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Control Systems Lab Report

This document summarizes a control systems laboratory experiment performed by a student. The experiment had two parts: 1) Equivalency of block diagrams - The student analyzed systems with blocks in cascade, parallel, and negative feedback and derived their equivalent transfer functions. Simulink models confirmed the equivalency. 2) System stability and effect of pole location - The student analyzed the step response of systems for different values of k in the transfer function (s^3+4s^2+4s+k). Responses ranged from overdamped to underdamped to undamped to unstable as k increased from 1 to 26. Pole location determines stability.

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abbas uddin
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49 views10 pages

Control Systems Lab Report

This document summarizes a control systems laboratory experiment performed by a student. The experiment had two parts: 1) Equivalency of block diagrams - The student analyzed systems with blocks in cascade, parallel, and negative feedback and derived their equivalent transfer functions. Simulink models confirmed the equivalency. 2) System stability and effect of pole location - The student analyzed the step response of systems for different values of k in the transfer function (s^3+4s^2+4s+k). Responses ranged from overdamped to underdamped to undamped to unstable as k increased from 1 to 26. Pole location determines stability.

Uploaded by

abbas uddin
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Course No: EEE 402 Group No: 02

Course Name: Control System I Laboratory Student No: 1306134

Experiment No: 03

Experiment Name:
a) Equivalency of block diagram

b) System stability and effect of pole location

Date of Performance: 10-10-2017 Name: AZIM UDDIN

Date of Submission : 17-10-2017 Level: 4 Term: 1

Department: EEE

Section: C

Partners’ Student No:

1306135

1306136
Part-A: Equivalency of block diagram
1. Blocks in cascade:
Equivalent transfer function = s+3/s^3+10s^2+29s+20
Simulink Model

Output
From Cascaded Blocks

From Equivalent Circuit


2. Blocks in Parallel:
the equivalent transfer function = (s^3+10s^2+34s+37)/ ( s^3+10s^2+29s+20)
Simulink Model
Output
From Parallel Blocks

From Equivalent Circuit

3. Negative Feedback:
the equivalent transfer function = (s^3+10s^2+34s+37)/ ( s^3+10s^2+29s+20)
Simulink Model

Output
From Feedback

From Equivalent Circuit


4. Moving Blocks Left and Right
Simulink Model

From time scope we get following curve for both of the system
5. Equivalency
We can find equivalency in the systems of parallel, cascade, negative feedback
and moving blocks system. We can see slightly variance in rise time only.
cascade Equivalent Parallel Equivalent Negative Equivalent Moving Moving
transfer transfer feedback transfer left right
function function function
of cascade of parallel of
negative
feedback

Rise time 2.188 2.18 2.231 2.221 6.638 6.644 6.647 6.644
(sec)

Amplitude 148.5 148.5 841.5 841.5 1.320 1.320 1.320 1.320


(mv)
Part-B: System stability and effect of pole location
Theory:

If the closed-loop system poles are in the left half of the plane and hence have a
negative real part, the system is stable. To be more precise, Stable systems have
closed-loop transfer functions with poles only in the left half-plane. Unstable
systems have closed-loop transfer functions with at least one pole in the right
half-plane and/or poles of multiplicity greater than 1 on the imaginary axis.
Marginally stable systems have closed-loop transfer functions with only imaginary
axis poles of multiplicity 1 and poles in the left half-plane.

1. Transfer function= (k)/(s^3+4s^2+4s+k)


For different values of k we find different step response
For k= 1 response is overdamped
For k<16 like k=12 response is underdamped

For k=16 response is undamped


For k>16 like k=26 system response become unstable

2. Gain goes to a saturate value for over damped and under damped
system. Oscillatory for undamped system an increasing for unstable
system.

DISCUSSION:

In this experiment we have learnt about block diagram and different step
response of the system. In the first part we have learnt about equivalent
transfer functions, moving block without changing the response, negative
feedback.
In the 2nd part we have seen hoe responses vary as the variation of poles, how
a stable system becomes unstable

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