Question

1. Compare the two nonminimum phase transfer functions: $$G_1(s) = \frac{-s+2}{s^2+11s+30}$$ (1) $$G_2(s) = \frac{s-2}{s^2+11s+30}$$ (2) and the corresponding minimum phase transfer function $$G_3(s) = \frac{s+2}{s^2+11s+30}$$ (3) (a) (9 points) Compare $G_1(s)$, $G_2(s)$, and $G_3(s)$ with linear techniques (use the step(), rlocus(), and bode() commands in Matlab). Are the pole and zero locations the same? Are the responses different? Comment on why. (b) (2 points) Examine what is meant by minimum phase by looking at the phase plot of the Bode diagram for the three systems. (c) (4 points) Consider elevators on an aircraft and explain how these could give rise to nonminimum phase behaviour. (d) (5 points) Using a proportional controller in a unity feedback loop with $G_3(s)$, determine the range of stability for $k_p$. (e) (6 points) Using a proportional controller in a unity feedback loop with $G_1(s)$, determine the range of stability for $k_p$. What does this imply for nonminimum phase systems?

Name: 1 compare the two nonminimum phase transfer functions g1s frac s2s211s30 1 g2s fracs 2s211s30 2 and the corresponding minimum phase transfer function g3s fracs2s211s30 3 a 9 points compar 42887
Uploaded: 2023-08-02T07:08:34-08:00
Duration: 3 min 56 s
Channel: Madhur L
Description: 1 compare the two nonminimum phase transfer functions g1s frac s2s211s30 1 g2s fracs 2s211s30 2 and the corresponding minimum phase transfer function g3s fracs2s211s30 3 a 9 points compar 42887

          1. Compare the two nonminimum phase transfer functions:
$$G_1(s) = \frac{-s+2}{s^2+11s+30}$$ (1)
$$G_2(s) = \frac{s-2}{s^2+11s+30}$$ (2)
and the corresponding minimum phase transfer function
$$G_3(s) = \frac{s+2}{s^2+11s+30}$$ (3)
(a) (9 points) Compare $G_1(s)$, $G_2(s)$, and $G_3(s)$ with linear techniques (use the step(), rlocus(), and bode() commands in Matlab). Are the pole and zero locations the same? Are the responses different? Comment on why.
(b) (2 points) Examine what is meant by minimum phase by looking at the phase plot of the Bode diagram for the three systems.
(c) (4 points) Consider elevators on an aircraft and explain how these could give rise to nonminimum phase behaviour.
(d) (5 points) Using a proportional controller in a unity feedback loop with $G_3(s)$, determine the range of stability for $k_p$.
(e) (6 points) Using a proportional controller in a unity feedback loop with $G_1(s)$, determine the range of stability for $k_p$. What does this imply for nonminimum phase systems?

$1 compare the two nonminimum phase transfer functions g1s frac s2s211s30 1 g2s fracs 2s211s30 2 and the corresponding minimum phase transfer function g3s fracs2s211s30 3 a 9 points compar 42887$

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