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Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and ...
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Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.
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Elementary nonlinear decoupling (END) is a model based control algorithm intended to decouple and linearize a nonlinear multivariable process in order to achieve better control than can be obtained by conventional decentralized li...
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Elementary nonlinear decoupling (END) is a model based control algorithm intended to decouple and linearize a nonlinear multivariable process in order to achieve better control than can be obtained by conventional decentralized linear feedback control. The application of END to the composition control of a theoretical binary distillation column illustrates that the quality achievable is very high. [References: 6]
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This work focuses on synthesizing nonlinear decoupling controllers for multivariable nonlinear systems represented by a state-space model, in the presence of deadtimes. The deadtimes appear in both the inputs and the outputs, but ...
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This work focuses on synthesizing nonlinear decoupling controllers for multivariable nonlinear systems represented by a state-space model, in the presence of deadtimes. The deadtimes appear in both the inputs and the outputs, but not in the states, and are physically associated with sensors and actuators. Simple sufficient conditions for feasibility of closed-loop deadtimes are derived, which rely only on the structural properties of the system. A control law is then derived so that the closed-loop system is input/output linear and decoupled, with deadtimes equal to the smallest ones that satisfy the feasibility conditions. The proposed method is applied to a chemical process. Its performance is evaluated through simulation in the presence of set-point and disturbance changes. (C) 2003 Elsevier Ltd. All rights reserved. [References: 9]
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In this paper we analyze the extent to which the US economy affects international business fluctuations across countries and we ask whether the nonlinear nature of the business cycle affects the degree of co-movement between count...
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In this paper we analyze the extent to which the US economy affects international business fluctuations across countries and we ask whether the nonlinear nature of the business cycle affects the degree of co-movement between countries. A multivariate nonlinear LSTAR model is estimated for the GDP cyclical components of China, France, Germany, the UK and the US. This nonlinear framework allows the asymmetries of the business cycle to be captured properly to identify the synchronization behavior across countries. Our results suggest that there is a relevant influence of the US cycle, specifically during recessions.
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The polynomial NARX model, where the output is a polynomial function of past inputs and outputs, is a commonly used equation error model for nonlinear systems. While it is linear in the variables, which simplifies its identificati...
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The polynomial NARX model, where the output is a polynomial function of past inputs and outputs, is a commonly used equation error model for nonlinear systems. While it is linear in the variables, which simplifies its identification, it suffers from two major drawbacks: the number of parameters grows combinatorially with the degree of the nonlinearity, and it is a black box model, which makes it difficult to draw any insights from the identified model. Polynomial decoupling techniques are used to replace the multiple-input single-output polynomial with a decoupled polynomial structure comprising a transformation matrix followed by bank of SISO polynomials, whose outputs are then summed. This approach is demonstrated on two benchmark systems: The Bouc-Wen friction model and the data from the Silverbox model. In both cases, the decoupling results in a substantial reduction in the number of parameters, and allows some insight into the nature of the nonlinearities in the system.
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Cellular model with improved decoupling approximation is proposed to study the effective nonlinear response in random nonlinear granular materials. The results are com- pared with numerical simulations on random nonlinear resistor...
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Cellular model with improved decoupling approximation is proposed to study the effective nonlinear response in random nonlinear granular materials. The results are com- pared with numerical simulations on random nonlinear resistor networks, a good agreement is obtained.
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Celular mode with improved decoupling approximation is proposed to study the effective nonlinear response in random nonlinear granular materials. The results are compared with numerical simulations on random nonlinear resistor net...
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Celular mode with improved decoupling approximation is proposed to study the effective nonlinear response in random nonlinear granular materials. The results are compared with numerical simulations on random nonlinear resistor networks, a good agreement is obtained.
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In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input an...
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In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. (C) 1997 by John Wiley & Sons, Ltd. [References: 22]
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A new time discretization method for strongly nonlinear parabolic systems is constructed by combining the fully explicit two-step backward difference formula and a second-order stabilization of wave type. The proposed method linea...
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A new time discretization method for strongly nonlinear parabolic systems is constructed by combining the fully explicit two-step backward difference formula and a second-order stabilization of wave type. The proposed method linearizes and decouples a nonlinear parabolic system at every time level, with second-order consistency error. The convergence of the proposed method is proved by combining energy estimates for evolution equations of parabolic and wave types with the generating function technique that is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.
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Abstract In this paper, a gain‐tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics is developed. Firstly, a linear subsystem is formed by linearizing the nonlinear system. Then, a line...
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Abstract In this paper, a gain‐tuning method for almost disturbance decoupling problems of nonlinear systems with zero dynamics is developed. Firstly, a linear subsystem is formed by linearizing the nonlinear system. Then, a linear matrix inequality can be formed for the linear subsystem. After that, a linear state‐feedback controller can be obtained by solving the linear matrix inequality. A nonlinear state‐feedback controller can be obtained for the original nonlinear system by using backstepping design method. Another linear state‐feedback controller can be derived by linearizing the nonlinear state‐feedback controller. Finally, the backstepping gains can be solved by equating the two linear controllers. The detailed derivations of the method are provided. Some comparisons with the existing techniques are discussed. Moreover, the designed method is verified by simulations and some comparisons are made accordingly.
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