Analytical synthesis algorithms of the controllers for the automatic control systems with maximum stability degree and imposed performance

Elaboration of the analytical algorithms for synthesis of typical controllers P, PD, PI and PID to the objects with arbitrary order of inertia and time delay, using the maximum stability degree criterion is proposed in this paper. The dependencies between dominant roots of the designed system and its dynamical performance were used. There were obtained the analytical expressions for calculation the maximum stability degree of the system and the values of dynamical parameters of typical controllers in dependence of known parameters of the control object and imposed performance: damping degree, oscillation degree, overshoot and settling time. To demonstrate the efficiency of proposed algorithms were analyzed three examples of tuning the typical algorithms to the diverse models of objects with imposed performance of the designed system.