The paper presents proposal of a model of the fluidized bed boiler adapted for use in model-based controllers e.g. predictive, adaptive or internal model control (IMC). The model has been derived in the form of transfer function matrix which allows its direct implementation in the controller structure. Formulated model takes into consideration the principal cross-coupling between process variables which enables the opportunity to search for feasibility of decoupling control. The results of the identification of the dynamics of the 2 MW industrial bubbling fluidized bed boiler using the proposed model form was presented. According to the experimental data it was found that despite of introduced simplifications presented model allows the boiler behavior prediction.

In this paper, the adaptive control based on symbolic solution of Diophantine equation is used to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The plate is excited by a uniform force over the bottom surface generated by a loudspeaker. The axially-symmetrical vibrations of the plate are measured by the application of the strain sensors located along the plate radius, and two centrally placed piezoceramic discs are used to cancel the plate vibrations. The adaptive control scheme presented in this work has the ability to calculate the error sensor signals, to compute the control effort and to apply it to the actuator within one sampling period. For precise identification of system model the regularized RLS algorithm has been applied. Self-tuning controller of RST type, derived for the assumed system model of the 4th order is used to suppress the plate vibration. Some numerical examples illustrating the improvement gained by incorporating adaptive control are demonstrated.