PI and PID controller design for nonlinear systems in the presence of a time delay via singular perturbation technique

The paper treat a question of proportional-integral and proportional-integral-derivative (PM) controller design for nonlinear same in the presence of a time delay, plant's parameter variations, and unknown external disturbances. The design of a universal controller, which is an extension of PI (PID) controller, I discussed as well The presented design methodology guarantees desired output transient performance indices by inducing of two-time-scale motions in the closed loop system. Stability conditions imposed on the fast and slow mode and sufficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop nonlinear system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and plant's parameter variations. The method of singular perturbations is used throughout the paper in order to got explicit expressions for evaluation of the controller parameters. Numerical examples with simulation results are presented.