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Research Papers

A Computation-Efficient Framework for the Integrated Design of Structural and Control Systems

[+] Author and Article Information
Yilun Liu

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

Lei Zuo

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061
e-mail: leizuo@vt.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 12, 2015; final manuscript received February 26, 2016; published online May 25, 2016. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 138(9), 091001 (May 25, 2016) (14 pages) Paper No: DS-15-1571; doi: 10.1115/1.4033074 History: Received November 12, 2015; Revised February 26, 2016

This paper proposes a new integrated design method to simultaneously optimize the coupled structural parameters and controllers of mechanical systems by combining decentralized control techniques and Riccati-based control theories. The proposed integrated design method aims at minimizing the closed-loop H2 norm from the disturbance to the system cost. In this paper, the integrated design problems have been formulated in the cases of full state-feedback controllers and full order output-feedback controllers. We extend the current linear time invariant (LTI) control system to a more general framework suitable for the needs of integrated design, where the structural design is treated as a passive control optimization tackled by decentralized control techniques with static output feedback, while the active controller is optimized by solving modified Riccati equations. By using this dual-loop control system framework, the original integrated design problem is transferred to a constrained structural design problem with some additional Riccati-equation based constraints simultaneously integrating the controller synthesis. This reduces the independent design variables from the structural design parameters and the parameters of the controller to the structural design parameters only. As a result, the optimization efficiency is significantly improved. Then the constrained structural design problem is reformed as an unconstrained optimization problem by introducing Lagrange multipliers and a Lagrange function. The corresponding optimal conditions for the integrated design are also derived, which can be efficiently solved by gradient-based optimization algorithms. Later, two design examples, an active–passive vehicle suspension system and an active–passive tuned mass damper (TMD) system, are presented. The improvement of the overall system performance is also presented in comparison with conventional design methods.

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References

Figures

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Fig. 1

(a) A typical linear mechanical system and (b) its integrated design configuration

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Fig. 2

Dual-loop block diagram of the ISSC

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Fig. 3

Dual-loop block diagram of the ISOC

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Fig. 4

(a) Conventional active–passive suspension system (nominal passive system), (b) conventional passive seat-suspension system (nominal active system), and (c) integrated active–passive suspension system (integrated design system)

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Fig. 5

(a) Frequency response from road velocity zr˙ to tire deflection (zu−zr); (b) frequency response from road velocity velocity z˙r to total stroke (zp−zu); (c) frequency response from road velocity z˙r to seat accelerations z¨p; and (d) frequency response from road velocity z˙r to square root of control power ua(z˙p−z˙s)

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Fig. 6

The system response of the vehicle passing through a speed bump: (a) Speed bump dimensions; (b) response of tire deflection (zu−zr); (c) response of total stroke (zp−zu); and (d) response of seat acceleration z¨p

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Fig. 7

The performance of the vehicle suspension system to the changes of the independent design variables: the suspension stiffness ks and the suspension damping cs

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Fig. 8

(a) Conventional passive series TMD system (nominal passive system); (b) conventional active–passive series TMD system (nominal active system); and (c) the integrated design model of an active–passive series TMD system (integrated design system)

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Fig. 9

Frequency response from the normalized wind loading to (a) the building displacement zb/F¯ex, (b) to the total TMD stroke z2−zb/F¯ex, and (c) to the normalized control power u¯a(z˙2−z˙1)/F¯ex

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Fig. 10

Unit impulse response: (a) the building displacement zb and (b) the total TMD stroke z2−zb

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Fig. 11

The performance of the active–passive series TMD system to the changes of the independent design variables: the stiffness of the first TMD k1 and the damping of the first TMD c1

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