Adaptive Control of Systems in Cascade with Saturation
Kannan, Suresh Kumar
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This thesis extends the use of neural-network-based model reference adaptive control to systems that occur as cascades. In general, these systems are not feedback linearizable. The approach taken is that of approximate feedback linearization of upper subsystems whilst treating the lower-subsystem states as virtual actuators. Similarly, lower-subsystems are also feedback linearized. Typically, approximate inverses are used for linearization purposes. Model error arising from the use of an approximate inverse is minimized using a neural-network as an adaptive element. Incorrect adaptation due to (virtual) actuator saturation and dynamics is avoided using the Pseudocontrol Hedging method. Using linear approximate inverses and linear reference models generally result in large desired pseudocontrol for large external commands. Even if the provided external command is feasible (null-controllable), there is no guarantee that the reference model trajectory is feasible. In order to mitigate this, nonlinear reference models based on nested-saturation methods are used to constrain the evolution of the reference model and thus the plant states. The method presented in this thesis lends itself to the inner-outer loop control of air vehicles, where the inner-loop controls attitude dynamics and the outer-loop controls the translational dynamics of the vehicle. The outer-loop treats the closed loop attitude dynamics as an actuator. Adaptation to uncertainty in the attitude, as well as the translational dynamics, is introduced, thus minimizing the effects of model error in all six degrees of freedom and leading to more accurate position tracking. A pole-placement approach is used to choose compensator gains for the tracking error dynamics. This alleviates timescale separation requirements, allowing the outer loop bandwidth to be closer to that of the inner loop, thus increasing position tracking performance. A poor model of the attitude dynamics and a basic kinematics model is shown to be sufficient for accurate position tracking. In particular, the inner-outer loop method was used to control an unmanned helicopter and has subsequently been applied to a ducted-fan, a fixed-wing aircraft that transitions in and out of hover, and a full-scale rotorcraft. Experimental flight test results are also provided for a subset of these vehicles.