Question

Find the poles of the following transfer function by hand, predict what type of system are they (stable, unstable, or marginally stable). (1) G(s)=

s
2
+5s+6
100s
​
(2) G(s)=
s
3
+s
2
+s+1
10
​
(3) G(s)=
s
2
−3s
1
​
(4) G(s)=
s
3
+10s
2
+31s+10
10
​
Exercise 2. Use MATLAB (either Command or Simulink) to simulate the responses of each system when inputs are S1(step input), S2 (ramp input), and S3 (unit sine wave). Discuss the results you observed. Exercise 3. Use Routh-Hurwitz test to evaluate the stability of transfer functions (3) and (4) in Exercise 1.

Answer 1

For transfer functions (1) and (2), the poles can be found by factoring the denominators. Transfer function (1) has real poles, indicating stability, while transfer function (2) has complex conjugate poles, also indicating stability. For transfer functions (3) and (4), the poles are identified as 0 and -1, respectively. These systems are marginally stable. The MATLAB simulation and Routh-Hurwitz test results would provide more detailed insights into the system responses and stability analysis.

Step-by-step explanation:

Transfer function (1) can be factored as (s + 2)(s + 3)/100s, yielding real poles at -2 and -3, indicating stability. Transfer function (2) can be factored as (s + 1)(s^2 + 1)/10, resulting in complex conjugate poles at -1 and ±j, also indicating stability. For transfer functions (3) and (4), the poles are at 0 and -1, respectively, suggesting marginally stable systems.