The method of PID controllers synthesis for sixth-order systems

Abstract

The methodical of proportional-integral-derivative (PID) controllers designing for systems the sixth order are suggested. At the first stage of implementation of the method algorithm, the transfer function of the corrected closed control system is determined. Then you can specify the number and type of roots of this polynomial. The roots of the polynomial are set taking into account the root quality indicators. The next step of the algorithm determines the values of the parameters desired polynomial of the corrected closed system. These parameters will depend on the imaginary parts of complex-conjugate roots. Parameters of the polynomial must be positive It follows from the stability condition of the system. For a sixth-order model, the four higher-order parameters of this polynomial do not depend on the controller parameters and their values cannot be changed, since they are determined by calculations. Next, the coefficients of the PID controller model are calculated. You can set the condition for positive values of the regulator parameters. Checking the results of calculating the parameters of the controller is performed by the step response of the system. The efficiency of the proposed method of the designing PID controller is performed on the example of a system with a sixth order object. © Published under licence by IOP Publishing Ltd.