• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.11
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• pp.73-79
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• 1997

This paepr is concerned with the design of linear parameter varying filter that ensures H$^{2}$/$H^{\infty}$ performance for a class of linear parameter varying(LPV) plants. The state space matrices of plant are assumed to be dependent affinely on a vector of time varying parameter, and each parameter is assumed to be measured in real time. Using the linear matrix inequalities(LMIs), we can solve the synthesis problem and the solution of LMIs is carried out off-line. The designed filter is parameter varying and automatically scheduled along parameter trajectories. Because the solution of LMIs is carried out off-line, computation time of filter gain is reduced. The validity of the proposed algorithm is verifed through computer simulation..

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.836-844
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• 2008

This paper presents an approach to order reduction of linear parameter varying controller for polytopic model. Feasible solutions which satisfy relevant linear matrix inequalities for constructing full-order parameter varying controller evaluated at each polytopic vertices are first found. Next, sufficient conditions are derived for the existence of a right coprime factorization of parameter varying controller. Furthermore, a singular perturbation approximation for time invariant systems is generalized to reduce full-order parameter varying controller via parameter varying right coprime factorization. This generalization is based on solutions of the parameter varying Lyapunov inequalities. The closed loop performance caused by using the reduced order controller is developed. To examine the performance of the reduced-order parameter varying controller, the proposed method is applied to reduce vibration of flexible structures having the transverse-torsional coupled vibration modes.

• Smart Structures and Systems
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• v.9 no.4
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• pp.373-392
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• 2012

Tracking control of systems with variable stiffness hysteresis using a gain-scheduled (GS) controller is developed in this paper. Variable stiffness hysteretic system is represented as quasi linear parameter dependent system with known bounds on parameters. Assuming that the parameters can be measured or estimated in real-time, a GS controller that ensures the performance and the stability of the closed-loop system over the entire range of parameter variation is designed. The proposed method is implemented on a spring-mass system which consists of a semi-active independently variable stiffness (SAIVS) device that exhibits hysteresis and precisely controllable stiffness change in real-time. The SAIVS system with variable stiffness hysteresis is represented as quasi linear parameter varying (LPV) system with two parameters: linear time-varying stiffness (parameter with slow variation rate) and stiffness of the friction-hysteresis (parameter with high variation rate). The proposed LPV-GS controller can accommodate both slow and fast varying parameter, which was not possible with the controllers proposed in the prior studies. Effectiveness of the proposed controller is demonstrated by comparing the results with a fixed robust $\mathcal{H}_{\infty}$ controller that assumes the parameter variation as an uncertainty. Superior performance of the LPV-GS over the robust $\mathcal{H}_{\infty}$ controller is demonstrated for varying stiffness hysteresis of SAIVS device and for different ranges of tracking displacements. The LPV-GS controller is capable of adapting to any parameter changes whereas the $\mathcal{H}_{\infty}$ controller is effective only when the system parameters are in the vicinity of the nominal plant parameters for which the controller is designed. The robust $\mathcal{H}_{\infty}$ controller becomes unstable under large parameter variations but the LPV-GS will ensure stability and guarantee the desired closed-loop performance.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.5
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• pp.351-356
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• 2002

This papaer deals with a model reduction problem for linear systems with time varying parameters. For this problem, a controllability Grammian and an observability Grammian are introduced and computed by solving linear matrix inequalities. Using the controllability/observability Grammian, a balanced state space realization for linear parameter varying systems is obtained. From the balanced state space realization, a reduced model can be obtained by truncating not only states but also time varying parameters and an upper bound of the model reduction error is derived as well.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.484-491
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• 2003

For most of linear time-varying (LTV) systems, it is difficult to design time-varying controllers in analytic way. Accordingly, by approximating LTV systems as uncertain linear time-invariant, control design approaches such as robust control have been applied to the resulting uncertain LTI systems. In particular, a robust control method such as quantitative feedback theory (QFT) has an advantage of guaranteeing the frozen-time stability and the performance specification against plant parameter uncertainties. However, if these methods are applied to the approximated linear. time-invariant (LTI) plants with large uncertainty, the resulting control law becomes complicated and also may not become ineffective with faster dynamic behavior. In this paper, as a method to enhance the fast dynamic performance of LTV systems with bounded time-varying parameters, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks.

• Journal of Electrical Engineering and Technology
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• v.8 no.5
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• pp.1202-1211
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• 2013

This paper deals with a robust controller for an induction motor (IM) which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback are associated. This approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic LPV system because of speed and rotor resistance affine dependence. Their values can be estimated on line during systems operations. The simulation and experimental results largely confirm the effectiveness of the proposed control.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.199-199
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• 2000

Most of linear time-varying(LTV) systems except special cases have no general solution for the dynamic equations. Thus, it is difficult to design time-varying controllers in analytic ways, and other control design approaches such as robust control have been applied to control design for uncertain LTI systems which are the approximation of LTV systems have been generally used instead. A robust control method such as quantitative feedback theory(QFT) has an advantage of guaranteeing the stability and the performance specification against plant parameter uncertainties in frozen time sense. However, if these methods are applied to the approximated linear time-invariant(LTI) plants which have large uncertainty, the designed control will be constructed in complicated forms and usually not suitable for fast dynamic performance. In this paper, as a method to enhance the fast dynamic performance, the approximated uncertainty of time-varying parameters are reduced by the proposed QFT parameter-scheduling control design based on radial basis function (RBF) networks for LTV systems with bounded time-varying parameters.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.68.5-68
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• 2001

This paper investigates the problem of linear parameter-dependent output feedback controllers design for interconnected linear parameter-varying(LPV) plant. By using a parameter-independent common Lyapunov function, sucient conditions for solving the problems are established, which allow us to design linear parameter dependent decentralized controllers in terms of scaled H-infinite control problems for related linear systems without interconnections. The solvability conditions are expressed in terms of finite-dimensional linear matrix inequalities(LMI´s) evaluated at the extreme points of the admissible parameter set.

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.809-817
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• 2012

We propose a semiparametric inference for a generalized varying coefficient partially linear model(VCPLM) for negative binomial data. The VCPLM is useful to model real data in that varying coefficients are a special type of interaction between explanatory variables and partially linear models fit both parametric and nonparametric terms. The negative binomial distribution often arise in modelling count data which usually are overdispersed. The varying coefficient function estimators and regression parameters in generalized VCPLM are obtained by formulating a penalized likelihood through smoothing splines for negative binomial data when the shape parameter is known. The performance of the proposed method is then evaluated by simulations.

• International Journal of Automotive Technology
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• v.8 no.4
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• pp.445-453
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• 2007

This paper presents a robust controller design approach for improving vehicle dynamic roll motion performance and guaranteeing the closed-loop system stability in spite of vehicle parameter variations resulting from aging elements, loading patterns, and driving conditions, etc. The designed controller is linear parameter-varying (LPV) in terms of the time-varying parameters; its control objective is to minimise the $H_{\infty}$ performance from the steering input to the roll angle while satisfying the closed-loop pole placement constraint such that the optimal dynamic roll motion performance is achieved and robust stability is guaranteed. The sufficient conditions for designing such a controller are given as a finite number of linear matrix inequalities (LMIs). Numerical simulation using the three-degree-of-freedom (3-DOF) yaw-roll vehicle model is presented. It shows that the designed controller can effectively improve the vehicle dynamic roll angle response during J-turn or fishhook maneuver when the vehicle's forward velocity and the roll stiffness are varied significantly.