Method of Large Coefficients in Synthesis of the Parametrically Robust Systems of Modal Control

Abstract

Parametric robustness is an important property of the systems synthesized by analytical methods. The article presents a solution to the problem of the parametrical robustness of the modal control systems with polynomial regulators, during which the parameters can vary in a wide range. The authors investigate a possible application of the approach, the basis of which is the use of a high coefficient of amplification in the control path. They also analyze certain methods of the robust systems' synthesis: the method of high coefficients of amplification by V. M. Meerov and the method of localization (control with the use of higher derivative) by A. S. Vostrikov. Their advantages and disadvantages are noted. The methodology of the synthesis of the automatic control single-loop system with polynomial regulators is proposed, it guarantees both a high coefficient of amplification in the control path and the necessary quality of the transients (operating speed and nature of the process). A high coefficient of amplification ensures the parametrical robustness and high static accuracy for the system. The methodology is based on the formation of a characteristic system of a polynom with two groups of roots: "fast" and "slow", the former one ensures a high coefficient of amplification and, consequently, a parametrical robustness, the latter ensures the quality of the transients. A possibility of variation within the magnitude of the "fast" roots of the characteristic polynom allows us to choose the rate of the automatic control of the system's robustness. The article presents versions of synthesis of the regulators with an irregular (physically unrealizable, differential), and a regular (physically realizable) transfer functions. The research based on a computing experiment with the use of the mathematical model of the typical dual-mass electromechanical object and variation of the control member moment of inertia as a parameter, most susceptible to alternation, confirmed the efficiency of the proposed synthesis methodology. In the supplement the authors provide confirmation of the given approach allowing one to increase the coefficient of amplification with preservation of the quality of the transients.