The paper presents application of a modified, symmetrical Bouc-Wen model to simulate the mechanical behaviour of high-frequency piezoelectric actuators (PAs). In order to identify parameters of the model, a two-step algorithm was developed. In its first stage, the mechanical parameters were identified by taking into account their bilinear variability and using a square input voltage waveform. In the second step, the hysteresis parameters were determined based on a periodic excitation. Additionally, in order to reduce the influence of measurement errors in determination of selected derivatives the continuum wavelet transform (CWT) and translation-rotation transformation (TRT) methods were applied. The results proved that the modified symmetrical Bouc-Wen model is able to describe the mechanical behaviour of PAs across a wide frequency range.
Today, a cascaded system of position loop, velocity loop and current loop is standard in industrial motion controllers. The exact knowledge of significant parameters in the loops is the basis for the tuning of the servo controllers. A new method to support the commissioning has been developed. It enables the user to identify the moment of inertia as well as the time constant of the closed current loop simultaneously. The method is based on the auto relay feedback experiment by Aström and Hägglund. The model parameters are automatically adjusted according to the time behaviour of the controlled system. For this purpose, the auto relay feedback experiment is combined with the technique of gradual pole compensation. In comparison to other existing methods, this approach has the advantage that a parametric model for the open velocity loop is derived directly.
An on-line optimising control strategy involving a two level extended Kalman filter (EKF) for dynamic model identification and a functional conjugate gradient method for determining optimal operating condition is proposed and applied to a biochemical reactor. The optimiser incorporates the identified model and determines the optimal operating condition while maximising the process performance. This strategy is computationally advantageous as it involves separate estimation of states and process parameters in reduced dimensions. In addition to assisting on-line dynamic optimisation, the estimated time varying uncertain process parameter information can also be useful for continuous monitoring of the process. This strategy ensures that the biochemical reactor is operated at the optimal operation while taking care of the disturbances that are encountered during operation. The simulation results demonstrate the usefulness of the two level EKF assisted dynamic optimizer for on-line optimising control of uncertain nonlinear biochemical systems.
The article aims at presenting the philosophy and model of the development vehicle to be understood as a new concept and tool to investigate and program local and regional development processes. The practical issues covered by the article include the identification and discovery of development vehicles, the elements of which can be observed in Polish metropolitan areas and agglomerations.
In this paper, the MFC sensor and actuators are applied to suppress circular plate vibrations. It is assumed that the system to be regulated is unknown. The mathematical model of the plate was obtained on the base of registration of a system response on a fixed excitation. For the estimation of the system’s behaviour the ARX identification method was used to derive the linear model in the form of a transfer function of the order nine. The obtained model is then used to develop the linear feedback control algorithm for the cancellation of vibration by using the MFC star-shaped actuator (SIMO system). The MFC elements location is dealt with in this study with the use of a laser scanning vibrometer. The control schemes presented have the ability to compute the control effort and to apply it to the actuator within one sampling period. This control scheme is then illustrated through some numerical examples with simulations modelling the designed controller. The paper also describes the experimental results of the designed control system. Finally, the results obtained for the considered plate show that in the chosen frequency limit the designed structure of a closed-loop system with MFC elements provides a substantial vibration suppression.