The aim of this paper is to present a way of ranking the nonlinearities of electrodynamic loudspeakers. For this purpose, we have constructed a nonlinear analytic model which takes into account the variations of the small signal parameters. The determination of these variations is based on a very precise measurement of the electrical impedance of the electrodynamic loudspeaker. First, we present the experimental method to identify the variations of these parameters, then we propose to study theoretically the importance of these nonlinearities according to the input level or the input frequency. We show that the parameter which creates most of the distortions is not always the same and depends mainly on both the input level and the input frequency. Such results can be very useful for optimization of electrodynamic loudspeakers.
Model predictive control (MPC) algorithms brought increase of the control system performance in many applications thanks to relatively easily solving issues that are hard to solve without these algorithms. The paper is focused on investigating how to further improve the control system performance using a trajectory of parameters weighting predicted control errors in the performance function of the optimization problem. Different shapes of trajectories are proposed and their influence on control systems is tested. Additionally, experiments checking the influence of disturbances and of modeling uncertainty on control system performance are conducted. The case studies were done in control systems of three control plants: a linear non- minimumphase plant, a nonlinear polymerization reactor and a nonlinear thin film evaporator. Three types of MPC algorithms were used during research: linear DMC, nonlinear DMC with successive linearization (NDMC–SL), nonlinear DMC with nonlinear prediction and linearization (NDMC–NPL). Results of conducted experiments are presented in greater detail for the control system of the polymerization reactor, whereas for the other two control systems only the most interesting results are presented, for the sake of brevity. The experiments in the control system of the linear plant were done as preliminary experiments with the modified optimization problem. In the case of control system of the thin film evaporator the researched mechanisms were used in the control system of a MIMO plant showing possibilities of improving the control system performance.