A New Data-Driven Approach to Robust PID Controller Synthesis

Recently, a new data-driven approach has been proposed for synthesizing the family of stabilizing PID controllers where the proposed approach could not handle any type of uncertainty in the plant model. This paper extends that results to plants with single uncertainty or uncertain plants that can be approximated as plants with a dominant uncertain parameter. It is shown that if an unknown plant with an uncertain parameter satisfies the certain inequalities in terms of real and imaginary parts of the specified plants, then the family of robust stabilizing PID controllers could be obtained using the frequency responses of only two plants corresponding to extreme values of uncertain parameter. No mathematical model is needed and the resulted controller is non-fragile toward its coefficients' variations. In addition, an exact low frequency band over which the plant data must be known with desired accuracy is sufficient for the controller synthesis and beyond this band the plant data might be approximated. The simulation results on harmonic drive system (HDS) subject to loss of actuator effectiveness show the efficiency of the proposed approach.