Academic literature on the topic 'Linearized model'

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Journal articles on the topic "Linearized model"

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BALAFOUTIS, C. A., and R. V. PATEL. "LINEARIZED ROBOT MODELS IN JOINT AND CARTESIAN SPACES." Transactions of the Canadian Society for Mechanical Engineering 13, no. 4 (1989): 103–12. http://dx.doi.org/10.1139/tcsme-1989-0017.

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In this paper, linearization of the Newton-Euler formulation of robot dynamics is considered, and linearized robot models in joint and Cartesian spaces are presented. A new computational method for recursive evaluation of linearized dynamic robot models, about a nominal trajectory is given. The proposed algorithms are designed to evaluate the “sensitivity matrices” necessary to determine the linearised robot models and can be implemented numerically or symbolically. To achieve an efficient formulation for the coefficient sensitivity matrices, concepts from tensor algebra are used. A numerical
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Xian, Ning, and Zhilong Chen. "A Quantum-behaved Pigeon-Inspired Optimization approach to Explicit Nonlinear Model Predictive Controller for quadrotor." International Journal of Intelligent Computing and Cybernetics 11, no. 1 (2018): 47–63. http://dx.doi.org/10.1108/ijicc-06-2017-0058.

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Purpose The purpose of this paper is to simplify the Explicit Nonlinear Model Predictive Controller (ENMPC) by linearizing the trajectory with Quantum-behaved Pigeon-Inspired Optimization (QPIO). Design/methodology/approach The paper deduces the nonlinear model of the quadrotor and uses the ENMPC to track the trajectory. Since the ENMPC has high demand for the state equation, the trajectory needed to be differentiated many times. When the trajectory is complicate or discontinuous, QPIO is proposed to linearize the trajectory. Then the linearized trajectory will be used in the ENMPC. Findings A
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Ogbikaya, Stephen, and M. Iqbal. "Reduced Order Model of A Microgrid System for A University Community in Nigeria." Jordan Journal of Electrical Engineering 8, no. 3 (2022): 266. http://dx.doi.org/10.5455/jjee.204-1653940509.

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This paper presents a reduced order model of a microgrid system for a university community in Nigeria. The designed microgrid system is simulated in MATLAB/Simulink environment to determine the system dynamics. The obtained dynamic system is then reduced to a single block subsystem with multiple inputs and a single output using system linearization. The microgrid model is then linearized with the aid of linearization tool in MATLAB/Simulink using linearized perturbation method. The transfer function of the multiple inputs with respect to the single output of the microgrid system is determined
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Murray, J. J., and C. P. Neuman. "Linearization and Sensitivity Models of the Newton-Euler Dynamic Robot Model." Journal of Dynamic Systems, Measurement, and Control 108, no. 3 (1986): 272–76. http://dx.doi.org/10.1115/1.3143779.

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Within the framework of the Newton-Euler formulation of robot dynamics, linearized and trajectory sensitivity models are constructed about a nominal trajectory. The approach illustrates the property that linearization of the O(N) recursive Newton-Euler formulation leads to O(N) recursive algorithms. These algorithms are conceived for simulation, parameter identification, and real-time control applications which require the numerical evaluation of the linearized or trajectory sensitivity models. The O(N) linearized recursive algorithms complement their O(N5) linearized Lagrange (Lagrange-Euler)
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Jiang, Ping, Tianyi Zhang, Jinpeng Geng, Peiguang Wang, and Lei Fu. "An MPPT Strategy for Wind Turbines Combining Feedback Linearization and Model Predictive Control." Energies 16, no. 10 (2023): 4244. http://dx.doi.org/10.3390/en16104244.

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This paper proposes a model predictive controller (MPC) design based on the optimal tip-speed ratio method for maximum power point tracking (MPPT) of a direct-driven permanent magnet synchronous generator (D-PMSG)-based wind energy conversion system (WECS). To eliminate system nonlinearity and time-varying characteristics, a control variable was added at the wind turbine and the system model was feedback-linearized to create a linear time-invariant system, reducing the computational burden of the MPC and improving system performance. MATLAB/Simulink simulations were performed and the results s
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Bourchtein, Andrei, and Ludmila Bourchtein. "On separation of variables in the linearized nonhydrostatic atmospheric model." Meteorologische Zeitschrift 25, no. 1 (2016): 79–84. http://dx.doi.org/10.1127/metz/2015/0690.

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Nwoko, Christopher Ikpe Amadi, Amarachi Udoka Nkwoada, and Peterclever Chidi Ihuoma. "Novel Linearized Kinetic Modeling of Starch Hydrolysis." Chemical Science International Journal 19, no. 3 (2017): 1–7. https://doi.org/10.9734/CSIJ/2017/34116.

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The hydrolysis of starch into glucose by acid and enzyme techniques has recorded higher glucose recovery and optimization of processes, but lacks the fitting of the results into a kinetic linear model. The application of kinetic linearized model effect of temperature on pH and acid concentration during hydrolysis of starch into glucose was studied. The experiment was conducted at different durations using reported preparatory techniques and average values of triplicates were reported. The maximum glucose yield of 18.20 mg/ml was observed on 4 hours at 60°C from acid hydrolysis and similarly ob
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Bak, Jimmy, and Anders Larsen. "Quantitative Gas Analysis with FT-IR: A Method for CO Calibration Using Partial Least-Squares with Linearized Data." Applied Spectroscopy 49, no. 4 (1995): 437–43. http://dx.doi.org/10.1366/0003702953964237.

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Calibration spectra of CO in the 2.38–5100 ppm concentration range (22 spectra) have been measured with a spectral resolution of 4 cm−1, in the mid-IR (2186–2001 cm−1) region, with a Fourier transform infrared (FT-IR) instrument. The multivariate calibration method partial least-squares (PLS1) was used to model the CO calibration spectra in order to improve the sensitivity and to flag possible outliers in the prediction step. The relation between the absorbance values and concentrations was strongly nonlinear. This result was caused mainly by the low spectral resolution of the instrument. To i
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Kozak, Kris, Imme Ebert-Uphoff, and William Singhose. "Locally Linearized Dynamic Analysis of Parallel Manipulators and Application of Input Shaping to Reduce Vibrations." Journal of Mechanical Design 126, no. 1 (2004): 156–68. http://dx.doi.org/10.1115/1.1640362.

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Input Shaping is a technique that seeks to reduce residual vibrations through modification of the reference command given to a system. Namely the reference command is convolved with a suitable train of impulses. Input shaping has proven to be successful in reducing the vibrations of a great variety of linear systems. This article seeks to apply input shaping to robotic manipulators of parallel architecture. Such systems have multiple degrees-of-freedom and non-linear dynamics and therefore standard input shaping techniques cannot be readily applied. In order to apply standard input shaping tec
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DANANI, A., and P. ZANARDI. "AUXILIARY FERMION LINEARIZED t-J MODEL." Modern Physics Letters B 09, no. 30 (1995): 1873–86. http://dx.doi.org/10.1142/s0217984995001856.

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The Auxiliary Fermion linearization scheme is applied to the ferromagnetic t-J model. Spectrum and self-consistency equations are obtained. The numerical analysis shows the existence of solutions describing metallic as well as magnetic phases of different kind. Their interplay is discussed.
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Dissertations / Theses on the topic "Linearized model"

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Schweighart, Samuel A. (Samuel Adam) 1977. "Development and analysis of a high fidelity linearized J₂ model for satellite formation flying." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/82204.

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Davis, Jake Daniel. "A Higher-Order Method Implemented in an Unstructured Panel Code to Model Linearized Supersonic Flows." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/1968.

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Since their conception in the 1960s, panel codes have remained a critical tool in the design and development of air vehicles. With continued advancement in computational technologies, today's codes are able to solve flow fields around arbitrary bodies more quickly and with higher fidelity than those that preceded them. Panel codes prove most useful during the conceptual design phase of an air vehicle, allowing engineers to iterate designs, and generate full solutions of the flow field around a vehicle in a matter of seconds to minutes instead of hours to days using traditional CFD methods. The
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Na, Wei. "Frequency Domain Linearized Navier-Stokes Equations Methodology for Aero-Acoustic and Thermoacoustic Simulations." Licentiate thesis, KTH, Aeroakustik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-179677.

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The first part of the thesis focuses on developing a numerical methodology to simulate the acoustic properties of a hybrid liner consisting of a perforated plate, a porous layer and a Helmholtz cavity. Liners are always a standard way to reduce noise in today’s aeroengines, e.g. the fan noise can be reduced effectively through the installation of acoustic liners as wall treatments in the ducts. In order to optimize a liner in the design phase, an accurate and efficient prediction tool is of interests. Hence, a unified Linearized Navier-Stokes equations(LNSE) approach has been implemented in th
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Ebenhoch, Raphael. "Simplified modeling of wind-farm flows." Thesis, KTH, Strömningsfysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-177309.

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Abstact: In order to address the wind-industry's need for a new generation of more advanced wake models, which accurately quantify the mean flow characteristics within a reasonably CPU-time, the two-dimensional analytical approach by Belcher et al. (2003) has been extended to a three-dimensional wake model. Hereby, the boundary-layer approximation of the Navier-Stokes equations has been linearized around an undisturbed baseflow, assuming that the wind turbines provoke a small perturbation of the velocity field. The conducted linearization of the well established actuator-disc theory brought va
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Rangel, Camilo Alberto Sepúlveda. "Modelo aproximado de sistemas de distribuição considerando geração distribuida e o efeito da tensão na carga." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127892.

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Esta dissertação apresenta um modelo aproximado de rede desenvolvido para análise de sistemas de distribuição em regime permanente. O modelo é detalhado do ponto de vista matemático e teórico considerando a representação dos elementos em derivação da rede (cargas e geradores) e dos limites operacionais empregando aproximações lineares. A modelagem linear permite determinar de forma simples os valores das tensões e correntes do sistema, podendo ser empregada em problemas de otimização relacionados ao planejamento e expansão de sistemas de distribuição. A representação da carga considera a influ
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Algarawi, Mohammed. "Non-linear discrete-time observer design by sliding mode." Thesis, Brunel University, 2007. http://bura.brunel.ac.uk/handle/2438/5072.

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Research into observer design for non-linear discrete-time systems has produced many design methods. There is no general design method however and that provides the motivation to search for a new simple and realizable design method. In this thesis, an observer for non-linear discrete-time systems is designed using the sliding mode technique. The equation of the observer error is split into two parts; the first part being a linearized model of the system and the second part an uncertain vector. The sliding mode technique is introduced to eliminate the uncertainty caused by the uncertain vector
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GRÖNLUND, ARTHUR, and CHRISTOS TOLIS. "Riderless self-balancing bicycle : Derivation and implementation of a time variant linearized state space model for balancing a bicycle in motion by turning the front wheel." Thesis, KTH, Mekatronik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-232995.

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Self-driving vehicles are becoming more and more prevalent in society, with buses and cars close to being implemented in the public domain. Self-driving two-wheeled vehicles could be a solution for space-efficient transportation in cities, where space is becoming a larger issue. The purpose of this project was to develop and implement a linearized time variant state space model for balancing such a two-wheeled vehicle in the form of a bicycle by turning its front wheel. To test the derived model a small demonstrator was built and experimented with. The final conclusion was that the model could
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Garg, Aditie. "Designing Reactive Power Control Rules for Smart Inverters using Machine Learning." Thesis, Virginia Tech, 2018. http://hdl.handle.net/10919/83558.

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Due to increasing penetration of solar power generation, distribution grids are facing a number of challenges. Frequent reverse active power flows can result in rapid fluctuations in voltage magnitudes. However, with the revised IEEE 1547 standard, smart inverters can actively control their reactive power injection to minimize voltage deviations and power losses in the grid. Reactive power control and globally optimal inverter coordination in real-time is computationally and communication-wise demanding, whereas the local Volt-VAR or Watt-VAR control rules are subpar for enhanced grid service
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Rothman, Keith Eric. "Validation of Linearized Flight Models using Automated System-Identification." DigitalCommons@CalPoly, 2009. https://digitalcommons.calpoly.edu/theses/81.

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Optimization based flight control design tools depend on automatic linearization tools, such as Simulink®’s LINMOD, to extract linear models. In order to ensure the usefulness and correctness of the generated linear model, this linearization must be accurate. So a method of independently verifying the linearized model is needed. This thesis covers the automation of a system identification tool, CIFER®, for use as a verification tool integrated with CONDUIT®, an optimization based design tool. Several test cases are built up to demonstrate the accuracy of the verification tool with respect
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Chechelnitsky, Michael Y. (Michael Yurievich) 1972. "Adaptive error estimation in linearized ocean general circulation models." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/58516.

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Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 1999.<br>Includes bibliographical references (p. 206-211).<br>Data assimilation methods, such as the Kalman filter, are routinely used in oceanography. The statistics of the model and measurement errors need to be specified a priori. In this study we address the problem of estimating model and measurement error statistics from observations. We start by testing the Myers and Tapley (1976, MT) method of
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Books on the topic "Linearized model"

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David, Hampton R., and Lewis Research Center, eds. The Microgravity Isolation Mount: A linearized state-space model á la Newton and Kane. National Aeronautics and Space Administration, Lewis Research Center, 1999.

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David, Hampton R., and Lewis Research Center, eds. The Microgravity Isolation Mount: A linearized state-space model á la Newton and Kane. National Aeronautics and Space Administration, Lewis Research Center, 1999.

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Lee, Myung W. Linearized inversion of reflection traveltimes. U.S. G.P.O., 1991.

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Chechelnitsky, Michael Y. Adaptive error estimation in linearized ocean general circulation models. Massachusetts Institute of Technology, 1999.

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M, Verdon Joseph, and United States. National Aeronautics and Space Administration., eds. A three-dimensional linearized unsteady Euler analysis for turbomachinery blade rows. National Aeronautics and Space Administration, 1996.

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M, Verdon Joseph, and United States. National Aeronautics and Space Administration., eds. A three-dimensional linearized unsteady Euler analysis for turbomachinery blade rows. National Aeronautics and Space Administration, 1996.

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Montgomery, Matthew D. A three-dimensional linearized unsteady Euler analysis for turbomachinery blade rows. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1997.

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C, Hall Kenneth, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Division., eds. Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1990.

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Bosworth, John T. Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data. National Aeronautics and Space Administration, 1992.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program., ed. Linearized aerodynamic and control law models of the X-29A airplane and comparison with flight data. National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1992.

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Book chapters on the topic "Linearized model"

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Gosse, Laurent. "Linearized BGK Model of Heat Transfer." In Computing Qualitatively Correct Approximations of Balance Laws. Springer Milan, 2013. http://dx.doi.org/10.1007/978-88-470-2892-0_14.

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Buchot, Jean-Marie, and Jean-Pierre Raymond. "A Linearized Model for Boundary Layer Equations." In Optimal Control of Complex Structures. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8148-7_3.

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Montorsi, Arianna, Mario Rasetti, and Allan I. Solomon. "The Fermi-Linearized Hubbard Model: Dimer Ground State." In Interacting Electrons in Reduced Dimensions. Springer US, 1989. http://dx.doi.org/10.1007/978-1-4613-0565-1_4.

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Kuchmin, A. Yu, and V. V. Dubarenko. "Linearized Model of the Mechanism with Parallel Structure." In Smart Electromechanical Systems: The Central Nervous System. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53327-8_13.

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Zhang, Zuorong, Lalita Udpa, Satish S. Udpa, et al. "Linearized MFL Model for Embedded Flaw Detection in Rails." In Review of Progress in Quantitative Nondestructive Evaluation. Springer US, 1996. http://dx.doi.org/10.1007/978-1-4613-0383-1_71.

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Munera, Hector A. "Prediction of Preference Reversals by the Linearized Moments Model." In Understanding Economic Behaviour. Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2470-3_15.

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Zamyshlyaeva, Alyona A., and Georgy A. Sviridyuk. "The Linearized Benney–Luke Mathematical Model with Additive White Noise." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12145-1_21.

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Evangelista, Luiz R., Arianna Montorsi, and Mario Rasetti. "Spectrum of the Fermi-Linearized Extended Hubbard Model on a Dimer." In NATO ASI Series. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4684-5961-6_36.

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Wonia, Adam, Michał Wonia, and Robert Piotrowski. "Control of a Nonlinear and Linearized Model of Self-balancing Electric Motorcycle." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50936-1_31.

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Pimentel-García, Ernesto. "Fully Well-Balanced Methods for Shallow Water Linearized Moment Model with Friction." In SEMA SIMAI Springer Series. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55264-9_17.

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Conference papers on the topic "Linearized model"

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Saetti, Umberto, Ashish Manjhi, Batin Bugday, Alessandro Cocco, and Joseph Horn. "Implementation and Linearization of a State-Space Free Wake Model with a Near-Wake Vortex Lattice Model." In Vertical Flight Society 80th Annual Forum & Technology Display. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1144.

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This paper describes the implementation and linearization of a state-space free-vortex wake model with a near-wake vortex lattice model as applied to a helicopter rotor. Following a detailed mathematical description, the wake model is implemented for a blade element model of a utility helicopter rotor and tested in multiple flight conditions including hover, forward flight, and vortex ring state (VRS), and for simple control inputs. The model is qualitatively verified against a Vortex Particle Method (VPM). Periodic solutions to the wake model are found by time marching the coupled rotor and v
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Manjhi, Ashish, Umberto Saetti, and Joseph Horn. "Analytical Linearization of a State-Space Free Vortex Wake Model." In Vertical Flight Society 80th Annual Forum & Technology Display. The Vertical Flight Society, 2024. http://dx.doi.org/10.4050/f-0080-2024-1254.

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This paper presents the development and application of analytical linearization of a State-Space Free Vortex Wake Model. Previous work developed a state-space free wake model that could be numerically linearized via finite differences into a Linear Time Periodic (LTP) system, but the numerical linearization process was computationally expensive. An improved method is developed that uses exact analytical linearization of the Biot-Savart Law. The analytical method is found to speed up linearization computations by O(N), where N is the number of free wake nodes. A simple decoupled wake model is u
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Kim, Da-Hwi, Jaell Jang, and Chang-Hun Lee. "Rocket Landing Guidance with Linearized Model Predictive Control via Second-order Cone Programming." In 2025 IEEE Aerospace Conference. IEEE, 2025. https://doi.org/10.1109/aero63441.2025.11068520.

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Jensen, Hans. "DC-DC Converter Linearized Model." In 2019 European Space Power Conference (ESPC). IEEE, 2019. http://dx.doi.org/10.1109/espc.2019.8932010.

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Tang, Gongguo, and Lei Guo. "Convergence Analysis of Linearized Vicsek's Model." In 2006 Chinese Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/chicc.2006.280992.

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Jian-xin, Liu, Deng Xiao-kang, Tong Xiao-zhong, Liu Chun-ming, Liu Peng-mao, and Cao Chuang-hua. "Application condition of linearized model uncertainty estimate." In 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet). IEEE, 2011. http://dx.doi.org/10.1109/cecnet.2011.5768451.

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Inovan, Reka, Ahmad Ataka, Hilton Tnunay, M. Qodar Abdurrahman, Adha Cahyadi, and Yoshio Yamamoto. "A cascade controller for linearized Quadrotor model." In 2014 International Conference on Advanced Robotics and Intelligent Systems (ARIS). IEEE, 2014. http://dx.doi.org/10.1109/aris.2014.6871516.

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Adzkiya, Dieky, Hendro Nurhadi, and Teguh Herlambang. "Design of Sliding Mode Control for Linearized Touristant ASV Model." In 2019 International Conference on Advanced Mechatronics, Intelligent Manufacture and Industrial Automation (ICAMIMIA). IEEE, 2019. http://dx.doi.org/10.1109/icamimia47173.2019.9223397.

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Murakami, Shintaroh, and Hidekazu Nishimura. "Modal Analysis of a Motorcycle Motion During Braking for its Stabilization Control System Design." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4013.

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In this paper, modal motion of a motorcycle during braking is analyzed to clarify influence of a stabilization control system designed to the modes. A thirteen degree-of-freedom nonlinear state-space model including rider’s motion is linearized around an equilibrium point of quasi-steady state straight running with constant deceleration, and the modal analysis is carried out using the linearized state-space models. Conducting mode separation and performing simulations utilizing the linearized state-space models, the behavior of the modes including capsize, weave, and wobble modes are analyzed.
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Romero-Camacho, S., V. R. Gonzalez-Diaz, R. C. Ambrosio-Lazaro, G. Mino-Aguilar, E. Bonizzoni, and F. Maloberti. "A new linearized behavioral model for solar cells." In 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe). IEEE, 2017. http://dx.doi.org/10.1109/eeeic.2017.7977498.

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Reports on the topic "Linearized model"

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Rugh, Wilson J. Linearized Model Matching for Single-Imput Nonlinear Systems. Defense Technical Information Center, 1988. http://dx.doi.org/10.21236/ada193642.

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Bach, Christian Friis, and Ken Pearson. Implementing Quotas in GTAP Using GEMPACK or How to Linearize an Inequality. GTAP Technical Paper, 2000. http://dx.doi.org/10.21642/gtap.tp04.

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The methods described in the paper below have been automated as part of Release 8.0 of GEMPACK. This new version of GEMPACK (which is being beta tested by several modellers now and will be officially released later in 2002) makes it very easy to implement quotas (including import/export quotas and tariff rate quotas). This means that many of the implementation details in the technical paper below are no longer required. To implement quotas etc in GEMPACK, please follow the methodology documented in chapter 16 of GEMPACK User documentation GPD-3, which you can find at http://www.copsmodels.com/
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Bonaldi-Varón, Jean Pietro. Identification problems in the solution of linearized DSGE models. Banco de la República, 2010. http://dx.doi.org/10.32468/be.593.

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Girigoudar, Kshitij. Linearized three-phase optimal power flow models for distribution grids. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1813820.

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Butcher, Eric A. Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes. Defense Technical Information Center, 2016. http://dx.doi.org/10.21236/ad1008779.

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An Input Linearized Powertrain Model for the Optimal Control of Hybrid Electric Vehicles. SAE International, 2022. http://dx.doi.org/10.4271/2022-01-0741.

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Models of hybrid powertrains are used to establish the best combination of conventional engine power and electric motor power for the current driving situation. The model is characteristic for having two control inputs and one output constraint: the total torque should be equal to the torque requested by the driver. To eliminate the constraint, several alternative formulations are used, considering engine power or motor power or even the ratio between them as a single control input. From this input and the constraint, both power levels can be deduced. There are different popular choices for th
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