …,a1, a0] sys = tf [num, den]

• Dr. –Ing. W. Wang, Dept. of Automatic Control,

SJTU Automatic Control System 3

Ex

) ( 1 3 2 10 6 12 6 ) ( ) (

2 3 4 2 3

s G s s s s s s s s R s C = + + + + + + + + = L

num = [6, 12, 6, 10] den = [1 2 3 1 1] sys = tf (num, den) Transfer function: 6 s^3 + 12 s^2 + 6 s + 10

• s^4 + 2 s^3 + 3 s^2 + s + 1

Input of vector , summation of two vectors Input of matrix, summation of two matrices

      =       +       = 6 5 4 3 5 4 3 2 1 1 1 1 c       =       +       = 5 3 4 2 1 1 c