Realtime controller tuning for periodic disturbance rejection with application to active noise control
Incomplete knowledge of either plant or disturbance dynamics complicates the design of a feedback control system. Uncertainty in plant dynamics can cause feedback instabilities and should at least be considered in the context of stability robustness. Inaccurate controller design due to uncertainty in disturbance dynamics will not destabilize the system but may deteriorate feedback performance. In this dissertation, we develop and analyze methods that can be used tune feedback controllers to overcome these two difficulties. Incomplete knowledge of disturbance dynamics, with exact knowledge of the plant, can be addressed by designing a family of controllers, identifying the disturbance model, and tuning the controller by switching from the current controller to the optimal controller in realtime. Care must be taken during tuning, especially if the disturbance model is changing in time. Rapidly switching between controllers during tuning can destabilize the feedback system even if each individual controller is by itself stabilizing. To address this issue, we present two different methods that guarantee stability during tuning. In addition to stability considerations, the question of complete regulation of time-varying disturbances remains. When dealing with time-invariant deterministic disturbance models, the internal model principle dictates that a suitably replicated model of the disturbance dynamics be placed in the feedback path. Does this principle still hold if the disturbance model is time-varying? In this dissertation, it is proven that this principle holds for time-varying disturbance added to the input of the plant, but will not hold in general for disturbances added to the output of the plant. This is strikingly different from the classical time-invariant case, where the cancellation of input and output disturbances can be accomplished with the same time-invariant controller. Finally, the situation where the disturbance and the plant models are both uncertain is considered, and a new algorithm is develop to cancel the uncertain disturbance while maintaining robust stability. The algorithm is developed by considering simultaneous perturbations to the plant and controller. The plant perturbation is used to represent the uncertainty in the plant model and the controller perturbation is identified with the algorithm to achieve the performance goals in the presence of the robustness constraints. A method of representing the plant uncertainty is presented that uses a nominal model, associated unstructured uncertainty, and weighting filters for the uncertainty. The nominal model is found to enhance the performance of the tuning algorithm, and a fixed-order weighting filter is found via convex optimization by posing and solving a spectral bounding problem. It is shown how the framework of simultaneous plant and controller perturbations can be used to recast the realtime tuning of a feedback controller as a robust estimation problem. The formulation as an estimation problem allows tuning of the controller in realtime on the basis of closed loop system data. Furthermore, robust estimation is obtained by constraining the parameter estimates so that feedback stability will be maintained during controller tuning in the presence of plant uncertainty. The combination of realtime tuning and guaranteed stability robustness opens the possibility to perform Robust Estimation for Automatic Controller Tuning (REACT) to slowly varying disturbance spectra. The procedure is illustrated via the active noise cancellation of cooling fans, where narrow-band disturbances are suppressed.