Multiple-Time-Scale Nonlinear Output Feedback Control of Systems With Model Uncertainties

Abstract

Systems with dynamics evolving in distinct slow and fast timescales include aircraft (Khalil & Chen, 1990), robotic manipulators, (Tavasoli, Eghtesad, & Jafarian, 2009), electrical power systems (Sauer, 2011), chemical reactions (Mélykúti, Hespanha, & Khammash, 2014), production planning in manufacturing (Soner, 1993), and so on. The Geometric Singular Perturbation theory (Fenichel, 1979) is a powerful control law development tool for multiple-timescale systems because it provides physical insight into the evolution of the states in more than one timescale. The behaviour of the full-order system can be approximated by the slow subsystem, provided that the fast states can be stabilised on an equilibrium manifold. The fast subsystem describes how the fast states evolve from their initial conditions to their equilibrium trajectory or the manifold. This presentation develops two nonlinear, multiple-time-scale, output feedback tracking controllers for a class of nonlinear, nonstandard systems with slow and fast states, slow and fast actuators, and model uncertainties. The class of systems is motivated by aircraft with uncertain inertias, control derivatives, engine time-constant, and without direct measurement of angle-of-attack and sideslip angle. One controller achieves the control objective of slow state tracking, while the other does simultaneous slow and fast state tracking. Each controller is synthesized using time-scale separation, lower-order reduced subsystems, and estimates of unknown parameters and unmeasured states. The estimates are updated dynamically, using an online parameter estimator and a nonlinear observer. The update laws are so chosen that errors remain ultimately bounded for the full-order system. The controllers are simulated on a six-degree-of-freedom, high-performance aircraft model commanded to perform a demanding, combined longitudinal and lateral/directional maneuver. Even though two important aerodynamic angles are not measured, tracking is adequate and as good as a previously developed full-state feedback controller handling similar parametric uncertainties. Additionally, even though the two controllers in theory achieve two different control objectives, it is possible to choose either one of them for the same maneuver. Of the two new output feedback controllers, the slow state tracker accomplishes the maneuver with less control effort, while the simultaneous slow and fast state tracker does so with a smaller number of gains to tune.