INSTITUTE OF BIOMEDICAL ENGINEERING & TECHNOLOGY
LIAQUAT UNIVERSITY OF MEDICAL AND HEALTH SCIENCES,
JAMSHORO
CONTROL SYSTEMS
RESPONSE OF
FIRST ORDER SYSTEM
1
TIME RESPONSE ANALYSIS
Transient State response
When the energy state of any system is disturbed, and disturbances occur
at input, output, or both ends:
• It takes some time to change from one state to another state.
• This time required for the transition is known as transient time.
• The values of current and voltage during this period are referred to as
transient response.
It deals with the nature of the response of a system when subjected to an
input.
As time tends to infinity, transient dies out and response achieves steady
state
2
TIME RESPONSE ANALYSIS
Steady State response
• The analysis on time after response attains steady state is define as
steady state analysis
• It gives an indication of accuracy of the system when output does not
agree with input, then the system is said to have a steady state error
• Steady state response depends on type of input, hence we will do the
analysis by taking all standard test signal.
3
STANDARD TEST SIGNALS
For the analysis of the time response of a control system, the
following input signals are used.
• If the inputs to a control system are gradually changing
functions of time, then a ramp function of time may be a
good test signal.
• If a system is subjected to sudden disturbances, a step
function of time may be a good test signal.
• If a system subjected to a shock input, a pulse or an
impulse function may be best.
4
STANDARD TEST SIGNALS
System Response:
For analysing system characteristics may be determined by the form of the input that
the system will be subjected to most frequently under normal operation.
5
FIRST ORDER SYSTEMS
System Response:
Consider the following block diagram of the closed loop control system. There is an
open loop transfer function, 1/sT is connected with a unity negative feedback.
In this figure transfer function of the closed loop control system has unity negative
feedback. It is parallel configuration, therefore apply parallel rule to find transfer.
Here, power of s is one in the denominator term. Hence, the above transfer function
is of the first order and the system is said to be the first order system.
The order of a system is defined as being the highest power of derivative in the
differential equation, or being the highest power of s in the denominator of the
transfer function.
6
FIRST ORDER SYSTEMS
System Response:
• Unit Step function: If a system is subjected to sudden disturbances, a step
function of time may be a good test signal.
7
FIRST ORDER SYSTEMS
System Response:
• Unit Step function: If a system is subjected to sudden disturbances, a step
function of time may be a good test signal.
To make step function follow steps.
Write equation in form
Put R(s)=1/s
8
FIRST ORDER SYSTEMS
System Response:
• Unit Step function:
9
FIRST ORDER SYSTEMS
System Response:
• Unit-Impulse response: If a system subjected to a shock input, a pulse or an
impulse function may be best.
To make Impulse function follow steps.
1-
2- Put R(s)=1
3- Take the inverse Laplace transform:
10
FIRST ORDER SYSTEMS
System Response:
• Unit-ramp response: If the inputs to a control system are gradually changing
functions of time, then a ramp function of time may be a good test signal.
To make Ramp function follow steps.
1- Write equation in form
2- Put R(s)=1/s2
3- Expanding C(s) into partial fractions:
4- Take the inverse Laplace transform:
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