Parametric Synthesis of Fractional-Order PID Controller for Given Oscillability Degree

The paper considers the parametric synthesis of a fractional-order PID controller, based on the optimization of the integral error with a pole placement, constrained by an oscillability degree as a damping ratio analog. Using the criterion for a low-frequency disturbance rejection (LFDR) allows reducing the number of tuning parameters. The research is conducted in the computer algebra system Maple. An algorithm and a program for calculating the settings of the fractional order PID controller are developed. The algorithm is checked on the test cases, including astatic and unstable processes, processes with time delay. The nomograms of controller’s settings for the first order plus time delay (FOPDT) process model is received.