PID Adaptive Control Design Based on Singular Perturbation Technique: A Flight Control Example
The paper treats a question of proportional-integral-derivative (PID) controller design for aircraft pitch attitude in the presence of uncertain aerodynamics. The presented design methodology guarantees desired pitch attitude transient performance indices by inducing of two-time-scale motions in the closed-loop system where the controller dynamics is a singular perturbation with respect to the system dynamics. 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 pitch attitude transient performances are desired and insensitive to external disturbances and variations of aerodynamic characteristics. The singular perturbation method is used throughout the paper in order to get explicit expressions for evaluation of the controller parameters. The high-frequency-gain online identification and gain tuning are incorporated in the control loop in order to maintain the stability of the fast-motion transients for large range of aerodynamic characteristics variations. Numerical example and simulation results are presented.