Designing of P controller to obtain desired time domain scenario of the output

One of the most applicable and simple controllers, which always attracts the researcherchr('39')s attention to obtain a proper closed-loop performance, is the P controller. Proper performance of a system defined in the presence of controller has been proposed with different expressions like rising time, settling time and maximum overshoot. But in the view of this paper, the proper performance of the system is the outputchr('39')s specific value at predefined times and it determines the controller gains at time intervals. In reality, a scenario is considered for the output which defines outputchr('39')s values at several times .These times make time intervals and variable gains in these intervals must be applied to the system. To ensure the existence of the P controller gains for this purpose, the output value must be in an admissible range at any specific time. In this paper, this admissible range is obtained for different cases of a system parameter and initial value. Also, controller gain in some admissible ranges wasnchr('39')t unique and each choice of it has its specific properties. Since in the present paper, this work is done with initial values, we can properly switch between several P controllers in some phases to achieve a predefined scenario of the output in the time domain.