Control of tracking mechatronic systems with rigid kinematic links under constraints on the main state coordinates

Abstract

Tracking mechatronic systems must ensure high-quality control of operating machines across a wide speed range under significant variations in control and disturbance inputs, achieve maximum acceleration of transient modes under state coordinate constraints, and provide smooth transitions from the linear zone of small deviations to the nonlinear zone of large coordinate deviations and vice versa. In cases of high kinematic rigidity, systems are designed based on the principle of cascaded control of the main state coordinates (current, speed, position) using standard regulators. State coordinate constraints are implemented by limiting the output signals of the regulators. However, the presence of nonlinear elements of the “saturation” (“constraints”) type can cause dangerous self-oscillations and lead to system failure, even when all control loops have a large stability margin in the small. The problem becomes most acute with an increase in the degree of astaticism of tracking systems and the number of integrating elements in the control loops. Thus, a detailed study of the dynamics of tracking MS with significant changes in operating modes associated with transitions from the linear zone of small to the nonlinear zone of large deviations of state coordinates caused by the limited capabilities of the power actuators, and the development of more effective methods to control systems under these conditions, is relevant. The study has been conducted using operator methods for structural representation of objects and systems in input-output relationships, as well as the harmonic balance method based on harmonic linearization of nonlinearities. The parametric synthesis of regulators and tuning of control loops have been performed using methods of cascaded (subordinate) coordinate control with sequential correction of feedback loop circuits. The effectiveness of the obtained results has been evaluated using detailed digital simulation methods. Three variants of DC tracking mechatronic systems with varying degrees of astaticism with respect to the control input have been synthesized and studied. Expressions of the transfer functions of their linear parts have been derived. A visual representation of the characteristics of linear and nonlinear parts in the complex plane has been provided, subject to constraints on current, motor speed, and supply voltage. Based on the analysis of these results, a method has been developed to modify the structure of each regulator with integrating elements when the corresponding coordinate is constrained. This also includes forced saturation of all integrating elements in the position regulator whenever any of the monitored state coordinates is limited, supplemented, if necessary, by inertia-free correction of the loop gain in the position control loop. The application of known technical solution such as installing static “constraints” elements at the outputs of position and speed regulators, as well as using mechanisms for local “anti-windup” of the integrating elements in the regulators still retains the possibility of self-oscillations and system failure in the studied systems. The developed control method proves to be more effective; it improves operational quality and eliminates the possibility of emergency situations across various operating modes of tracking mechatronic systems.