PID Controller Design for Nonlinear Systems Based on Two-Time-Scale Motions

The paper treats in a tutorial manner a question of PI and PID controller design in the presence of plant's parameter variations and unknown external disturbances. The presented design methodology of PID control guarantees desired transients by inducing of two-time-scale motions in the closed-loop system. Stability conditions imposed on the fast and slow modes 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 transient performances are desired and insensitive to external disturbances and plant's parameter variations. The method of singular perturbations is used throughout the paper.