Development of a tunable method for PID controllers to achieve the desired phase margin

• We propose a new method of tuning PID controller.
• We suggest a choose of crossover frequency for achieving desire phase margin.
• Overshoot depend on the Nyquist plot.

A new method for classical PID controller adjustment is broached. It allows to provide the required phase margin in a designed system. The mathematical formulation of the method and assumptions to implement it are given. The transfer functions of the plant are converted into real and imaginary parts at the frequency. Based on them, the analytical expressions for the controller settings are obtained. Thereby, the tuning parameters are the phase margin and crossover frequency. Some guidelines are provided for the selection of the crossover frequency on the basis of an integral performance index (ITAE). Several simulation examples are included to show the effectiveness of the proposed method.