A study on the generalization of the Manabe standard forms with the genetic algorithm

The step response of the Manabe standard form (1998) has few overshoots and shows almost same waveforms regardless of the order of the characteristic polynomial. In some situations it is difficult to control the rise time and settling time simultaneously of the step response of the Manabe standard form. To control its rise time and settling time efficiently, we develop the generalization of the Manabe standard form: we try to find out the SRFS (slow rise time and fast settling time) form which has the slower rise time and faster settling time than those of the Manabe standard form, we also consider the other three forms: the FRSS form, the FRFS form, and the SRSS form. In this paper, by using the genetic algorithm, we obtain the four forms we mentioned above. Finally, we design a controller for a given plant so that the overall system has the performance that the rise time is faster and the settling time is slower than those of the Manabe standard form