Improvement of the inverse dynamics method for high-precision control of nonlinear objects under conditions of uncertainty

Abstract

Synthesis of automatic control systems (ACS) of nonlinear objects is a well-known scientific problem. The method of inverse dynamics makes it possible to synthesize high-precision ACSs of nonlinear objects. However, under conditions of uncertainty, control quality is significantly compromised and ACS does not fulfill the set task. The result of present research is the further elaborated method of inverse dynamics for the synthesis of high-precision ACS of nonlinear objects under conditions of uncertainty. We have synthesized a generalized structure of the inverse control law as a basis for control of nonlinear objects under conditions of uncertainty. Under this structure, the inverse control law is built based on an imprecise inverse model of the object of control and contains an uncertain component of controlling influence to compensate for uncertainties. We have synthesized a law to compensate for uncertainties based on the method of minimizing local functionals. It includes an imprecise model of the object of control and ensures that its output approaches the controlled magnitude. The compensation law makes it possible for ACS to operate under conditions of uncertainty and, at the proper choice of reference models, to provide for a high dynamic accuracy in control over a nonlinear object. We have synthesized ACS of the vertical movement of a tethered remotely operated underwater vehicle. The synthesis was implemented based on an imprecise model of the object of control. The model's order was one order of magnitude less than the object’s order; part of the model responsible for generating a controlling force was considerably simplified; the disturbing influences of a tether-cable were not taken into consideration. Thus, the structural and parametrical uncertainties were accounted for. The dynamics of ACS transient processes were studied based on computer implementation of the model of one-dimensional motion of a remotely operated underwater vehicle as a third-order object taking into account the disturbing influence of a tether-cable. Results of computer experiment showed high dynamic accuracy of ACS under conditions of structural and parametrical uncertainties of the control object's model under the influence of uncertain disturbances of a tether-cable