Terminal Control of a Single Nonlinear Object by the SDRE Method

Abstract

The possibility of synthesizing terminal control in the form of feedback by a nonlinear first-order object with parameters depending on the state of the object and additive control action is investigated. The use of a linear-quadratic regulator for this purpose is not possible due to the essentially nonlinear nature of the object’s dynamics. The SDRE method is used to construct the control law. It is theoretically proved that the constructed nonlinear SDRE controller ensures the transfer of an object from an arbitrary initial state to a small neighborhood of a given state in a predetermined finite time. The terminal error of regulation tends to zero when the penalty coefficient of the terminal term of the quality criterion is increased. A similar reduction in error is also achieved regardless of the value of the penalty factor by increasing the control time. The terminal properties of the regulator are demonstrated by the example of controlling the shutdown of an electric drive with a DC motor of sequential excitation, which is widely used in industrial robot drives. This electric motor belongs to devices with nonlinear dynamic characteristics. Calculations show that the regulator stops the electric drive in a short designated time with a favorable course of the transient shutdown process. The feedback of the control law helps to overcome the disturbing effect of possible uncontrolled loads on the shaft