| The main exercise of this thesis is the formulation of a mathematical framework for analyzing an existing industrial adaptive control algorithm labeled Model weighting adaptive control (MWAC). The algorithm is then analyzed under this framework. The exercise is complemented by a set of algorithmic additions aimed at solving questions that so far had remained open (e.g. the treatment of undermodelling errors). Those solutions, on the other hand build on results derived from the analysis.; A key result for analyzing the algorithm is that when an external excitation is applied (in the form of a control task such as a setpoint change), the adaptive controller behaves, in a short time that follows the application of the excitation, as a linear equation whose parameters are completely known at design time. It follows that during this short period, the input signal provided to the estimation subsystem is at least partially known (except for disturbances) and that the estimation virtually takes place in open loop. Using this information and assuming boundedness of the disturbance signals, it is possible to bound the behaviour of the adaptive system at an early stage.; With the MWAC algorithm, the plant model is formed by making a weighted sum of a finite number of possible plant models. It is shown that, under adequate conditions and in a time corresponding to the apparent plant delay, the plant model will “jump” to a neighborhood of the true plant. The size of this neighborhood will depend in part on how sharply the bad models are discriminated from the good models. On the other hand, disturbances will smooth the weight map towards a uniform distribution. The sharpness or smoothness of the weight map can be measured online by computing the sum of the square root of all the weights in the set. The remarkable property of this measure is that an upper bound on the distance between the true plant and its model can be found which an affine function of the measure.; The effect of external disturbances such as measurement errors can be reduced by an external excitation of sufficient magnitude. This is not true however of disturbances caused by undermodelling errors which are almost always present to a lesser or greater degree. Two solutions are proposed to counteract this undesirable effect. The first method consists in bandpass filtering the input/output data in such a way that the frequency content of the data is consistent with data obtained from some first order plus delay (FOPD) model. The second method adjusts the sampling period online such that a compromise between satisfying the FOPD assumption and the coarseness of the control is obtained. |
