Question

STATE SPACE SYSTEMS USING MATLAB

Problem 2: Obtain the unit-ramp response of the system defined as follows lu. y=[1 0] |xi Show both the input ramp, and the system output response curve on a single graph.

Answer 1

Transfer function of above stste space matrix is

Matlab program

A=[0 2;-3 -3];

B=[0;2];

C=[1 0];

D=[0];

[num,den]=ss2tf(A,B,C,D)

G(s)=(4)÷(s²+3s+6)

Matlab progrqm to plot response of given system

Response can be obtained by dividing the transfer function by s and

Taking step response

G(s) will become

G(s)=(4)÷(s³+3s²+6s)

Comment for step reaonse is

G=(4/(s³+3s²+6s))

step (G)

Program for unit ramp input is

R(s)=1÷s²

^{and finally it will be}

r=1÷s³

^{step (r)}

^{above comment will get the unit ramp response}

hold comment used to hold 2 functions together