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.