• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.503-505
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• 1999

Linear cheap control problem is a special form of linear quadratic regulator problem in which a small parameter ${\varepsilon}^2$ is multiplied with the control term. The joint problem in which cheap control is applied to a weakly coupled discrete system has not been reported in the literature. In this paper, the high-gain problem and decoupling problem on discrete weakly coupled system are considered together. We derive Hamiltonian matrix when the cheap control is applied to a weakly coupled discrete system and use it in developing numerical formulations in the process of applying parallel algorithm to the system.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.84-91
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• 2006

The synthesis of optimal controllers for multivariable systems usually requires an accurate linear model of the plant dynamics. Real systems, however, contain nonlinearities and high-order dynamics that may be difficult to model using conventional techniques. This paper presents a novel loaming method for the synthesis of LQR controllers that doesn't require explicit modeling of the plant dynamics. This method utilizes the sign of Jacobian and gradient descent techniques to iteratively reduce the LQR objective function. It becomes easier and more convenient because it is relatively very easy to get the sign of Jacobian instead of its Jacobian. Simulations involving an overhead crane and a hydrofoil catamaran show that the proposed LQR-LC algorithm improves controller performance, even when the Jacobian information is estimated from input-output data.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.660-664
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• 2003

The optimal thickness distribution of an active damping layer is sought so that it satisfies a certain constraint on the dynamic performance of a system minimizing control efforts. To obtain a topologically optimized configuration, which includes size and shape optimization, thickness of the active damping layer is interpolated using linear functions. With the control energy as the objective function to be minimized, the state error energy is introduced as the dynamic performance criterion for the system and used lot a constraint. The optimal control gains are evaluated from LQR simultaneously as the optimization of the layer position proceeds. From numerical simulation, the topologically optimized distribution of the active damping layer shows the same dynamic performance and cost as the Idly covered counterpart, which is optimized only in terms of control gains, with less amount of the layer.

• Structural Engineering and Mechanics
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• v.67 no.1
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• pp.33-43
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• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.

• 한국기계연구소 소보
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• s.17
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• pp.157-165
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• 1987

The SWATH concept hull form which is capable of high speed navigation with small oscillatory motions in waves, was developed from the catamaran type hull forms. This paper describes how the motion of a SWATH ship in irregular waves can be reduced by regulating the stabilizing fins. The optimal regulator and LQG (Linear Quadratic Gaussian) controller for vertical plane motion have been applied for both platforming mode and contouring mode controls. The calculations of hydrodynamic coefficients and external forces are possible for defining the system equation for the design purpose of motion control. Performances of the controlled system are compared with those of original system.

• Journal of Ocean Engineering and Technology
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• v.30 no.2
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• pp.134-140
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• 2016

An envelope protection system is a control system that allows a submarine to operate freely using its own operational envelope without exceeding the structural limit, dynamic limit, and control input limit. In this paper, an envelope protection system for the pitch angle of a submarine is designed using a dynamic trim algorithm. A linear quadratic regulator and artificial neural network are used for the true dynamics approximation. A submarine maneuvering simulation program developed using experimental data is used to validate the designed envelope protection system. Simulation results show the effectiveness of the designed envelope protection system.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2566-2569
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• 2003

An alternative optimal control law formulation is introduced and compared with two different control law, a conventional linear quadratic regulator and the control law based on game theory. This formulation eliminates the undesired modes of the system by the projection of a controller onto the subspace orthogonal to that of the bad modes. In conventional LQR control law, the control performance can be improved only by using proper weighting matrices in performance index, normally, with high cost. The control law formulation by game theory may provide various ways to obtain the desired performance. The control law modified by the elimination of bad modes provides efficient ways to get rid of an undesired performance since it eliminates the exact modes which cause the bad control performance.

• East Asian mathematical journal
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• v.34 no.5
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• pp.661-681
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• 2018

In this paper, we discuss a reduced-order modeling for the Benjamin-Bona-Mahony-Burgers (BBMB) equation and its application to a distributed feedback control problem through the centroidal Voronoi tessellation (CVT). Spatial distcritization to the BBMB equation is based on the finite element method (FEM) using B-spline functions. To determine the basis elements for the approximating subspaces, we elucidate the CVT approaches to reduced-order bases with snapshots. For the purpose of comparison, a brief review of the proper orthogonal decomposition (POD) is provided and some numerical experiments implemented including full-order approximation, CVT based model, and POD based model. In the end, we apply CVT reduced-order modeling technique to a feedback control problem for the BBMB equation.

• 전기의세계
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• v.25 no.5
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• pp.70-74
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• 1976

In this paper, the problem of controlling deterministic contimuous linear system with a slightly modified quadratic performance criteria is studied. When the number of out put variables is much lesser then that of state variables, either the controller becomes complex or the performance measure becomes much higher with only output feedback. So the design philosphy treated in this paper lies in finding a compromising point between the controller complexity and the performance measure. thd controller is composed of stasic plus dynamic compensator with order equal to the mtmber of output variables. Several unknowns are unknown parameters are bundled into one, and using Pontryagin's minimum principle, conditions and formula for optimum control are induced which are different from that of Kalman optimal regulator.