A New Data Driven Approach to Robust PID Controller Synthesis

Abstract

Recently, a new data-driven approach is proposed for synthesizing the family ofstabilizing PID controllers. The proposed approach couldn’t handle any type of uncertainty inthe plant model. This paper extends that results to plants with single uncertainty or uncertainplants that can be approximated as plants with a dominant uncertain parameter. It is shown thatif an unknown plant with an uncertain parameter satisfies the certain inequalities in terms of realand imaginary parts of the specified plants, then the family of robust stabilizing PID controllerscould be obtained using the frequency spectrum of only two plants corresponding to extremevalues of uncertain parameter. No mathematical model is needed and the resulted controller cansuffer from the variation in its coefficients. In addition, an exact low frequency band over whichthe plant data must be known with desired accuracy is sufficient for the controller synthesis andbeyond this band the plant data might be approximated. The simulation results on harmonicdrive system (HDS) subject to loss of actuator effectiveness show the efficiency of the proposedapproach.