Performance analysis of control system tuning under inner disturbance influence by means of least square approximation to suboptimal algorithm and calculation using frequency optimality criteria

Abstract

The performance of two known variants of automatic control system tuning has been analysed. The control systems contained PI and PID-regulators and disturbances influenced the process under consideration, the transfer function of the process was the second order with a transport delay typical for thermal processes. The methods used were the least square approximation to the suboptimal algorithm and the calculation method using indirect frequency optimality criteria. The PID-regulator used had a second order filter in the differentiator. The suboptimal algorithm had a second order filter with time constant T c and correction coefficient k τ for the regulator step response argument. Dependencies and approximation formulae for unambiguous definition of parameters T c and k τ using the process model parameters for the systems with PI and PID-regulators are obtained, some recommendations for determining approximation frequency range are given. When choosing these parameters the frequency oscillation index of the system is taken into account. When tuning for the indirect indexes approximating formulae determining the indirect indexes optimal values according to the process model parameters in the wide range are used. It is shown that for the system with a PID-algorithm when disturbances influence the process the tuning method using the indirect frequency indexes provides better performance of the control system. Moreover, it is more convenient for implementation in controllers, because it allows to make all the necessary calculations automatically during the one working cycle of the controller. For the system with a PI-algorithm both methods provide approximately equal performance of the control system.