In many practical applications, the desired performance of control systems are specified in terms of time-domain quantities. Systems with energy storage cannot respond instantaneously and will show transient whenever they are subjected to inputs or disturbances. The transient response of a system to a unit step depends on the initial conditions. The transient response of a practical control system often show damped oscillations before reaching a steady state. This post includes Control system Notes on Transient Response Analysis with explanation of Time Domain Specification in detail.
In specifying the transient response of a control system to a unit-step input, it is common to specify the following:
a) Delay td
b) Rise time tr
c) Settling time, ts
d) Maximum overshoot, Mp
e) Peak time tp
Transient Response Analysis in Control System is shown in below figure
Explanation of Transient Response Analysis in Control System is as follows:
Delay Time: Rise Time is the time required for the response to reach 50% of the final value in the first attempt. It is denoted by Td.
Rise Time: Rise time is the time refers to the time required from the signal to change from a specific low value to high value. These value are 10% to 90% of the step height. Rise time is denoted by Tr.
Application of rise time is high speed electronic, compared to the attainable state of the art. Factor affecting of rise time in a resistive circuit are primarily due to stray capacitance and inductance but also capacitance and inductance a delay in voltage and current at the load is apparent until the steady state is reached.In a pure RC circuit rise time is 10% to 90%.
Setting Time:Settling time is the time elapsed from the application of an ideal instantaneous step-input to the time at which the output has entered and remained within a specific error band. settling time is denoted by Ts.
The settling time is defined as the time required for the step response to decrease and stay within a specified percentage i.e; 2% or 5% of its final value. The settling time is related to the largest time constant of the control system.
Peak Overshoot Time: Peak overshoot time is denoted by Mp. It is the maximum peak value of the response curve measured from unity. it is therefore the largest error between input and output during the transient period.
The peak overshoot is when a signal or function exceed its target. Its arises especially in the step response of band limit of the system such as lower pass filter. Overshoot represents a distortion of the signal. peak overshoot time denoted by Tp. The % peak overshoot is the maximum value minus the step value divided by the step value.
Peak Time: Peak time is the required for the response to reach first peak.
Related links for Control System notes
- Types of Traction Systems
- Steady State Error in Control System
- Open Loop and Closed Loop Control System
- Sample Question Paper of Basic Electronics
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