Synthesis of a robust control system for a manipulation robot with polynomial controllers based on Gramian method

Abstract

Since manipulation robots can have several control channels, and their nonlinear coordinate relationships lead to internal parametric disturbances, along with variations in mechanical parameters, the use of Gramian methods for the synthesis of robust automatic control systems seems to be an effective way to improve the quality of control of such objects. When developing a robust control system for a manipulative robot, the method of polynomial modal control is used, local regulators are synthesized for both parts of the manipulator and a centralized controller is synthesized using an object model adjusted by the Gramian method. The calculations of the regulator based on the linear model of a two-link robot manipulator and the analysis of the transient characteristics of the movement of its links are carried out in the MATLAB software package. A method to synthesize a robust control system for a manipulation robot is proposed. It is based on a linearized mathematical model of a control object with a dynamic (polynomial) controller, aimed at changing the singular number of controllability and observability Gramians and subsequent calculation of a centralized controller to control the original nonlinear object. The use of a modified object model makes it possible to improve the robust properties and increase the speed of the control system for a nonlinear robotic object while maintaining the aperiodic nature of the processes under conditions of mutual influence of links and parameter variations. The proposed method makes it possible to improve the quality of control of manipulative robots and their productivity in conditions of intensification of technological production.