This paper proposes a modeling method for fully closed-loop system of hemispherical resonator gyroscope (HRG) under force-to-rebalance mode. A fully closed-loop system consists of two parts: driving loop and detecting loop. First, dynamic equations of driving loop are derived to obtain vibration differential equations of a hemispherical resonator driven by electrostatic forces, further obtain accurate output models of wave amplitude and angular rate, which establishes a model of driving loop. Next, the output model of wave amplitude is analyzed to clarify the relationship between amplitude voltage and wave amplitude. Simultaneously, influences of interference factors on amplitude voltage and angular rate voltage are analyzed, which can result in the HRG output error. Then, a model of detecting capacitance is built based on deformation equations of the hemispherical resonator. A model of detecting loop is established to analyze its performance and precision. Finally, by tests of amplitude voltage and resonant frequency, accuracy of the models of driving loop and detecting loop is proved. A model of fully closed-loop system of the HRG is proposed based on the models of driving loop and detecting loop. The HRG output errors caused by resonator’s deformation, detecting error and nonuniformity of quality factor are identified and compensated accurately by the proposed model. It is verified by simulations and tests that the proposed model of fully closed-loop system is effective, which can not only identify the main errors of the HRG accurately, but also provide an accurate model for error analysis.

Preserving data privacy in data-driven modeling for the Industrial Internet of Things (IIoT) has become critically important due to the susceptibility of communication data from numerous devices to cyber-attacks. Given its multi-subsystem integration, nonlinear interactions, and networking characteristics, IIoT can be modeled as nonlinear networked systems (NNSs). This paper presents a federated learning-based offset-free distributed control (FL-OFDC) method for NNSs with multiple subsystems to preserve data privacy and achieve offset-free control, with potential applications to IIoT. First, a novel FL algorithm with personalized optimization (FLPO) is proposed to simultaneously obtain global and local models using a simple algorithm framework, which can preserve data privacy and address the heterogeneity issue among subsystems. Subsequently, a novel information-theoretic bound for the generalization error of the FLPO algorithm with iteration properties is constructed using individual sample mutual information. Next, an FL-OFDC scheme for NNSs under external disturbances is developed to eliminate the offset, and its closed-loop stability criteria are derived. Finally, a chemical process network, that is, a specific case of IIoT, is employed to demonstrate the practicality of the FLPO and FL-OFDC methods.

Vibratory gyroscopes are the most ideal inertial sensors in the 21st century. The amplitude is an important index of vibratory gyroscopes. This article investigates an asynchronous tracking control approach for amplitude signals in vibratory gyroscopes. Since the manufacturing error of vibratory gyroscopes can result in the stochastic signal of the amplitude, Markov stochastic systems are adopted to approximate vibratory gyroscopes. Because the stochastic signal results in the amplitude jitter, a novel doubly fed tracking controller with the stochastic stability performance is proposed for reducing the amplitude jitter. In the practical application, regarding the known degree of the stochastic process, the partially unknown mode information is approximately given. By considering the asynchronous phenomenon between the system mode and controller mode, a hidden Markov model is constructed to name the resultant tracking error system. It is proved that the tracking error system is stochastically stable. Furthermore, the presented asynchronous tracking controller can well track the reference amplitude signal and significantly reduce the amplitude jitter. Finally, comparative results show the control precision of amplitude signals is significantly improved such that the better precision and performance of vibratory gyroscopes are achieved, which demonstrates the effectiveness and practicability of the proposed control approach.

The Hemispherical Resonator Gyro (HRG) is a solid-state and widely used vibrating gyroscope, especially in the field of deep space exploration. The flat-electrode HRG is a new promising type of gyroscope with simpler structure that is easier to be fabricated. In this paper, to cover the shortage of a classical generalized Coriolis Vibration Gyroscope model whose parameters are hard to obtain, the model of flat-electrode HRG is established by the equivalent mechanical model, the motion equations of unideal hemispherical shell resonator are deduced, and the calculation results of parameters in the equations are verified to be reliable and believable by comparing with finite element simulation and the reported experimental data. In order to more truthfully reveal the input and output characteristics of HRG, the excitation and detection models with assemble errors and parameters are established based on the model of flat-electrode capacitor, and they convert both the input and output forms of the HRG model to voltage changes across the electrodes rather than changes in force and capacitance. An identification method of assemble errors and parameters is proposed to evaluate and improve the HRG manufacturing technology and adjust the performance of HRG. The average gap could be identified with the average capacitance of all excitation and detection capacitors; fitting the approximate static capacitor model could identify the inclination angle and direction angle. With the obtained model, a firm and tight connection between the real HRG system and theoretical model is established, which makes it possible to build a fully functional simulation model to study the control and detection methods of standing wave on hemispherical shell resonator.

Contextual information has been widely used to improve results of semantic segmentation. However, most approaches investigate contextual dependencies through self-attention and lack guidance on which pixels should have strong (or weak) relationships. In this paper, a category-guided graph convolution network (CGGCN) is proposed to reveal the relationships among pixels. First, we train a coarse segmentation map under the supervision of the ground truth and use it to construct an adjacency matrix among pixels. It turns out that the pixels belonging to the same category have strong connections, and those belonging to different categories have weak connections. Second, a GCN is exploited to enhance the representation of pixels by aggregating contextual information among pixels. The feature of each pixel is represented by node, and the relationship among pixels is denoted by edge. Subsequently, we design four different kinds of network structures by leveraging the CGGCN module and determine the most accurate segmentation result by comparing them. Finally, we reimplement the CGGCN module to refine the final prediction from coarse to fine. The results of extensive evaluations demonstrate that the proposed approach is superior to the existing semantic segmentation approaches and has better convergence.