PID control and optimum of the third-order monotone nondecreasing and nonovershooting

In the paper, the necessary and sufficient condition of 2nd-order controlled object´s parameters and PID controller´s parameters which must be satisfied with the system´s response of nonovershooting and monotone nondecreasing has deduced when the system has three real poles. Under the circumstance of the 2nd-order controlled object´s parameters are fixed, this paper has made a deep research for the selection of PID controller parameters. The optimal PID controller parameters are obtained.