In general, most of the control system is designed to have 0 < đ” < 1. The value of zeta(đ”) to be chosen depends upon the application of that control system and for this, we define some of the parameters called as time domain specifications. These include
1. Delay time
2. Rise time
3. Peak time
4. Peak overshoot
5. Settling time
In other words, in order to analyse the performance of a control system following performance indices are considered.
1. How fast a system moves to follow the input?
2. How oscillatory is it?
3. How long does it take to practically reach the final value?
For practical applications, the performance of control system is specified in term of Time Domain Quantities.
1. Delay time
It is the time required to reach 50% of the desired value during rising from its zero state. It is denoted by Td.
2. Rise time
It is the time required for the response to rise from zero to 100% of the desired value for the first time for an underdamped system and 10% to 90% for an overdamped system. It is denoted by Tr.
3. Peak time
It is the time required for the response to reach the first peak of the overshoot is called as peak time. It is denoted by Tp.
4. Peak (maximum) overshoot
The maximum positive deviation of the response with respect to the desired value is called as maximum overshoot. It is denoted by Mp.
5. Settling time
It is the time required for the response to reach and stay within a specified tolerance band usually 2-5% of its desired value. It is denoted by Ts.
6. Steady state error
It is the difference between the actual output and the desired output as time approaches infinity. It is denoted by ess.
Note:
1. Time at which the first undershoot occurs = period of oscillation =
2. The number of oscillations completed before reaching steady state =
Exercise
Q. What is meant by overshoot?
Ans. It is the maximum difference between the transient and steady state solutions for a unit step function input.
