To the Question on the ADOR and the ADAR Methods in the Problems of Synthesis of Nonlinear Control Systems

Abstract

In the paper the authors to continue comparison of known methods of Analytical Design of the Optimum Regulators (ADOR) and Analytical Design of the Aggregated Regulators (ADAR), discussed in paper [1]. Their comparison with method ADOR by criterion of accuracy of regulating is resulted. It is shown that the ADOR method by criterion of accuracy possesses more considerable advantages connected with easier procedure of analytical design of the nonlinear laws of the optimal control — is direct on the equations of the control object, not demanding the solution of any differential equations or artificial introduction in consideration of any functions of transformation in the form of the aggregated macrovariables, and the most difficult mathematical procedure is differentiation of variables and substitution of the equations of control object. The main difference of method ADOR by criterion of accuracy in the theoretical plot from all known methods that this method gives absolutely exact solution, he reliably secures a zero error of regulating, and all factors of errors (on a position, speed, acceleration, jerk etc.) also are equal to zero.
Unlike known ADOR methods, in known Bellman`s method relay optimum control by criterion of accuracy of regulating function of switching and corresponding to this optimum control is defined. The method of decomposition of control process on n control intervals is for this purpose applied, on each of which there is continuous partial derivative Bellman`s function and, hence, the functional equations on each interval are fair. In an investigated method optimising functional is a real and concrete criterion of performance. Synthesised laws of control by criterion of accuracy of regulating also can provide multicriteria optimization of transients in system: optimum on accuracy and simultaneously optimum on fast operation, or optimum on accuracy and simultaneously optimum on an energy consumption. At the expense of emersion in system of zeroovershoot responses double invariance as to any (including, casual) to external affectings, and to changes of parametres of control object is provided. On synthesis examples clear advantages of method ADOR by criterion of accuracy of regulating as concerning the elementary procedures of analytical control laws disign for nonlinear objects, and concerning validity of analytical definition of parametres of regulators depending on extent of fast operation of optimum regulating on accuracy in the closed system are illustrated.