• Structural Engineering and Mechanics
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• v.30 no.5
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• pp.593-602
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• 2008

This paper presents a new linearization algorithm to find the periodic solutions of the Duffing equation, under harmonic loads. Since the Duffing equation models a single degree of freedom system with a cubic nonlinear term in the restoring force, finding its periodic solutions using classical harmonic balance (HB) approach requires numerical integration. The algorithm developed in this paper replaces the integrals appearing in the classical HB method with triangular matrices that are evaluated algebraically. The computational cost of using increased number of frequency components in the matrixbased linearization approach is much smaller than its integration-based counterpart. The algorithm is computationally efficient; it only takes a few iterations within the region of convergence. An example comparing the results of the linearization algorithm with the "exact" solutions from a 4th order Runge- Kutta method are presented. The accuracy and speed of the algorithm is compared to the classical HB method, and the limitations of the algorithm are discussed.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.740-756
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• 2017

This paper proposes a feedback-linearization-based control algorithm for multirotor unmanned aerial vehicles (UAVs). The feedback linearization scheme is highly efficient for considering nonlinearity between the rotational and translational motion of multirotor UAVs. We also propose a dynamic equation that reflects the aerodynamic effects of the vehicles; the equation's parameters can be determined through curve fitting using actual flight data. We derive the feedback linearization controller from the proposed dynamic equation, and propose a Luenberger observer to attenuate measurement noises. The proposed algorithm is implemented using our in-house flight control computer, and we describe its implementation in detail. To investigate the performance of the proposed algorithm, we carry out two flight scenarios: the first scenario, an autonomous landing on a moving platform, is a test of maneuverability; the second, picking up and replacing an object, test the algorithm's accuracy. In these scenarios, the proposed algorithm precisely controls multirotor UAVs, and we confirm that it can be successfully applied to real flight environments.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.56.5-56
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• 2002

This paper studies on the feedback linearization of the looper system for hot strip mills, where the looper system plays an important role in regulating the strip tension. Firstly, nonlinear dynamic equations of the looper system are simply introduced. Secondly, using the static feedback linearization algorithm, a linear model of the looper system is obtained, of which usefulness is validated from comparison between the linear model and the nonlinear model, and design of LQI(Linear Ouadratic Integral optimal control) and ILQ (Inverse Linear Quadratic optimal control) looper control systems. In result, it is shown that the linear looper model by the feedback linearization well describes nonlin...

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.4
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• pp.578-585
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• 2015

Electromagnetic levitation system(EMLS) is one of the well known nonlinear systems. Often, it is not easy to control an EMLS due to its high nonlinearity. In this paper, we first apply two linearization method(jacobian and input-output feedback linearization) to design two feedback controllers for an EMLS. Then, by observing the advantages of each controller, we design a switching control algorithm which engage two controllers depending on the position of the steel ball in order to achieve the improved performance over each controller. The validity of our switching control approach is verified via both simulation and actual experimental results.

• Journal of Yeungnam Medical Science
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• v.16 no.2
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• pp.237-243
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• 1999

We conducted this study to find the optimal correction factor(${\alpha}$) of Lassen's linearization algorithm which has been applied for correction of flow-limited uptake at a high flow range in $^{99m}Tc$ d,l-hexamethylpropy leneamine oxime(HMPAO) and $^{99m}Tc$ ethyl cysteinate dimer(ECD). Ten patients with chronic cerebral infarction were involved in this study. We obtained the corrected $^{99m}Tc$ HMPAO and $^{99m}Tc$-ECD brain SPECT(single photon emission computed tomography) using the algorithm with ${\alpha}$ values that varied from 0.1 to 10 and compared the results with regional cerebral blood flow determined by positron emission tomography (PET-rCBF). The multi-modal volume registration by maximization of mutual information was used for matching between PET-rCBF and SPECT images. The highest correlation coefficient between $^{99m}Tc$-HMPAO and $^{99m}Tc$-ECD brain uptake and PET-rCBF was revealed at ${\alpha}$ 1.4 and 2.1, respectively. We concluded that the ${\alpha}$ values of Lassen's linearization algorithm for $^{99m}Tc$-HMPAO and $^{99m}Tc$-ECD brain SPECT images were 1.4 and 2.1, respectively to indicate cerebral blood flow with comparison of PET-rCBF.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1221-1224
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• 1996

As in most industrial processes, the dynamic characteristics of an electric power system are subject to changes. Amongst those effects which cause the system to be uncertain, faults on transmission lines are considered. For the stabilization of the power system, we present an indirect adaptive control method, which is capable of tracking a sudden change in the effective reactance of a transmission line. As the plant dynamics are nonlinear, an input-output feedback linearization method is combined with an identification algorithm which estimates the effect of a fault.

• Journal of Mechanical Science and Technology
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• v.17 no.11
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• pp.1608-1615
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• 2003

This paper studies on the linearization of a looper system in hot strip mills, that plays an important role in regulating a strip tension or a strip width. Nonlinear dynamic equations of the looper system are analytically linearized by a static feedback linearization algorithm with a compensator. The proposed linear model of the looper is validated by a comparison with a linear model using Taylor's series. It is shown that the linear model by static feedback well describes nonlinearities of the looper system than one using Taylor's series. Furthermore, it is shown from the design of an ILQ controller that the linear model by static feedback is very useful in designing a linear controller of the looper system.

• Journal of Korean Institute of Industrial Engineers
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• v.39 no.4
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• pp.253-259
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• 2013

Investment scenarios in the transportation network design problem usually contain installation or expansion of multi-mode transportation links. When one applies the mode choice analysis and traffic assignment sequentially for each investment scenario, it is possible that the travel impedance used in the mode choice analysis is different from the user equilibrium cost of the traffic assignment step. Therefore, to estimate the travel impedance and mode choice accurately, one needs to develop a combined model for the mode choice and traffic assignment. In this paper, we derive the inverse demand and the excess demand functions for the multi-mode multinomial logit mode choice function and develop a combined model for the multi-mode variable demand traffic assignment problem. Using data from the regional O/D and network data provided by the KTDB, we compared the performance of the partial linearization algorithm with the Frank-Wolfe algorithm applied to the excess demand model and with the sequential heuristic procedures.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.10
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• pp.127-136
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• 2004

This paper is the first of two companion papers concerning the analysis and design of a pneumatic vibration isolation system. The design optimization of the pneumatic vibration isolation system is required for the reduction of cost, endeavor and time, and it needs modeling and calculation algorithm. The nonlinear models are devised from the fluid mechanical expression for components of the system and the calculation algorithm is derived from the mathematical relationship between the models. It is shown that the orifice makes the nonlinear property of the transmissibility curve that the resonant frequency changes by the amplitude of excited vibration. Linearization of the nonlinear models is tried to reduce elapsed time and truncation error accumulation and to enable the transmissibility calculation of the system with multi damping chambers. The equivalent mechanical models generated by linearization clarify the function of each component of the system and lead to the linearized transfer function that can give forth to the transmissibility exactly close to that of nonlinear models. The modified successive under-relaxation method is developed to calculate the linearized transfer function.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.253-263
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• 2002

This paper presents an adaptive feedback linearization control scheme for induction motors using stator fluxes. By using stator flukes as states, overparameterization is prevented and control inputs can be determined straightforwardly unlike in existing schemes. This approach leads to the decrease of the relative degree for the flux modulus and thus yields a simpler control algorithm than the prior results. In this paper. adaptation schemes are suggested to compensate for the variations of stator resistance. rotor resistance and load torque. In particular, the adaptation to the variation of stator resistance with a feedback linearization control is a new trial. In addition, to improve the convergence of rotor resistance estimation, the differences between stator currents and its estimates are used for the parameter adaptation. The simulations show that torque and flux are controlled independently and that the estimates of stator resistance, rotor resistance, and load torque converge to their true values. Actual experiments on a 3.7㎾ induction motor verify the effectiveness of the proposed method.