CONTROL LAB
EXP. NO. (1)
TIME DOMAIN ANALYSIS OF A 2nd ORDER CLOSED LOOP
SYSTEM USING BLOCK DIAGRAM REDUCTION BY MATLAB
OBJECT:
To study time domain analysis of a 2nd order closed loop system using step,
ramp and impulse input functions before and after system reduction.
APPARTUS:
A computer device type (Pentium I or Pentium II).
THEORY:
Time response analysis investigate the time-domain transient behaviour of
control models for particular classes of inputs and disturbances. You can
determine such system characteristics as rise time, overshoot and steady- state
error from the time response.
The control system Toolbox contains a set of commands that provide the basic
time domain analysis tools required for control system engineering.
These commands are:
Step (sys) — investigate the step response of a control system.
Impulse (sys) - investigate the step response of a control system.
Note: There is no direct command to obtain the ramp response of any control
system, so we must make an integration to the transfer function of this
system and using the step command to the resulted system in order to obtain
the ramp response.
The transient response method is one of the methods that use to analysis system
performance. This method of analysis is based on “Test Signals” in order to
compare the performance of various systems. There are many types of typical test
signals such as step function, ramp function, impulse function, acceleration
function, sinusoidal function etc. The using any kind of these signals depends on
the system itself
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CONTROL LAB
EXP. NO. (1)
BLOCK DIAGRAM ALGEBRA
The block diagram shown below in fig.(l) is called the economical form of a
feedback control system:
Fig. (1)
Where
G(s) = Forward transfer function.
H(s) = Feedback transfer function.
G(s).H(s) = Open loop transfer function.
𝐶(𝑠)
𝑅(𝑠)
𝐸(𝑠)
𝑅(𝑠)
= closed loop transfer function = (
𝐺(𝑠)
1+𝐺(𝑠)𝐻(𝑠)
)
= Actuating signal ratio = error ratio
Note1: If H(s) = 1, Then the system is called unity feedback system.
A complicated block diagram involving many feedback loops can be simplified
by a step-by-step rearrangement, using rules of block diagram algebra. These
rules are given as in table (1).
Note2: The economical form can be reduced also to get only one an open loop
block diagram (without feedback path).
Steps for Reduction of Complicated Block Diagram
1. Combine all cascade blocks.
2. Combine all parallel blocks.
3. Eliminate all minor feedback.
4. Shift summing points to the left and take off point to the
right of major loop.
5. Repeat steps 1-4 until you obtain the comical form.
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CONTROL LAB
EXP. NO. (1)
PROCEDURE:
1. Run a MATLAB program on a PC.
2. Give the Simulink for the block diagram shown in fig. (2).
3. Draw the output response with the step input signal.
4. From the output response of transfer function of that system, calculate the
following time constants’ values (td, tr, tp, ts and Mp).
5. Draw the output response with the ramp input signal.
6. Determine the steady state error of the drawing signals of step (5).
7. Simplify the block diagram of fig. (2) until you get an economical form of a
control system as in fig.(l). Repeat steps (3, 4, 5 and 6).
8. Write a MATLAB program to enter the open loop transfer function of
the system in fig. (2) and draw the output response using step (sys),
impulse (sys) commands.
9. Use the step (sys) command to draw the ramp response of that system.
Fig. (2)
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CONTROL LAB
EXP. NO. (1)
DISCUSSION:
1. Reduce the following block diagram to a economical form.
2.
Reduce the following block diagram to an open loop control system
3. How can we get a ramp and an impulse function from a step functions?
4. Why we use transient response analysis method in control system? What are
the test signals used in this method and which one we should use in control
systems?
5. What is the difference in readings for the control system used in your
experiment before and after reduction theorem?
Answer the question showing a detailed comparison between the practical and
theoretical results. Finally comment on your results.
4
CONTROL LAB
EXP. NO. (1)
Table (1) Basic rules with block diagram transformation
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