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.