A novel ultrasonic levitating bearing excited by three piezoelectric transducers is presented in this work. The transducers are circumferentially equispaced in a housing, with their center lines going through the rotation center of a spindle. This noncontact bearing has the ability to self-align and carry radical and axial loads simultaneously. A finite element model of the bearing is built in ANSYS, and modal analysis and harmonious response analysis are conducted to investigate its characteristics and driving parameters. Based on nonlinear acoustic theory and a thermodynamic theory of ideal gas, the radical and lateral load-carrying models are built to predict the bearing's carrying capacity. In order to validate the bearing's levitation force, a test system is established and levitating experiments are conducted. The experimental data match well with the theoretical results. The experiments reveal that the maximum radical and axial levitating loads of the proposed bearing are about 15 N and 6 N, respectively, when the piezoelectric transducers operate at a working frequency of 16.11 kHz and a voltage of 150 V p-p .
High-accuracy motion tracking of hydraulic systems is of great significance in industrial applications. Nevertheless, dynamic nonlinearity, modeling uncertainty, generalized disturbance, and measurement noise are inevitably existed in hydraulic systems, which severely deteriorates the practical control performance. Aimed at enhancing the motion-tracking accuracy of hydraulic systems, a novel command filtered adaptive backstepping controller with extended state observer is proposed in this article. On the basis of the established system’s nonlinear model, the extended state observer utilizing only position output feedback information is first designed to estimate the system’s unmeasurable states, and time-varying disturbances of the hydraulic system are also obtained for subsequent active disturbance compensation. Next, a second-order command filter is constructed to generate specific command signals and their derivatives, which significantly simplifies the controller design process by avoiding complicated analytical differential calculations in contrast to traditional adaptive backstepping algorithm. Subsequently, with consideration of system’s nonlinearity, parametric uncertainty, and time-varying disturbance, the developed extended state observer and command filter are introduced into the adaptive backstepping design process of the proposed controller, and theoretical stability of the proposed controller is guaranteed via Lyapunov analysis. Finally, the effectiveness and superiority of the proposed controller are demonstrated by comparative experimental results.
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