A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form

A systematic method to select gains of a discrete proportional-integral-derivative (PID) controller is presented. The PID controller with the gains obtained by the proposed method can robustly control nonlinear multiple-input-multiple-output (MIMO) plants in a second-order controller canonical form, such as robot dynamics. This method has been made possible by the finding that the discrete PID control is equivalent to the discrete form of time-delay control (TDC), a robust control method for nonlinear plants with uncertainty. By using this equivalence, relationships are obtained between PID gains and parameters of TDC, which enable a systematic method for the select PID gains. In addition, based on the systematic method, a simple and effective method is proposed to tune PID gains applicable to nonlinear plants with inaccurate models. This method incorporates a set of independent tuning parameters that is far less than those for conventional methods for PID gain selection. The usefulness of the proposed methods is verified through the ease and simplicity of determining PID gains for six degrees-of-freedom (DOF) programmable universal machine for assembly (PUMA)-type robot manipulator; the effectiveness of these PID gains is confirmed by the adequate and robust performance through experimentation on the robot.