Fixed-Feedback SISO Adaptive Control

Doctoral thesis, 2010

Adaptive control is an attractive method to solve control problems since the tedious task of identifying process behavior to find a suitable design for the controller is taken care of by the adaptive controller itself. It may be difficult, however, to guarantee robustness (in the sense of desired disturbance attenuation and stability margins) for traditional adaptive schemes since their corresponding loop gain is time varying. This is part of the reason why adaptive control has not yet found widespread use in industry. This thesis focuses on an adaptive-control structure whose adaptive feature is restricted to the open-loop or feedforward part of a two-degrees-of-freedom controller. It may be seen as a traditional model reference adaptive controller with fixed loop gain. This can lead to easier robustness analysis (in the sense of desired disturbance attenuation and stability margins) compared to traditional adaptive schemes whose loop gains are time varying. Although the underlying idea of feedforward adaptation is simple and natural, little research has been carried out on how it should be applied. Existing schemes which resemble the structure investigated herein, such as Feed\-back Error Learning and Simple Adaptive Control, require the feedback loop to be strictly positive real to guarantee error convergence. This condition is successfully removed in this thesis by basing the update law on an estimation error or a prediction error instead of a tracking error. Parameter projection is applied to guarantee the desired convergence properties. The control structure is not merely of academic nature. Industrial control problems exist where the structure may be a suitable alternative to other adaptive-control schemes. The scheme is therefore simulated for possible industrial problems, and different update laws are evaluated in the appended papers. The results in this thesis may be helpful for engineers that consider to use modest adaptation to solve industrial control problems.