Synthesis of robust control system for transportation of long-length material based on Gramian method

Abstract

Material transportation control systems are part of many automated technological complexes for continuous production in various industries. For the coordinated operation of the aggregated machines, it is required to ensure a given quality of control of the tension of material transportation under conditions of initial uncertainty and possible variations in the internal parameters of the ACS, primarily the inertia of rotation of the measuring roller and changes in the geometry of the deformation zone of the material, i.e., it is required to provide a significant increase in robust properties. A method for the synthesis of robust control systems with dynamic (polynomial) input-output regulators is proposed. It is based on an iterative approach, at each step of which the singular numbers of gramians of controllability and/or observability are purposefully changed, a preregulator is formed. It transforms the structure of the computational model of the object in the direction of increasing controllability and/or observability. The authors have proposed a method for the synthesis of a robust control system for the transportation of long-length material based on the Gramian method. The use of an improved model of the object makes it possible to form a basic polynomial input-output controller capable of providing and maintaining the desired quality and performance indicators within the specified limits of changing the parameters of the object and the controller, including when reducing the corrective pre-regulator. The results obtained allow us to demonstrate the high efficiency of a Gramian method for the synthesis of control systems with low sensitivity to variations in both the parameters of the control object and the controller own parameters.