SKEDSOFT

Definitions of transient-response specifications:

5. Settling time, t_s:The settling time is the time required for the response curve to reach and stay within a range about the final value of size specified by absolute percentage of the final value (usually 2% or 5%). The settling time is related to the largest time constant of the control system. Which percentage error criterion to use may be determined from the objectives of the system design in question.

Fig: 2

The time-domain specifications just given are quite important since most control systems are time-domain systems; that is, they must exhibit acceptable time responses. (This means that the control system must be modified until the transient response is satisfactory.) Note that if we specify the values of t_d, t_r t_p, t_s, and M_p, then the shape of the response curve is virtually determined. This may be seen clearly from Figure 2.

A few comments on transient-response specifications:

Except for certain applications where oscillations cannot be tolerated, it is desirable that the transient response be sufficiently fast and be sufficiently damped. Thus, for a desirable transient response of a second-order system, the damping ratio must be between 0.4 and 0.8. Small values of 0.4) yield excessive overshoot in the transient response, and a system with a large value of > 0.8) responds sluggishly.

The maximum overshoot and the rise time conflict with each other. In other words, both the maximum overshoot and the rise time cannot be made smaller simultaneously. If one of them is made smaller, the other necessarily becomes larger.