Free-model-based adaptive controller for nonlinear dynamic systems

This thesis presents the concept of the free model and its implementation in the design of neuro-identifier and neuro-controller in the model reference adaptive control scheme for nonlinear dynamic systems. By applying the backward difference operator, the free model is developed for identification of an unknown dynamic system, and this does not require the knowledge of mathematical model and sampling time for the system, but uses only its input and output measurements. Since the free model is developed to be system independent, it has a particular application to nonlinear systems in general.; The approximation error is derived for the free-model representation and conditions for satisfactory approximation performance are discussed. Under certain conditions, it is shown that the increased free-model order does not improve the approximation performance significantly when a suitable free-model order is chosen. The approximated Taylor series is derived and compared with the free-model representation, and their differences call for the adaptation of weights in the free-model representation. When implemented in neural networks, the free-model based neuro-identifier becomes a direct adaptive predictor. In identifying a certain class of dynamic systems, the free-model based neural network is shown to have smaller sum-squared errors than the conventional neural network in the initial phase of training.; In order to utilize the smaller error of the free-model based neural network, the on-line training of the model reference adaptive control scheme is applied to control an unknown plant. Depending on the memory requirement, two different sets of stability conditions for both neuro-identifier and neuro-controller in the control scheme are derived. For more complicated plants, an off-line version of the model reference adaptive control scheme is developed also.; The usefulness of the free-model based model reference adaptive control scheme is demonstrated through numerical examples by comparing it with the use of conventional neural networks. The on-line version of the control scheme is applied in different nonlinear plants with satisfactory performance. The off-line version of the control scheme is applied to the benchmark inverted pendulum problem and its satisfactory tracking and disturbance rejection performance is demonstrated. Finally, the control scheme is applied to a boiler-turbine power plant as a practical system. The performance of the control scheme is examined both locally and globally. Satisfactory performance is demonstrated even when the plant is moving between different operating points.