Polynomial matrix method for synthesizing regulators for objects with a control signal delay

Abstract

In this paper, we consider the synthesis of control systems for objects with a control signal delay by a polynomial matrix method, which is used to locate the poles and, if possible, zeros in the required position. The controller is calculated from the output, i.e. only from the measured values in the plant, which is an advantage over other modal direction synthesis methods where a state vector must be used. It is proposed to approximate the delay link with a Padé series with a limited number of terms, thus obtaining transfer functions of the first and second orders. The desired characteristic polynomial of the closed system is chosen so that it contains the denominators of the approximation transfer functions, which will keep their poles in the closed system. The polynomial synthesis method makes it possible to calculate multichannel controllers both for objects with multiple inputs and multiple outputs (multi input - multi output, MIMO) and for objects with one input and several outputs (single input - multi output, SIMO). The latter include a DC motor with independent excitation, where the armature current and rotor speed are outputs, and the control signal applied to the semiconductor converter is the input. In this work, the control signal is formed with a delay exceeding the time of the transient process of the engine, which significantly affects its dynamics. By applying the proposed approach, it was possible to synthesize a rotor speed control system that is resistant to changes in the delay time in a fairly wide range.