Using the Gramian Method to Synthesize Robust Control Systems for Conveying Long Materials

Material transportation control systems are part of a large number of automated technological complexes for continuous production of 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 automatic control systems. A methodology of synthesizing robust control systems with dynamic (polynomial) “input-output” controllers is proposed, based on the iterative approach, at each step of which singular Gramian numbers of control and/or observability are deliberately changed, with the formation of a precontroller, converting the structure of the design object model to improve controllability and/or observability. Using an improved object model permits the formation of the main polynomial “input-output” controller, capable of ensuring and maintaining the desired indicators of quality and rapid action within the specified parameter variation limits for the controlled object and controller.