Synthesis of a Nonlinear System for Transporting Long-Length Material Based on a Set of Control Theory Methods

The study is devoted to the development of a methodology for the synthesis of a control system for the transportation of a long, deformable, elastic material that is subject to external disturbances and variations in internal parameters. To achieve this, the features of flow lines as control objects have been identified, which significantly complicate the achievement of high-quality technological processes. А set of methods for the synthesis of controllers for linear and nonlinear dynamic systems has been determined, as well as the sequence of their application, which allows for the most effective overcoming of the complexity factors of the controlled object while meeting the specified technical requirements. The developed complex four-stage methodology for the synthesis of a two-channel nonlinear control system is based on the joint use of the principles of separating the rates of motion of the " fast" and "slow" subsystems, as well as robust modal control of the specified accuracy, to form the dynamics and ensure the specified static accuracy of the local channels, followed by the use of the method of analytical design of aggregated controllers for the linearization of nonlinear material deformation by feedback and the adaptation of the system to multiple changes in the elastic properties of the moving web. To illustrate the effectiveness of the proposed approach, a step-by-step example of applying the developed methodology for the synthesis of an automatic control system for a real technological object is considered. In the first step, a mathematical model of a section of a production line consisting of a two-channel DC electric drive and a transporting zone for a deformable material with second-order elasticity as a control object is created. Next, a control subsystem for the local channel is synthesized, which has the desired dynamic, static, and robust properties. In the next step, a subsystem is developed to ensure the linearity of the dynamic properties of the transporting process for the processed material. And, finally, an option for adapting the system to changes in the elastic properties of the moving web is proposed. During the study of the ACS, the reduction of mathematical models was applied twice: in the first case, to achieve robust properties, and in the second case, to simplify the procedure for synthesizing the controller. The effectiveness of the proposed approach has been confirmed by the results of digital simulation modeling at each stage of the automatic control system synthesis.

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