First-Order Prototype System
Let us examine two specific cases, first- and second-order prototype systems. Consider Eq. (2-177), which may also be represented by the first-order prototype form:
Where, τ is known as the time constant of the system, which is a measure of how fast the system responds to initial conditions of external excitations.
By the use of example we will understand the first order proto type system.
Find the solution of the first-order differential Eq. (2-179).
Typical unit-step responses of y(t) are shown in Fig. 2-22 for a general value of t. As the value of time constant decreases, the system response approaches faster to the final value.
Fig. 2-22, Unit-step response of afirst-order RC circuit system.