08-05-2012, 04:45 PM
DIGITAL SIMULATION OF LINEAR SYSTEM
51355420-LAB-MANUAL-FOR-E-E-CS.pdf (Size: 523.09 KB / Downloads: 31)
THEORY
The desired performance characteristics of control system are specified in terms of time
domain specification. Systems with energy storage elements cannot respond instantaneously and
will exhibit transient responses, whenever they are subjected to inputs or disturbances.
The desired performance characteristics of a system pf any order may be specified in
terms of the transient response to a unit step input signal.
The transient response of a system to unit step input depends on the initial conditions.
Therefore to compare the time response of various systems it is necessary to start with standard
initial conditions. The most practical standard is to start with the system at rest and output and
all time derivatives there of zero. The transient response of a practical control system often
exhibits damped oscillations before reaching steady state.
The transient response characteristics of a control system to a unit step input are
specified in terms of the following time domain specifications.
1. Delay Time
It is the taken for response to reach 50% of the final value, for the very first time.
EC2259 Electrical Engineering And Control System Lab Manual
Prepared by G.Panneerselvam, Vel Tech Multi Tech
2. Rise Time
It is the time taken for response to raise from 0 to 100% for the very first time. For under
damped system, the rise time is calculated from 0 to 100%. But for over damped system it is the
time taken by the response to raise from 10% to 90%. For critically damped system, it is the
time taken for response to raise from 5% to 95%.
Damped frequency of oscillation d n 1 2
w =w −x
3. Peak Time
It is the time taken for the response to reach the peak value for the very first time. (or) It is the
taken for the response to reach the peak overshoot p
d4. Peak Overshoot (Mp)
It is defined as the ration of the maximum peak value measured from final value to the final
value.
Let final value = c(e)
Maximum vale c(t )
5. Settling Time
It is defined as the time taken by the response to reach and stay within a specified error. It is
usually expressed as % of final value. The usual tolerable error is 2% or 5% of the final value.
PROCEDURE
• Enter the command window of the MATLAB.
• Create a new M – file by selecting File – New – M – File.
• Type and save the program.
• Execute the program by either pressing F5 or Debug – Run.
• View the results.
• Analysis the time domain specifications of the system.