代写ENG3018、MATLAB设计编程代做

日期：2024-02-26 09:16

ENG3018: Control Engineering

MATLAB Practical 2

Christopher Edwards

This is an individual piece of work contributing 6% of the total assessment for the module Control

Engineering ENG3018. Once completed it needs to be electronically submitted via eBART.

Consider the feedback loop shown in Figure 1,

Figure 1: Block Diagram.

where the transfer functions are

G(s) = 10(s + 4)

s(s

2 + 4s + 5) and K(s) = (s + 1)

(s + 3) .

a) Find the closed loop transfer function T(s) between r and y in the feedback loop (a.k.a.

as the complementary sensitivity function) shown in Figure 1. Make use of the MATLAB

commands tf, poly, conv and feedback.

T(s) =

b) Determine the poles and zeros of T(s) of the feedback loop in Figure 1.

The poles are:

The zeros are:

c) The DC gain associated of T(s) is:

d) Determine the poles and zeros of the sensitivity function S(s) associated with the closed loop

system in Figure 1.

The poles are:

The zeros are:

1

e) Sketch the unit step response of T(s) using the axes given in Figure 2.

0 1 2 3 4 5 6 7 8 9 10

Time

0

0.2

0.4

0.6

0.8

1

1.2

Output

Figure 2: Unit step response

f) Sketch the response of the closed loop system y(t) in Figure 1 to a reference input r = sin(wt)

for w = 1.7 over the time interval [0, 10], sampled at intervals of 0.01, using the axes given in

Figure 3. Sketch the reference input r(t) on the same set of axes.

0 1 2 3 4 5 6 7 8 9 10

Time

-1.5

-1

-0.5

0

0.5

1

1.5

Output

Figure 3: Sinusoidal Response

g) Use the information obtained above to estimate the phase shift associated with T(s).

C Edwards

February 15, 2023

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