5.8.  THE ITAE PERFORMANCE CRITERION FOR OPTIMIZING THE TRANSIENT RESPONSE

The ITAE performance index, as defined by Eq. (5.46), is considered further in this section. As discussed in Section 5.6, this performance index does not penalize large initial errors that are unavoidable. However, it does penalize long-duration transients. We now consider the form that the system transfer function should take, for various order systems, in order to achieve zero stedy-state step and ramp error systems and minimize the ITAE.

In the case of the zero steady-state step error system, Eq. (5.52) shows that the form of the system transfer function is given by

Image

The procedure used to produce a table of standard system transfer functions of the form C(s)/R(s) was to vary each coefficient in Eq. (5.56) separately until the integral of time multiplied by the absolute value of error became a minimum. Then the successive coefficients were varied in sequence to minimize the ITAE value.

If this criterion is applied to the second-order system described by Eq. (5.38), the optimum damping ratio is found to be 0.7. A listing of system transfer functions, C(s)/R(s), has been prepared by Graham and Lathrop [2], They show the optimum form of the denominator, for systems whose transfer functions are of the form given by Eq (5.56), which will minimize the integral of Eq. (5.46). For example, the optimum form for a ...

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