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Zeitschriftenartikel zum Thema „System Linearization“

Autor: Grafiati

Veröffentlicht am 28. Juni 2021

Zuletzt aktualisiert am 14. Februar 2022

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1

Brzózka, Jerzy. "Design and Analysis of Model Following Control Structure with Nonlinear Plant." Solid State Phenomena 180 (November 2011): 3–10. http://dx.doi.org/10.4028/www.scientific.net/ssp.180.3.

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Abstract. Linearization methods of the object: input-state and input-output linearization are used usually in a standard feedback control system. However, these systems are sensitive to the changes of nonlinear characteristics of the plant. These changes can be compensated in two types of control systems: in the model following control (MFC) and adaptive. The article presents the first solution and contains: miscellaneous structures of linear control systems with model following, brief description of the linearization’s methods, simulation example of the course control of vessel and the advantages of this solution.

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2

Chao, Kao-Shing Hwang, Horng-Jen. "REINFORCEMENT LINEARIZATION CONTROL SYSTEM." Cybernetics and Systems 31, no. 1 (2000): 115–35. http://dx.doi.org/10.1080/019697200124946.

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3

Cardoso, Gildeberto S., and Leizer Schnitman. "Analysis of Exact Linearization and Aproximate Feedback Linearization Techniques." Mathematical Problems in Engineering 2011 (2011): 1–17. http://dx.doi.org/10.1155/2011/205939.

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This paper presents a study of linear control systems based on exact feedback linearization and approximate feedback linearization. As exact feedback linearization is applied, a linear controller can perform the control objectives. The approximate feedback linearization is required when a nonlinear system presents a noninvolutive property. It uses a Taylor series expansion in order to compute a nonlinear transformation of coordinates to satisfy the involutivity conditions.

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4

Li, Chunbiao, Julien Clinton Sprott, and Wesley Thio. "Linearization of the Lorenz system." Physics Letters A 379, no. 10-11 (2015): 888–93. http://dx.doi.org/10.1016/j.physleta.2015.01.003.

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5

Zhang, Bin, and Yung C. Shin. "A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems." Applied Sciences 11, no. 1 (2020): 62. http://dx.doi.org/10.3390/app11010062.

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A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy models can closely approximate the original unknown nonlinear system with a reduced number of linearizations. Based on T-S fuzzy models, optimal controllers are designed and implemented for a nonlinear two-link flexible joint robot, which demonstrates the possibility of implementing the well-established model-based optimal control method onto unknown nonlinear dynamic systems.

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Ayalur Krishnamoorthy, Parvathy, Kamaraj Vijayarajan, and Devanathan Rajagopalan. "Generalized Quadratic Linearization of Machine Models." Journal of Control Science and Engineering 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/926712.

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In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.

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Lenz, Henning, and Dragan Obradovic. "Robust Control of the Chaotic Lorenz System." International Journal of Bifurcation and Chaos 07, no. 12 (1997): 2847–54. http://dx.doi.org/10.1142/s0218127497001928.

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This paper presents a global approach for controlling the Lorenz system. The basic idea is to partially cancel the nonlinear cross-coupling terms such that the stability of the resulting system can be guaranteed by sequentially proving the stability of each individual state. The method combines ideas from feedback linearization, classical control theory, and Lyapunov's second method. Robust behavior with respect to model uncertainties in the feedback loop is proven. The performance of partial linearization compared to input-state linearization is illustrated on tracking of several trajectories including a periodic orbit and a steady state.

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Lin, Faxing. "Hartman’s linearization on nonautonomous unbounded system." Nonlinear Analysis: Theory, Methods & Applications 66, no. 1 (2007): 38–50. http://dx.doi.org/10.1016/j.na.2005.11.007.

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9

Diallo, Amadou, and R. Joel Rahn. "Direct linearization of system dynamics models." System Dynamics Review 6, no. 2 (1990): 214–18. http://dx.doi.org/10.1002/sdr.4260060207.

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10

Yong-guang, Yu, and Zhang Suo-chun. "Controlling lü-system using partial linearization." Applied Mathematics and Mechanics 25, no. 12 (2004): 1437–42. http://dx.doi.org/10.1007/bf02438302.

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11

Athorne, C., C. Rogers, U. Ramgulam, and A. Osbaldestin. "On linearization of the Ermakov system." Physics Letters A 143, no. 4-5 (1990): 207–12. http://dx.doi.org/10.1016/0375-9601(90)90740-f.

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12

Cover, Alan, James Reneke, Suzanne Lenhart, and Vladimir Protopopescu. "RKH Space Methods for Low Level Monitoring and Control of Nonlinear Systems II. A Vector-Case Example: The Lorenz System." Mathematical Models and Methods in Applied Sciences 07, no. 06 (1997): 823–45. http://dx.doi.org/10.1142/s0218202597000426.

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By using techniques from the theory of reproducing kernel Hilbert (RKH) spaces, we continue the exploration of the stochastic linearization method for possibly unknown and/or noise corrupted nonlinear systems. The aim of this paper is twofold: (a) the stochastic linearization formalism is explicitly extended to the vector case; and (b) as an illustration, the performance of the stochastic linearization for monitoring and control is assessed in the case of the Lorenz system for which the dynamic behavior is known independently.

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13

Wang, Dini, Fanwei Meng, and Shengya Meng. "Linearization Method of Nonlinear Magnetic Levitation System." Mathematical Problems in Engineering 2020 (June 22, 2020): 1–5. http://dx.doi.org/10.1155/2020/9873651.

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Linearized model of the system is often used in control design. It is generally believed that we can obtain the linearized model as long as the Taylor expansion method is used for the nonlinear model. This paper points out that the Taylor expansion method is only applicable to the linearization of the original nonlinear function. If the Taylor expansion is used for the derived nonlinear equation, wrong results are often obtained. Taking the linearization model of the maglev system as an example, it is shown that the linearization should be carried out with the process of equation derivation. The model is verified by nonlinear system simulation in Simulink. The method in this paper is helpful to write the linearized equation of the control system correctly.

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Ciușdel, C. F., S. Coman, Cr Boldișor, et al. "Effect of Linearization in a WNT Signaling Model." Computational and Mathematical Methods in Medicine 2019 (June 10, 2019): 1–9. http://dx.doi.org/10.1155/2019/8461820.

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A nonlinear model consisting of a system of coupled ordinary differential equations (ODE), describing a biological process linked with cancer development, is linearized using Taylor series and tested against different magnitudes of input perturbations, in order to investigate the extent to which the linearization is accurate. The canonical wingless/integrated (WNT) signaling pathway is considered. The linearization procedure is described, and special considerations for linearization validity are analyzed. The analytical properties of nonlinear and linearized systems are studied, including aspects such as existence of steady state and initial value sensitivity. Linearization is a useful tool for speeding up drug response computations or for providing analytical answers to problems such as required drug concentrations. A Monte Carlo-based error testing workflow is employed to study the errors introduced by the linearization for different input conditions and parameter vectors. The deviations between the nonlinear and the linearized system were found to increase in a polynomial fashion w.r.t. the magnitude of tested perturbations. The linearized system closely followed the original one for perturbations of magnitude within 10% of the base input vector which yielded the state-space fixed point used for the linearization.

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15

Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 03 (1998): 718–30. http://dx.doi.org/10.1017/s0021900200016363.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Kozin (1987). In this contribution, using large deviation principles, several mathematically founded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Donsker–Varadhan entropy of a Gaussian measure relatively to a Markov kernel. The method of ‘true linearization’ (Roberts and Spanos (1990)) is justified.

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Bernard, Pierre, and Liming Wu. "Stochastic linearization: the theory." Journal of Applied Probability 35, no. 3 (1998): 718–30. http://dx.doi.org/10.1239/jap/1032265219.

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Very little is known about the quantitative behaviour of dynamical systems with random excitation, unless the system is linear. Known techniques imply the resolution of parabolic partial differential equations (Fokker–Planck–Kolmogorov equation), which are degenerate and of high dimension and for which there is no effective known method of resolution. Therefore, users (physicists, mechanical engineers) concerned with such systems have had to design global linearization techniques, known as equivalent statistical linearization (Roberts and Spanos (1990)). So far, there has been no rigorous justification of these techniques, with the notable exception of the paper by Kozin (1987). In this contribution, using large deviation principles, several mathematically founded linearization methods are proposed. These principles use relative entropy, or Kullback information, of two probability measures, and Donsker–Varadhan entropy of a Gaussian measure relatively to a Markov kernel. The method of ‘true linearization’ (Roberts and Spanos (1990)) is justified.

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17

Trebi-Ollennu, A., and B. A. White. "Non-Linear Robust Control Designs for a Remotely Operated Underwater Vehicle Depth Control System." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 210, no. 3 (1996): 201–14. http://dx.doi.org/10.1243/pime_proc_1996_210_455_02.

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This paper describes the heave and pitch control of a non-linear longitudinal model of a remotely operated vehicle (ROV) using three robust non-linear control techniques. The techniques are based on input-output (I/O) linearization, comprising basic I/O linearization control, I/O linearization with sliding mode control and I/O linearization with adaptive fuzzy systems. Robustness of the designs is investigated by examining the closed-loop zero dynamics, which are shown to be bounded. The robustness of each control scheme is also investigated by varying the ROV hydrodynamic coefficients by 50 per cent. Simulation results are presented to compare the control schemes.

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18

Chang, R. J., and S. J. Lin. "Statistical Linearization Model for the Response Prediction of Nonlinear Stochastic Systems Through Information Closure Method." Journal of Vibration and Acoustics 126, no. 3 (2004): 438–48. http://dx.doi.org/10.1115/1.1688762.

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A new linearization model with density response based on information closure scheme is proposed for the prediction of dynamic response of a stochastic nonlinear system. Firstly, both probability density function and maximum entropy of a nonlinear stochastic system are estimated under the available information about the moment response of the system. With the estimated entropy and property of entropy stability, a robust stability boundary of the nonlinear stochastic system is predicted. Next, for the prediction of response statistics, a statistical linearization model is constructed with the estimated density function through a priori information of moments from statistical data. For the accurate prediction of the system response, the excitation intensity of the linearization model is adjusted such that the response of maximum entropy is invariant in the linearization model. Finally, the performance of the present linearization model is compared and supported by employing two examples with exact solutions, Monte Carlo simulations, and Gaussian linearization method.

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19

Qian, Hua Ming, Zhen Duo Fu, Liang Chen, and Xiu Li Ning. "Exact Linearization Algorithm of Tight Coupling Nonlinear System Based on Differential Manifold." Applied Mechanics and Materials 380-384 (August 2013): 686–91. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.686.

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Dealt with the short precision the traditional Taylor series expansion induced and shortage that the system mechanics is hard to match with the exact linearization conditions, a novel exact linearization algorithm of tight coupling nonlinear system based on differential manifold to the missile attitude control system is proposed. A dimension expansion method is proposed, the method solves the problem that the input and output dimensions can not meet the exact linearization conditions; the algorithm application range is widened. Using the principle of the differential manifold, the missile velocity and height information are selected as the measure output, the exact linearization of the missile attitude system is derived based on the diffeomorphism transformations. The simulations are performed on the missile attitude control system. Simulation results show that the effectiveness of the algorithm proposed.

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20

Yildirim, Kenan, and Ismail Kucuk. "A nonlinear plate control without linearization." Open Mathematics 15, no. 1 (2017): 179–86. http://dx.doi.org/10.1515/math-2017-0011.

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Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

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21

Kao-Shing Hwang and Horag-Jen Chao. "Adaptive reinforcement learning system for linearization control." IEEE Transactions on Industrial Electronics 47, no. 5 (2000): 1185–88. http://dx.doi.org/10.1109/41.873231.

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22

Li, Changpin, and Yutian Ma. "Fractional dynamical system and its linearization theorem." Nonlinear Dynamics 71, no. 4 (2012): 621–33. http://dx.doi.org/10.1007/s11071-012-0601-1.

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23

Kaczorek, Tadeusz. "Positivity and Linearization of a Class of Nonlinear Continuous–Time Systems by State Feedbacks." International Journal of Applied Mathematics and Computer Science 25, no. 4 (2015): 827–31. http://dx.doi.org/10.1515/amcs-2015-0059.

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Abstract The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.

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24

Różowicz, Sebastian, and Andrzej Zawadzki. "Input-Output Transformation Using the Feedback of Nonlinear Electrical Circuits: Algorithms and Linearization Examples." Mathematical Problems in Engineering 2018 (November 6, 2018): 1–13. http://dx.doi.org/10.1155/2018/9405256.

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This paper addresses the problem of nonlinear electrical circuit input-output linearization. The transformation algorithms for linearization of nonlinear system through changing coordinates (local diffeomorphism) with the use of closed feedback loop together with the conditions necessary for linearization are presented. The linearization stages and the results of numerical simulations are discussed.

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25

Liu, Si Jia, Yu Fan, Jun Di, Ya Jing Liu, Wei Qin, and Shuo Li. "Nonlinear Control Approach of an Electromagnetic Bearing System." Applied Mechanics and Materials 538 (April 2014): 387–93. http://dx.doi.org/10.4028/www.scientific.net/amm.538.387.

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This paper proposes a two-electromagnet double degrees of freedom active magnetic bearing (AMB) model. Considering the nonlinearity between the electromagnetic force and the air gap, the authors put forward a nonlinear control approach based on feedback linearization which decouples and linearizes the original system. For the linearized system, pole placement strategy is used to achieve expected steady and dynamic performances. Simulation results show that this approach can successfully implement the decoupling and linearization, and is effective of different initial values.

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Yu, Xinghuo. "Controlling Chaos Using Input–Output Linearization Approach." International Journal of Bifurcation and Chaos 07, no. 07 (1997): 1659–64. http://dx.doi.org/10.1142/s021812749700128x.

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In this article the input–output linearization approach is used for controlling chaos. It is shown that by using only partial states, the entire chaotic system is stabilizable, provided the zero dynamics is stable. Generally speaking, trajectories of chaotic systems do not grow exponentially and are usually bounded. In particular, for dissipative chaotic systems the stable zero dynamics can always be found. Hence the stabilization as well as tracking periodic signals are possible. The Lorenz system is used to inform the discussion. Simulation results are presented to show the effectiveness of the approach.

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27

WAGG, DAVID J. "PARTIAL SYNCHRONIZATION OF NONIDENTICAL CHAOTIC SYSTEMS VIA ADAPTIVE CONTROL, WITH APPLICATIONS TO MODELING COUPLED NONLINEAR SYSTEMS." International Journal of Bifurcation and Chaos 12, no. 03 (2002): 561–70. http://dx.doi.org/10.1142/s0218127402004589.

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We consider the coupling of two nonidentical dynamical systems using an adaptive feedback linearization controller to achieve partial synchronization between the two systems. In addition we consider the case where an additional feedback signal exists between the two systems, which leads to bidirectional coupling. We demonstrate the stability of the adaptive controller, and use the example of coupling a Chua system with a Lorenz system, both exhibiting chaotic motion, as an example of the coupling technique. A feedback linearization controller is used to show the difference between unidirectional and bidirectional coupling. We observe that the adaptive controller converges to the feedback linearization controller in the steady state for the Chua–Lorenz example. Finally we comment on how this type of partial synchronization technique can be applied to modeling systems of coupled nonlinear subsystems. We show how such modeling can be achieved where the dynamics of one system is known only via experimental time series measurements.

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Youcef-Toumi, K., and S. T. Wu. "Input/Output Linearization Using Time Delay Control." Journal of Dynamic Systems, Measurement, and Control 114, no. 1 (1992): 10–19. http://dx.doi.org/10.1115/1.2896491.

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A control procedure that uses Time Delay Control to achieve input/output linearization of a class of nonlinear systems is presented. The control system is characterized by a simple algorithm and enhanced robustness properties in comparison with current control algorithms. The paper first reviews the fundamentals of input/output linearization. The use of Time Delay Control is then shown to result in an exact linear system for sufficiently small delay time. Modified controllers for systems with a low-pass filter are also investigated. Simulation results show that the algorithm works well with measurement noise. The controller is also tested on a single-link flexible arm to show the effectiveness of the simple algorithm in the control of complicated systems.

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Jeong, Min-Gil, and Ho-Lim Choi. "Switching Control of Electromagnetic Levitation System based on Jacobian Linearization and Input-Output Feedback Linearization." Transactions of The Korean Institute of Electrical Engineers 64, no. 4 (2015): 578–85. http://dx.doi.org/10.5370/kiee.2015.64.4.578.

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30

Bouchiba, Bousmaha, Abdeldjebar Hazzab, Hachemi Glaoui, Fellah Med-Karim, Ismaïl Bousserhane, and Pierre Sicard. "Control of multi-machine using adaptive fuzzy." Serbian Journal of Electrical Engineering 8, no. 2 (2011): 111–26. http://dx.doi.org/10.2298/sjee1102111b.

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An indirect Adaptive fuzzy excitation control (IAFLC) of power systems based on multi-input-multi-output linearization technique is developed in this paper. The power system considered in this paper consists of two generators and infinite bus connected through a network of transformers and transmission lines. The fuzzy controller is constructed from fuzzy feedback linearization controller whose parameters are adjusted indirectly from the estimates of plant parameters. The adaptation law adjusts the controller parameters on-line so that the plant output tracks the reference model output. Simulation results shown that the proposed controller IAFLC, compared with a controller based on tradition linearization technique can enhance the transient stability of the power system.

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Young, G. E., and R. J. Chang. "Optimal Control of Stochastic Parametrically and Externally Excited Nonlinear Control Systems." Journal of Dynamic Systems, Measurement, and Control 110, no. 2 (1988): 114–19. http://dx.doi.org/10.1115/1.3152660.

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A sub-optimal nonlinear controller which is synthesized by using the external linearization approach is applied to the optimal control of stochastic parametrically and externally excited nonlinear systems with complete state information. Algebraic necessary conditions are derived for the minimization of the quadratic cost function through the concepts of equivalent external excitation. The concepts and applications of the statistical linearization approach for the externally excited nonlinear systems are extended to the nonlinear systems subjected to both stochastic parametric and external excitations. Two examples which include a first-order nonlinear and a second-order Duffing type stochastic system are used to illustrate the performance of the present design. The applications of the statistical linearization approach to the optimal control of a stochastic parametrically and externally excited Duffing type system is illustrated and compared with the present approach by using Monte Carlo simulation.

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Li, Na, and Wu Wang. "Feedback Linearization Control for PMSG Wind Power Generation System with Application of Wind Turbine in Mechanical Engineering." Advanced Materials Research 644 (January 2013): 115–18. http://dx.doi.org/10.4028/www.scientific.net/amr.644.115.

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The fluctuation, intermittence and uncertain are the characteristics of wind energy which cause wind energy output power fluctuation, so the wind power generation system was a typical nonlinear system, which was hard to be controlled exactly by traditional controllers, so, the feedback linearization control was applied to wind power generation system (WPGS) in mechanical engineering, which was to reduce the cost of wind energy conversion system and improve its performance. Feedback linearization control contains coordinate transformation, Lie derivative solving, and inverse coordinate transformation module, the control strategy was proposed. The WPGS model was constructed under MATLAB platform, with feedback linearization control theory based on differential geometry, the coordinated transformation and nonlinear state feedback were obtained. the simulation parameters was designed and the simulation result shows the control model was stable and direct feedback linearization control with higher tracking performance, which can effectively implement maximum energy capture.

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Rugh, W. "An extended linearization approach to nonlinear system inversion." IEEE Transactions on Automatic Control 31, no. 8 (1986): 725–33. http://dx.doi.org/10.1109/tac.1986.1104385.

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34

Kalinowski, Krystian, and Roman Kaula. "Linearization of a Coal Blending Process Control System." IFAC Proceedings Volumes 39, no. 22 (2006): 199–203. http://dx.doi.org/10.1016/s1474-6670(17)30136-2.

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35

Neo, Y. S., S. M. Idrus, M. F. Rahmat, S. E. Alavi, and I. S. Amiri. "Adaptive Control for Laser Transmitter Feedforward Linearization System." IEEE Photonics Journal 6, no. 4 (2014): 1–10. http://dx.doi.org/10.1109/jphot.2014.2335711.

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36

Rourke, David E., and Matthew P. Augustine. "Exact Linearization of the Radiation-Damped Spin System." Physical Review Letters 84, no. 8 (2000): 1685–88. http://dx.doi.org/10.1103/physrevlett.84.1685.

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37

Crespo, L. G., and J. Q. Sun. "On the Feedback Linearization of the Lorenz System." Journal of Vibration and Control 10, no. 1 (2004): 85–100. http://dx.doi.org/10.1177/107754604773684911.

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Crespo, L. G., and J. Q. Sun. "On the Feedback Linearization of the Lorenz System." Journal of Vibration and Control 10, no. 1 (2004): 85–100. http://dx.doi.org/10.1177/1077546304030944.

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In this paper we present a control study of the Lorenz system via feedback linearization using the Rayleigh number as a control variable. The effects of the state transformation on the dynamics of the system are studied first. Then, composite controls are derived for both stabilization and tracking problems. The transition through the manifold where the state transformation is singular and the system is insensitive to the control is achieved by inducing the natural chaotic response of the system within a boundary layer. Outside the boundary layer, the control designed via feedback linearization is applied. Tracking problems that involve single and cooperative objectives are studied by using differential flatness. A good understanding of the system dynamics proves to be invaluable in the design of better controls.

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V. Dinh, Nghiep, and Hien N. Nguyen. "Exact Linearization Control for Twin Rotor MIMO System." International Journal of Electrical and Electronics Engineering 3, no. 12 (2016): 40–45. http://dx.doi.org/10.14445/23488379/ijeee-v3i12p107.

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40

Guardabassi, Guido O., and Sergio M. Savaresi. "System linearization via feedback: A control engineering perspective." Rendiconti del Seminario Matematico e Fisico di Milano 66, no. 1 (1996): 391–431. http://dx.doi.org/10.1007/bf02925367.

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Gontier, C., and Ying Li. "Lagrangian formulation and linearization of multibody system equations." Computers & Structures 57, no. 2 (1995): 317–31. http://dx.doi.org/10.1016/0045-7949(94)00599-x.

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42

Kotta, U. "Application of inverse system for linearization and decoupling." Systems & Control Letters 8, no. 5 (1987): 453–57. http://dx.doi.org/10.1016/0167-6911(87)90086-7.

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43

Chen, Jin Li, Ya Li Xue, and Dong Hai Li. "Decentralized Robust Feedback Linearization Control Based on Integrity." Applied Mechanics and Materials 411-414 (September 2013): 1687–96. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1687.

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Decentralized Robust Feedback Linearization (DRFL) approach based on integrity for multivariable systems is presented. It uses a model observer to compensate the non-modeled dynamics, system uncertainties, and external disturbances of a system. Firstly, the existence of DRFL controllers with integrity is examined. Then, stable regions of each DRFL controller parameters are calculated, and some parameters are obtained by placing suitable closed-loop poles, for meeting the design specifications for the whole control system. The proposed method is applied to an illustrative example. Results demonstrate that DRFL control is feasible and robust for complicated multivariable systems.

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Basu, B., and V. K. Gupta. "On Equivalent Linearization Using Wavelet Transform." Journal of Vibration and Acoustics 121, no. 4 (1999): 429–32. http://dx.doi.org/10.1115/1.2893998.

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This paper proposes a wavelet-based formulation for linearizing a base-excited single-degree-of-freedom nonlinear system to a time-variant linear (TVL) system. The given system is assumed to be nonlinear in stiffness, and the time-dependent natural frequency of the equivalent system is proposed to he estimated through instantaneous minimization of the mean-square error. A duffing oscillator has been considered to illustrate the performance of the proposed TVL system.

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Zeng, Run Zhang, та Huang Qiu Zhu. "Mathematical Model and Control of Axial Hybrid Magnetic Bearings Based on α-th Order Inverse System Theory". Applied Mechanics and Materials 529 (червень 2014): 539–43. http://dx.doi.org/10.4028/www.scientific.net/amm.529.539.

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A linearization control research based on α-th order inverse system method has been developed for an axial hybrid magnetic bearing, which is a nonlinear system. The configuration of the axial hybrid magnetic bearing is briefly introduced, the working principle of the hybrid magnetic bearing is analyzed, and then the suction equations are set up. Based on expounding of α-th order inverse system method, and aiming at dynamics model of the axial hybrid magnetic bearing, the feasibility of linearization control is discussed in detail, the linearization control arithmetic based on α-th order inverse system method is deduced, and then close system controller is designed. Finally, the simulation system is set up with MATLAB software. The step response of system, the start up displacement curve of rotor and the performance of anti-disturbance of system are simulated. The simulation results have shown that the α-th order inverse system control strategy can realize accurate linearization for nonlinear mathematical model of the axial hybrid magnetic bearing, and the designed close control system has good dynamic and static performance.

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Li, Huan, Cheng Sheng Pan, Yu Zhang, and Bo Ren. "On Adaptive Identification Algorithm for PA Linearization." Applied Mechanics and Materials 29-32 (August 2010): 1268–73. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.1268.

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According to the nonlinear amplification characteristic with memory effection of power amplifier(PA) in WCDMA systems, we have analyzed the structure of Wiener digital predistortion system in which Hammerstein power amplifier model with memory is adopted. LR algorithm and LMS algorithm were used respectively to identify and update parameters of Wiener predistortion system. An LR / LMS identification algorithm is proposed for syetem adaptive Identification. The method has a very good suppression of signal spectral regrowth. Theoretical analysis and computer simulation verified the effectiveness and practicability of the algorithm.

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Gao, Yuan, and Xiao He Liu. "Feedback Linearization Control of Electric Arc Furnace System Based on dSPACE Simulation." Applied Mechanics and Materials 538 (April 2014): 394–97. http://dx.doi.org/10.4028/www.scientific.net/amm.538.394.

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In this paper, the method of feedback linearization control based on dSPACE simulation for electric arc furnace system is discussed. With the linear feedback method of differential geometry dealing with non-linear part of electric arc furnace system, the controller was designed. Then the hardware-in-the-loop simulation system was built, and several simulations was done. Simulation results show that the feedback linearization control has better performance.

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Freeman, Walter J. "Neural system stability." Behavioral and Brain Sciences 19, no. 2 (1996): 298–99. http://dx.doi.org/10.1017/s0140525x00042722.

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AbstractTwo hypotheses concerning nonlinear elements in complex systems are contrasted: that neurons, intrinsically unstable, are stabilized through embedding in networks and populations; and, conversely, that cortical neurons are intrinsically stable, but are destabilized through embedding in cortical populations and corticostriatal feedback systems. Tests are made by piecewise linearization of nonlinear dynamics at nonequilibriumoperating points, followed by linear stability analysis.

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Behera, Namita. "Generalized Fiedler pencils with repetition for rational matrix functions." Filomat 34, no. 11 (2020): 3529–52. http://dx.doi.org/10.2298/fil2011529b.

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We introduce generalized Fiedler pencil with repetition(GFPR) for an n x n rational matrix function G(?) relative to a realization of G(?). We show that a GFPR is a linearization of G(?) when the realization of G(?) is minimal and describe recovery of eigenvectors of G(?) from those of the GFPRs. In fact, we show that a GFPR allows operation-free recovery of eigenvectors of G(?). We describe construction of a symmetric GFPR when G(?) is symmetric. We also construct GFPR for the Rosenbrock system matrix S(?) associated with an linear time-invariant (LTI) state-space system and show that the GFPR are Rosenbrock linearizations of S(?). We also describe recovery of eigenvectors of S(?) from those of the GFPR for S(?). Finally, We analyze operation-free Symmetric/self-adjoint structure Fiedler pencils of system matrix S(?) and rational matrix G(?). We show that structure pencils are linearizations of G(?).

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Fnaiech, Mohamed Amine, Hazem Nounou, Mohamed Nounou, and Aniruddha Datta. "Intervention in Biological Phenomena via Feedback Linearization." Advances in Bioinformatics 2012 (November 6, 2012): 1–9. http://dx.doi.org/10.1155/2012/534810.

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The problems of modeling and intervention of biological phenomena have captured the interest of many researchers in the past few decades. The aim of the therapeutic intervention strategies is to move an undesirable state of a diseased network towards a more desirable one. Such an objective can be achieved by the application of drugs to act on some genes/metabolites that experience the undesirable behavior. For the purpose of design and analysis of intervention strategies, mathematical models that can capture the complex dynamics of the biological systems are needed. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of biological phenomena. Due to the complex nonlinear dynamics of the biological phenomena represented by S-systems, nonlinear intervention schemes are needed to cope with the complexity of the nonlinear S-system models. Here, we present an intervention technique based on feedback linearization for biological phenomena modeled by S-systems. This technique is based on perfect knowledge of the S-system model. The proposed intervention technique is applied to the glycolytic-glycogenolytic pathway, and simulation results presented demonstrate the effectiveness of the proposed technique.

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