Analytical Algorithms for Synthesis of Modal Controllers by the Maximum Stability Degree Criterion

Abstract

The practice of synthesis the controllers demonstrates, that for the determination of the dynamic tuning parameters of the controller is more convenient to operate with the analytical expressions with a low volume of calculations that dependent on the known parameters of control object. The analytical synthesis expressions, on the one hand have the advantage of decreasing the volume of calculation of tuning parameters (compared with the synthesis methods and algorithms that include a number of steps) and, by the other hand, using of the analytical expressions is a good alternative in case of the controllers with auto-tuning and adaptive control, where the controller retuning is done in function of the parameters variation of the control object during operation of the control system. Based on this consideration, in this paper it is proposed the analytical algorithms of synthesis the modal controllers, in form of algebraic expressions, for control objects with arbitrary order inertia and astatism by the maximum stability degree criterion. This criterion offers to the designed control systems an aperiodic step response, high performance and better robustness. The elaborated algorithms represent simple analytical procedures with reduced volume of calculation and without any imposing conditions to the complexity of the control object. They allow also to impose or to optimize the settling time of the designed automatic control system.