Mathematical Equation of a System
If the mathematical notation of a control system is given then follow the following equation to determine time-variant and time-invariant control system.
Let the given mathematical equation of a control system is –
y(t)=kx(2t)
1. first find the value of y(t,t0), to find y(t,t0) replace the value of x(t) by value of x(t-t0).
2. second find the value of y(t-t0) by replacing the value of ‘t‘ by t-t0.
3. compare the value of y(t,t0) with the value of y(t-t0)
if, y(t,t0) = y(t-t0), then the given system is time invariant.
if, y(t,t0) ≠ y(t-t0), then the given system is time-variant.
y(t,t0) is the calculation of response of system with input x(t-t0).
y(t-t0) is the calculation of response of system with time delay t0 means at time (t-t0).
Time-Variant and Invariant Control System
Control systems play an important role in engineering, they help in regulating and controlling a process or a system to obtain controlled output. There are different types of control systems such as Linear and non-linear systems, Causal and Non-causal systems. Time variant and Time invariant control systems are one of them. In this article, we’ll learn about the time-variant and invariant systems.
Table of Content
- Time-Variant System
- Time-Invariant System
- Determination of Time-Variant and Time-Invariant Control System
Mathematical Equation of a System- Solved Examples of Time-Variant and Invariant Control System
- Difference Between Time-Variant and Time-Invariant System
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