Direct sliding mode control of a three-phase AC/DC power converter for the velocity regulation of a DC motor

A DC voltage source and a DC/DC power converter can be used to control the position, speed, or torque of a DC motor. In such operational conditions, a rectifier is needed to use a DC voltage source if only a three-phase voltage source is available. The objective of this study is to replace a rectifier and DC/DC power converter by one AC/DC power converter, such that its output would be equal to the voltage needed to control a DC motor. It is assumed that the control algorithm of a DC motor is selected, which means that the desired output voltage of the AC/DC converter as a time function or function of the motor state is known. First, a sliding mode methodology is applied to control the converter's three shoulders to make the three-phase input current track the source voltages multiplied by a time-varying gain. The gain is then selected such that the converter output voltage is equal to the desired input of the DC motor. It is shown that this condition holds if the time-varying gain satisfies a first-order differential equation, which can be implemented as part of the controller. The application of Lyapunov theory confirms that the speed regulation process has a stable equilibrium point at the origin and that the time gain variation is bounded. The power efficiency is equal to one if the gain is positive. A numerical simulation demonstrates application of the developed control methodology for both constant and time-varying angular speed reference inputs.