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Research Papers

Using Constrained Bilinear Quadratic Regulator for the Optimal Semi-Active Control Problem

[+] Author and Article Information
I. Halperin

Department of Civil Engineering,
Faculty of Engineering,
Ariel University,
Ariel 40700, Israel
e-mail: idoh@ariel.ac.il

G. Agranovich

Professor
Department of Electrical
and Electronics Engineering,
Faculty of Engineering,
Ariel University,
Ariel 40700, Israel
e-mail: agr@ariel.ac.il

Y. Ribakov

Professor
Department of Civil Engineering,
Faculty of Engineering,
Ariel University,
Ariel 40700, Israel
e-mail: ribakov@ariel.ac.il

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 31, 2016; final manuscript received June 21, 2017; published online August 9, 2017. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 139(11), 111011 (Aug 09, 2017) (8 pages) Paper No: DS-16-1424; doi: 10.1115/1.4037168 History: Received August 31, 2016; Revised June 21, 2017

Semi-active systems provide an attractive solution for the structural vibration problem. A useful approach, aimed to simplify the control design, is to divide the control system into two parts: an actuator and a controller. The actuator generates a force that tracks a command which is generated by the controller. Such approach reduces the complexity of the control law design as it allows for complex properties of the actuator to be considered separately. In this study, the semi-active control design problem is treated in the framework of optimal control theory by using bilinear representation, a quadratic performance index, and a constraint on the sign of the control signal. The optimal control signal is derived in a feedback form by using Krotov's method. To this end, a novel sequence of Krotov functions which suits the multi-input constrained bilinear-quadratic regulator problem is formulated by means of quadratic form and differential Lyapunov equations. An algorithm is proposed for the optimal control computation. A proof outline for the algorithm convergence is provided. The effectiveness of the suggested method is demonstrated by numerical example. The proposed method is recommended for optimal semi-active feedback design of vibrating plants with multiple semi-active actuators.

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References

Figures

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Fig. 1

CBQR—Successive improvement of control process

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Fig. 2

A scheme of the analyzed building and the actuators location

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Fig. 3

Performance index values for each iteration

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Fig. 4

Control signals for cases C and D

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Fig. 5

Case B—control force versus actuator velocity

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Fig. 6

Case D—control force versus actuator velocity

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Fig. 7

Roof displacements

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Fig. 8

Peak DOFs accelerations

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Fig. 9

Nonlinear frequency response function

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