control system by doctor jamshed iqbal Lec18

7/29/2019 control system by doctor jamshed iqbal Lec18

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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


Kve oc y rror ons an


Ka(Acceleration Error Constant)


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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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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

[email protected] 424 - EE Deptt.

control system by doctor jamshed iqbal Lec18

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