Methods of Improving Controllability and Observability of a Computational Object Model during Synthesis of Robust Mechatronic Systems with Polynomial Controllers

The object of this study is a single-channel dual mass mechatronic system with flexible kinematic links that is widely used for controlling the motion of work machines. In the event of difficulty in measuring all state coordinates relating to the object, the required control quality may be ensured by using dynamic "input-output" (polynomial) controllers synthesized by the polynomial modal control method. The problem of studying the influence of the internal parameters of the object on the degree of its controllability and observability, and also on the parametric robustness of the synthesized system, is addressed. Methods are developed for improving the above system properties of the object or its computational model, and for creating on this basis a robust mechatronic system with a polynomial controller. For a comparative evaluation of the degree of controllability and observability, of various kinds of objects, use is made of diagonal forms of representing controllability and observability Gramians, and also the first norms of matrices reflecting the degree of closeness of system properties of the object represented in real coordinates and canonical forms of controllability and observability. The influence of small time constants (rapid motions) of the power converter, electromagnetic circuit of the electric motor and mechanical section, and also the internal friction value of kinematic transmission on system properties of the object and parametric robustness of synthesized systems, is researched. The negative conditions of the above influence are identified and methods of its compensation are proposed, based on further reduction of the above parameters and their exclusion from computational object models to improve initial system properties and synthesis of robust systems, and also on increasing the speed of the main control loop with elimination of additional boosts by correcting the inertia of the outof-loop prefilter. In the presence of internal friction in the kinematics leading to zero in object transfer function, improvement of system properties in the computational model is ensured by using the developed Gramian method, introducing additional virtual control channels and performing modal synthesis of the basic polynomial controller based on the improved object model.

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