Formation of a reference model for the method of inverse dynamics in the tasks of control of underwater complexes - Blintsov, Oleksandr (Eastern-European Journal of Enterprise Technologies, 2016)
Main requirements to the systems of automatic control of underwater complexes are specified. Main points of the synthesis of control systems by the method of inverse dynamics are given. The drawbacks of the method of inverse dynamics are defined, which consist in the limiting of the choice of the structure of a reference model and the necessity of bringing a mathematical model of the object of control to the view of a reference model. A mathematical model of an underwater complex is developed for the synthesis and study of the systems of its control that simulates a one-dimensional motion of an underwater vehicle under conditions of perturbing influence of a tether cable. Impossibility of the use of the method of inverse dynamics in the classic form for the synthesis of automatic control systems of underwater complexes is determined because their mathematical models contain elements that are set in arbitrary form. The method of inverse dynamics was improved by applying the principle of decomposition of a reference model, which boils down to its formation as a set of reference submodels based on the actual structure of an object. Decomposition of a reference model makes it possible to synthesize high–precision control systems of underwater complexes by the method of inverse dynamics and to set reference submodels of dynamics of phase coordinates of an object in the form of arbitrary functions of time. Automatic control system of a one-dimensional motion of an underwater complex was synthesized by the method of inverse dynamics using the principle of decomposition of a reference model. The author proposed three variants of a reference model of an automatic control system. The first variant makes it possible not to execute conversion of a mathematical model of the object to the view of a reference model. The second and the third variants are formed on the basis of the structure of a mathematical model of an object, presented in the form of Cauchy. This allows setting the dynamics of transition processes for each phase coordinate of the object in the form, accordingly, of differential equations of the first order and arbitrary functions of time. Computer simulation of an automatic control system revealed that the transitional process of eliminating an error of the controlled magnitude corresponds to the reference one. After eliminating the error, the controlled magnitude strictly follows the set one without delay.