A class of PID controllers tuned in fractional representation

Abstract

The contribution is focused on design and tuning of simple controllers for continuous-time SISO systems without and with time delays by algebraic methods. The control synthesis is based on general solutions of linear Diophantine equations in the ring of proper and Hurwitz stable rational functions (R PS). Both, feedback (1DOF) a feedback and feed forward (2DOF) structures of the control system are considered. A scalar positive parameter is introduced for tuning and influencing control responses. In the paper, this parameter is used for aperiodic tuning of PI controllers. The methodology is utilized for autotuning principles and for robust applications. Interval perturbations in controlled systems and robustness of proposed algorithms are outlined through the value set concept, zero exclusion condition and Kharitonov theorem. For both applications user-friendly program packages were developed in the Matlab+Simulink environment with the support of Polynomial Toolbox.