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Control Systems (EEE325)
Dr. Jamshed IqbalAssistant Professor
Department of Electrical Engineering
Institute of Information Technology,Islamabad
Outlines
Steady State Error
System Responses
Transient response
Steady-state response
A distinct advantage of f/back control system is theability to adjust transient and steady-state response
Steady State Error
Steady State Error (ess): The difference b/wthe steady state output value and the reference
input value at steady state Reflects the accuracy of the system
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Expression of Steady State Error
E(s) is Error Signal
Putting the value of C(s) in the first Eq. and re-arranging
But Steady state error means Final value of error.This can be evaluated using Final Value Theorem (FVT)
This is general expression of Error
Final Value Theorem (FVT)The FVT allows the evaluation of the steady-state value of a time function from its Laplacetransform. FVT is onl valid for stable s stems(all poles are in the Left Hand Plane (LHP))
The FVT allows the time domain behavior to
e rec y ca cu a e y a ng a m o afrequency domain expression
Final Value Theorem (FVT)Example: For the following function, find g()using
i Inverse La lace methodii) FVT
2nd Method (FVT)
Expression of Steady State Error
Applying FVT on the E(s), we get
For a unity F/back system, H(s) = 1
Steady State Error is a function of
i) Input R(s)ii) Open loop transfer function G(s)
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SSE Subjected to Test Inputs
The actual input in a physical system is often arandom signal, thus SSE are obtained from the
s an ar es s gna s a u a e e ow:
SSE For Various Inputs
Kpos on rror ons an
SSE For Various Inputs
Kve oc y rror ons an
SSE For Various Inputs
Ka(Acceleration Error Constant)
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SSE For Various Inputs
SummaryFor unity F/back,
ype o p
Unit Step
Unit Ramp
Unit Parabolic
Dependence on G(s)
For a unity F/back system, H(s) = 1
Now is the time to see the effect of G(s) oness. General form of G(s)
Concept of Type of a system. This is DIFFERENTthan the order of the system.
Highest power in denominator determine = Order No. of poles present at origin determines = Type Examples (W/Board)
Dependence on G(s)
As s0, the term Sr becomes moredominant. i.e. the poles are the origin dominatethe expression for G(s). What are poles ator g n s as ca y e ype o sys em
The SSE depends on the type of system
Dependence on G(s): Type 0 System
r=0 in this case of type 0 systems
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Dependence on G(s): Type 1 System
r=1 in this case of type 1 systems
Dependence on G(s): Type 2 System
r=2 in this case of type 2 systems
Summary Assignment 4
Find the steady state error for unit step, unitramp and unit parabolic inputs for the followingsystems:
Deadline:10th April 2012 BEFORE
the lecture
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LT Table
jamshed.iqbal@comsats.edu.pkRoom 424 - EE Deptt.