Torsional Vibration Response of Helical Gears Under Non-Linear Time-Varying Parameters Using HBM

Faced with serious growing global warming problem, it is important to predict carbon emissions. As there are a lot of factors affecting carbon emissions, a novel multi-variable grey model (GM(1,N) model) based on linear time-varying parameters discrete grey model (TDGM(1,N)) has been established. In this model, linear time-varying function is introduced into the traditional model, and dynamic optimization of fixed parameters which can only be used for static analysis is carried out. In order to prove the applicability and effectiveness of the model, this paper compared the model with the traditional model and simulated the carbon emissions of Anhui Province from 2005 to 2015. Carbon emissions in the next two years are also predicted. The results show that the TDGM(1,N) model has better simulation effect and higher prediction accuracy than the traditional GM(1,N) model and the multiple regression model(MRM) in practical application of carbon emissions prediction. In addition, the novel model of this paper is also used to predict the carbon emissions in 2018–2020 of Anhui Province.

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Fractional-Order Accumulative Linear Time-Varying Parameters Discrete Grey Forecasting Model

Mathematical Problems in Engineering ◽

10.1155/2019/6343298 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Pumei Gao ◽

Jun Zhan ◽

Jiefang Liu

Keyword(s):

Fractional Order ◽

Linear Time ◽

Forecasting Model ◽

Time Varying ◽

Order Linear ◽

Varying Parameters ◽

Grey Forecasting ◽

Grey Forecasting Model ◽

Significant Downward Trend ◽

Time Varying Parameters

Traditional discrete grey forecasting model can effectively predict the development trend of the stabilizing system. However, when the system has disturbance information, the prediction result will have larger error, and there will appear significant downward trend in the stability of the model. In the presence of disturbance information, this paper presents a fractional-order linear time-varying parameters discrete grey forecasting model to deal with the system that contains both linear trend and nonlinear trend. The modeling process of the model and calculation method are given. The perturbation bounds of the new model are analyzed by using the least-squares method of perturbation theory. And it is compared with that of the first-order linear time-varying parameters discrete grey forecasting model. Finally, two real cases are given to verify the effectiveness and practicality of the proposed method.

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Control of Dynamic Systems With Nonlinearities and Time Varying Parameters

14th Biennial Conference on Mechanical Vibration and Noise: Dynamics and Vibration of Time-Varying Systems and Structures ◽

10.1115/detc1993-0114 ◽

1993 ◽

Author(s):

Dirk Söffker ◽

Peter C. Müller

Keyword(s):

Dynamic Systems ◽

Disturbance Rejection ◽

Linear Time ◽

Time Varying ◽

Varying Parameters ◽

Linear Time Invariant ◽

Time Variance ◽

Disturbance Rejection Control ◽

Time Varying Parameters ◽

Time Invariant

Abstract The well-known theory of disturbance rejection control and the experience of using a generalized technique with universal fault model for building observers and regulators for the estimation and compensation of disturbances and unmodeled or uncertain effects as well, could be used for controlling dynamic systems with time varying parameters and nonlinearities. Based on a linear time-invariant model the effects of non-linearities and unmodeled dynamics are estimated by an extended observer scheme. Using this information these dynamic effects will be compensated by the developed compensation scheme. Here also different compensation techniques of disturbance rejection control are discussed, compared, and modified. The simulation example of an inverted flexible pendulum shows the efficiency of the method controlling an unstable mechanical system without exact knowledge of structure and parameters of nonlinearity and time-variance.

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Modelling and control of urea-SCR systems through the triple-step non-linear method in consideration of time-varying parameters and reference dynamics

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331216656754 ◽

2016 ◽

Vol 40 (1) ◽

pp. 287-302 ◽

Cited By ~ 4

Author(s):

Jinghua Zhao ◽

Yunfeng Hu ◽

Xun Gong ◽

Hong Chen

Keyword(s):

Catalytic Reduction ◽

Operation Mode ◽

Linear Method ◽

Design Procedure ◽

Time Varying ◽

Varying Parameters ◽

Coverage Ratio ◽

Time Varying Parameters ◽

Non Linear ◽

Non Linear System

Owing to the dynamic operation mode of urea selective catalytic reduction (urea-SCR) systems, advanced control strategies are required to improve urea dosing control. A new control-oriented model presentation of urea-SCR systems is developed in this study. A novel controller based on the triple-step non-linear method is designed. The controller drives the non-linear system with time-varying parameters to track the variable ammonia coverage ratio. Unlike the existing triple-step non-linear method, the third design procedure in the proposed method is adjusted as an [Formula: see text] error feedback control. The proposed method provides a concise design process so that derivation of the control law can be simple and straightforward. The robustness of the controller against measurement noises and system uncertainties is analysed. A transient simulation is conducted to evaluate the effectiveness of the proposed control strategy.

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