• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.607-620
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• 2023

The classical optimal control (COC) method has been widely used for linear quadratic regulator (LQR) problems of structural control. However, the equation of motion of the structure is incorporated into the optimization model as the constraint condition for the LQR problem, which needs to be solved through the Riccati equation under certain assumptions. In this study, an explicit optimal control (EOC) method is proposed based on the explicit time-domain method (ETDM). By use of the explicit formulation of structural responses, the LQR problem with the constraint of equation of motion can be transformed into an unconstrained optimization problem, and therefore the control law can be derived directly without solving the Riccati equation. To further optimize the weighting parameters adopted in the control law using the gradient-based optimization algorithm, the sensitivities of structural responses and control forces with respect to the weighting parameters are derived analytically based on the explicit expressions of dynamic responses of the controlled structure. Two numerical examples are investigated to demonstrate the feasibility of the EOC method and the optimization scheme for weighting parameters involved in the control law.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.956-960
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• 1987

This paper investigates the control problem which is specified by an uncertain linear system and a linear quadratic performance index. Only the size of parameter uncertainty is assumed to be given instead of its statistics. In addition, a mathing condition which constrains the system structure is assumed to be satisfied. The control law can be obtained by solving an LQ optimal control problem for a nominal system.

• Animal Bioscience
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• v.36 no.3
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• pp.498-505
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• 2023

Objective: This study was conducted to determine the optimal dose of novel iron amino acid complexes (Fe-Lys-Glu) by measuring laying performance, egg quality, egg iron (Fe) concentrations, and blood biochemical parameters in laying hens. Methods: A total of 1,260 18-week-old healthy Beijing White laying hens were randomly divided into 7 groups with 12 replicates of 15 birds each. After a 2-wk acclimation to the basal diet, hens were fed diets supplemented with 0 (negative control, the analyzed innate iron content was 75.06 mg/kg), 15, 30, 45, 60, and 75 mg Fe/kg as Fe-Lys-Glu or 45 mg Fe/kg from FeSO₄ (positive control) for 24 wk. Results: Results showed that compared with the negative and positive control groups, dietary supplementation with 30 to 75 mg Fe/kg from Fe-Lys-Glu significantly (linear and quadratic, p<0.05) increased the laying rate (LR) and average daily egg weight (ADEW); hens administered 45 to 75 mg Fe/kg as Fe-Lys-Glu showed a remarkable (linear, p<0.05) decrease in feed conversion ratio. There were no significant differences among all groups in egg quality. The iron concentrations in egg yolk and serum were elevated by increasing Fe-Lys-Glu levels, and the highest iron content was found in 75 mg Fe/kg group. In addition, hens fed 45 mg Fe/kg from Fe-Lys-Glu had (linear and quadratic, p<0.05) higher yolk Fe contents than that with the same dosage of FeSO₄ supplementation. The red blood cell (RBC) count and hemoglobin content (linear and quadratic, p<0.05) increased obviously in the groups fed with 30 to 75 mg Fe/kg as Fe-Lys-Glu in comparison with the control group. Fe-Lys-Glu supplementation also (linear and quadratic, p<0.05) enhanced the activity of copper/zinc-superoxide dismutase (Cu/Zn-SOD) in serum, as a result, the serum malonaldehyde content (linear and quadratic, p<0.05) decreased in hens received 60 to 75 mg Fe/kg as Fe-Lys-Glu. Conclusion: Supplementation Fe-Lys-Glu in laying hens could substitute for FeSO₄ and the optimal additive levels of Fe-Lys-Glu are 45 mg Fe/kg in layers diets based on the quadratic regression analysis of LR, ADEW, RBC, and Cu/Zn-SOD.

• Journal of Astronomy and Space Sciences
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• v.19 no.2
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• pp.107-122
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• 2002

Multi-body spacecraft attitude and configuration control formulations based on the use of collaborative control theory are considered. The control formulations are based on two-player, nonzero-sum, differential game theory applied using a Nash strategy. It is desired that the control laws allow different components of the multi-body system to perform different tasks. For example, it may be desired that one body points toward a fixed star while another body in the system slews to track another satellite. Although similar to the linear quadratic regulator formulation, the collaborative control formulation contains a number of additional design parameters because the problem is formulated as two control problems coupled together. The use of the freedom of the partitioning of the total problem into two coupled control problems and the selection of the elements of the cross-coupling matrices are specific problems ad-dressed in this paper. Examples are used to show that significant improvement in performance, as measured by realistic criteria, of collaborative control over conventional linear quadratic regulator control can be achieved by using proposed design guidelines.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.19-32
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• 2005

It is shown that the problem of minimizing (maximizing) a quadratic cost functional (quadratic gain functional) given the dynamics dx = (fx + gu)dt + hdb(t, a) where b(t, a) is a fractional Brownian motion of order a, 0 < 2a < 1, can be solved completely (and meaningfully!) by using the dynamical equations of the moments of x(t). The key is to use fractional Taylor's series to obtain a relation between differential and differential of fractional order.

• Smart Structures and Systems
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• v.18 no.6
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• pp.1111-1123
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• 2016

The present study aims at proposing an analytical method for semi-active structural control by using block pulse functions. The performance of the resulting controlled system and the requirements of the control devices are highly dependent on the control algorithm employed. In control problems, it is important to devise an accurate analytical method with less computational expenses. Block pulse functions (BPFs) set proved to be the most fundamental and it enjoyed immense popularity in different applications in the area of numerical analysis in systems science and control. This work focused on the application of BPFs in the control algorithm concerning decrease the computational expenses. Variable orifice dampers (VODs) are one of the common semi-active devices that can be used to control the response of civil Structures during seismic loads. To prove the efficiency of the proposed method, numerical simulations for a 10-story shear building frame equipped with VODs are presented. The controlled response of the frame was compared with results obtained by controlling the frame by the classical clipped-optimal control method based on linear quadratic regulator theory. The simulation results of this investigation indicated the proposed method had an acceptable accuracy with minor computational expenses and it can be advantageous in reducing seismic responses.

• 전기의세계
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• v.30 no.8
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• pp.509-516
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• 1981

The optimal control theory is applied to the design of a digital control system for a nuclear reactor. A linear dynamic model obtained at 85% of rated power and a quadratic performance index are used. A minimal order observer used in cascade with the feedback controller is suggested as a state estimator. The total reactor power control is studied in the range of 80% to 100% of rated power, with the steady state and load-following control. The control algorithm considered is suitable for implementation in direct digital control.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.1724_1725
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• 2009

In this paper, new approaches to optimal controller design for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems are proposed based on a relaxed approach, in which non-quadratic Lyapunov function and non-parallel distributed compensation (PDC) control law are used. New relaxed conditions and linear matrix inequality (LMI) based design methods are proposed that allow outperforming previous results found in the literature. Finally, an example is given to demonstrate the efficiency of the proposed approaches.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.209-211
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• 1986

The continuous time linear quadratic problem (LQP) has been applied to the control of a 8-tray distillation column using the code VASP. The weighting matrices for the state variables and control variables were adjusted iteratively. The simulation results of the optimal control with 2 inputs and 2 outputs showed that the LQP method is very satisfactory for a rapid response and feedback control, and any desired response could be obtained by adjusting the weighting matrices Q under = and R under =. The feedback gain matrix K under = was also determined.

• Structural Engineering and Mechanics
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• v.39 no.1
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• pp.147-168
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• 2011

To ensure safety and long term performance, structural control has rapidly matured over the past decade into a viable means of limiting structural responses to strong winds and earthquakes. Nonlinear response history analysis requires rigorous procedure to compute seismic demands. Therefore the simplified nonlinear analysis procedures are useful to determine performance of the structure. In this investigation, application of improved capacity demand diagram method in the control of structural system is presented for the first time. Developed pole assignment method (DPAM) in structural systems control is introduced. Genetic algorithm (GA) is employed as an optimization tool for minimizing a target function that defines values of coefficient matrices providing the placement of actuators and optimal control forces. The ground acceleration is modified under induced control forces. Due to this, performance of structure based on improved nonlinear demand diagram is selected to threshold of nonlinear behavior of structure. With small energy consumption characteristics, semi-active devices are especially attractive solutions for limiting earthquake effects. To illustrate the efficiency of DPAM, a 30-story steel moment frame structure employing the semi-active control devices is applied. In comparison to the widely used linear quadratic regulation (LQR), the DPAM controller was shown to be just as effective and better in the reduction of structural responses during large earthquakes.