Question

1. Build a block diagram representation of this model in Simulink, including integration and

2. summation blocks.

3. Apply a step input to the system and plot the output y(t) for 5 seconds. Assume initial conditions for all states are 0.

4. Discuss the system step response: based on visual observation, is this system stable or unstable? Based on the plot, why?

5. Use the Matlab command ’ss2tf’ to get a transfer function representation for the system.

6. Determine the poles of the system (consider using ’roots’ on the denominator coefficients resulting from using the ’ss2tf’ command); do these poles correspond roughly to what you see in the system step response? Why or why not (a brief answer)?

1000 4000 9001 5010 5100

Answer 1

50)= 2(t) . uai shewn elow 4.5 The model is onwula tal (binolink and the respanre ant the modet i shnun elo

Step Integrator Gain Integrator Integrator2 Integrator Gain Scope Scope 台@ eyPQy rG 술 둑 Gain2 80 60 40 Gain4 2 Time offset: 0

As can be seen from the response of the model, the output of the system y(t) keeps on increasing for first 5 seconds. The system is unstable.

MATLAB code to get transfer function and the poles of the system:

clear all;
clc;
A =[-4.5 0.5 9 -4; 1 0 0 0; 0 1 0 0; 0 0 1 0];
B=[1;0;0;0];
C=[0 0 1 3];
D=0;
[num,den]=ss2tf(A,B,C,D)
poles=roots(den)

Results:

num =

0 0 0 1 3

den =

1.0000 4.5000 -0.5000 -9.0000 4.0000

poles =

-4.0000
-2.0000
1.0000
0.5000

It can be seen that among the four poles of the system, two poles i.e s= (-4) and s=(-2) lies in the left half of s-plane but the rest of the two poles i.e s=1 and s =0.5 lies is the right half of s-plane leading to the instability of the system.