• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1127-1144
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• 2013

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order $k(k{\geq}1)$. $L^2$ and $L^{\infty}$-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.

• Proceedings of the KIPE Conference
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• 2007.07a
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• pp.421-423
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• 2007

In this paper, The authors apply a state feedback control using an optimal control theory to improve the stability of the control and the dynamic response of the DC-DC converter system with a number of different loads. To execute a this state feedback control, The authors present the pole placement technique using Linear Quadratic Regulator(LQR) to optimally control the system. An integrator can also be included in the open-loop path in order to minimize the steady-state error of the output voltage. To confirm the superiority of the controller, The simulation results are presented.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.2
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• pp.121-126
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• 2000

In the fast sampling limit the delta operator model tends to the analog system model. This fundamental property of the delta operator model unifies continuous and discrete time control system. In this paper we study robust linear optimal model following servo system in the presence of disturbances and parameter perturbations. A technique to directly design the generalized differential operator based unified control system that covers both differential operator based continuous time and delta operator based discrete time case is presented. The quadratic criterion function for a linear system is used to design the robust unified servo control system The characteristics of the proposed servo system are analysed and simulated to verify the robustness.

• Smart Structures and Systems
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• v.6 no.8
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• pp.921-938
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• 2010

Most of studies on control of beams containing piezoelectric sensors and actuators have been based on linear quadratic regulator (LQR) with state feedback or output feedback law. The aim of this study is to develop velocity-acceleration feedback law in the optimal control of smart piezoelectric beams. A new controller which is an optimal control system with velocity-acceleration feedback is presented. In finite element modeling of the beam, the variation of mechanical displacement through the thickness is modeled by a sinus model that ensures inter-laminar continuity of shear stress at the layer interfaces as well as the boundary conditions on the upper and lower surfaces of the beam. In addition to mechanical degrees of freedom, one electric potential degree of freedom is considered for each piezoelectric element layer. The efficiency of this control strategy is evaluated by applying to an aluminum cantilever beam under different loading conditions. Numerical simulations show that this new control scheme is almost as efficient as an optimal control system with state feedback. However, inclusion of the acceleration in the control algorithm increases practical value of a system due to easier and more accurate measurement of accelerations.

• Proceedings of the KIPE Conference
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• 2018.07a
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• pp.344-345
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• 2018

In order to alleviate the negative impacts of harmonically distorted grid condition on grid-connect inverters, an optimal control design-based gain selection scheme of an LCL-filtered grid-connected inverter and its ability to compensate selective harmonics are presented in this paper. By incorporating resonant terms into the control structure in the state-space to provide infinity gain at selected frequencies, the proposed control offers an excellent steady-state response even under distorted grid voltage. The proposed control scheme is achieved by using a state feedback controller for stabilization purpose and by augmenting the resonant terms as well as intergral term into a control structure for reference tracking and harmonic compensation. Furthermore, the optimal linear quadratic control approach is adopted for choosing an optimal feedback gain to ensure an asymptotic stability of the whole system. A discrete-time full state observer is also introduced into the proposed control scheme for the purpose of reducing a total number of sensors used in the inverter system. The simulation results are given to prove the effectiveness and validity of the proposed control scheme.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.1-10
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• 2003

This paper presents a high-precision magnetically levitated (maglev) stage to meet demanding motion specifications in the next-generation precision manufacturing and nanotechnology. Characterization of dynamic behaviors of such a motion stage is a crucial task. In this paper, we address the issues related to the stochastic modeling of the stage including transfer function identification, and noise/disturbance analysis and prediction. Provided are test results on precision dynamics, such as fine settling, effect of optical table oscillation, and position ripple. To deal with the dynamic coupling in the platen, we designed and implemented a multivariable linear quadratic regulator, and performed time-optimal control. We demonstrated how the performance of the current maglev stage can be improved with these analyses and experimental results. The maglev stage operates with positioning noise of 5 nm rms in $\chi$ and y, acceleration capabilities in excess of 2g(20 $m/s^2$), and closed-loop crossover frequency of 100 Hz.

• 전기의세계
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• v.26 no.2
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• pp.99-103
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• 1977

The object of this work is to study an optimal design problem of the proportional load-frequency controller for the single-control area power system. The selfservice power station is still a popular means as a power supplying source on ships or in a certain manufacturing area. The power system of this kind can be formulated as a single control-area system and it attracts a certain academic interest in controlling the system frequency under disturbances. In this paper, the single control-area system is mathematically formulated as a linear, time-invariant system in state-space under certain assumptions. The optimal proportional control law and the realization of the controller in closed loop-version is studied so that the final system designed can attain the system frequency to the nominal stationing value after the small load-disturbance. As in general cases of optimal design problems, the performance index is assumed to be quadratic in states and the control effort, and the infinite time control process is assumed in this work. The final control system realized depicts certain improvements in case study; in stability, transient responses and in steady-state frequency deviation, even though the steady state error did not attain the zero value.

• Proceedings of the KIEE Conference
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• 2005.07d
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• pp.2471-2473
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• 2005

We present a receding horizon control [RHC] algorithm for compensation of backlash at the input of a stable linear system under control rate constraints. The problem is posed as a receding horizon optimal control [RHOptC] problem for a piecewise affine [PWA] system by modelling the backlash nonlinearity as a PWA system with a state space partition consisting of three regions. The RHC problem involves solving, at each step, $3^N$ quadratic programmes[QP], where N is the optimization horizon. This strategy leads, at the cost of some performance degradation, to much smaller computational load since a feasible rather than optimal solution has to be obtained at each step.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.11
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• pp.1118-1124
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• 2014

This paper proposes a novel controller design scheme for multimachine power systems based on the explorized policy iteration. Power systems have several uncertainties on system dynamics due to the various effects of interconnections between generators. To solve this problem, the proposed method solves the LQR (Linear Quadratic Regulation) problem of isolated subsystems without the knowledge of a system matrix and the interconnection parameters of multimachine power systems. By selecting the proper performance indices, it guarantees the stability and convergence of the LQ optimal control. To implement the proposed scheme, the least squares based online method is also investigated in terms of PE (Persistency of Excitation), interconnection parameters and exploration signals. Finally, the performance and effectiveness of the proposed algorithm are demonstrated by numerical simulations of three-machine power systems with governor controllers.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.365-370
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• 2000

A sliding mode fuzzy control (SMFC) algorithm is applied to design a controller for a benchmark problem on a wind- excited building. The structure is a 76-story concrete office tower with a height of 306 meters, hence the wind resistance characteristics are very important for the serviceability as well as the safety. A control system with an active tuned mass damper is assumed to be installed on the top floor. Since the structural acceleration is measured only at ,limited number of locations without measurement of the wind force, the structure of the conventional continuous sliding mode control may have the feed-back loop only. So, an adaptive least mean squares (LMS) filter is employed in the SMFC algorithm to generate a fictitious feed-forward loop. The adaptive LMS filter is designed based on the information of the stochastic characteristics of the wind velocity along the structure. A numerical study is carried out. and the performance of the present SMFC with the ,adaptive LMS filter is investigated in comparison with those of' other control, of algorithms such as linear quadratic Gaussian control, frequency domain optimal control, quadratic stability control, continuous sliding mode control, and H/sub ∞///sub μ/, control, which were reported by other researchers. The effectiveness of the adaptive LMS filter is also examined. The results indicate that the present algorithm is very efficient .