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Research Papers

Combined Plant and Controller Design Using Batch Bayesian Optimization: A Case Study in Airborne Wind Energy Systems

[+] Author and Article Information
Ali Baheri

Department of Mechanical Engineering and
Engineering Science,
University of North Carolina,
Charlotte, NC 28223
e-mail: akhayatb@uncc.edu

Chris Vermillion

Department of Mechanical and
Aerospace Engineering,
North Carolina State University,
Raleigh, NC 27695;
Altaeros Energies, Inc.,
Boston, MA 02143
e-mail: cvermil@ncsu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 24, 2018; final manuscript received March 8, 2019; published online May 2, 2019. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 141(9), 091013 (May 02, 2019) (11 pages) Paper No: DS-18-1398; doi: 10.1115/1.4043224 History: Received August 24, 2018; Revised March 08, 2019

This paper presents a novel data-driven nested optimization framework that addresses the problem of coupling between plant and controller optimization. This optimization strategy is tailored toward instances where a closed-form expression for the system dynamic response is unobtainable and simulations or experiments are necessary. Specifically, Bayesian optimization, which is a data-driven technique for finding the optimum of an unknown and expensive-to-evaluate objective function, is employed to solve a nested optimization problem. The underlying objective function is modeled by a Gaussian process (GP); then, Bayesian optimization utilizes the predictive uncertainty information from the GP to determine the best subsequent control or plant parameters. The proposed framework differs from the majority of codesign literature where there exists a closed-form model of the system dynamics. Furthermore, we utilize the idea of batch Bayesian optimization at the plant optimization level to generate a set of plant designs at each iteration of the overall optimization process, recognizing that there will exist economies of scale in running multiple experiments in each iteration of the plant design process. We validate the proposed framework for Altaeros' buoyant airborne turbine (BAT). We choose the horizontal stabilizer area, longitudinal center of mass relative to center of buoyancy (plant parameters), and the pitch angle set-point (controller parameter) as our decision variables. Our results demonstrate that these plant and control parameters converge to their respective optimal values within only a few iterations.

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Figures

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Fig. 1

Altaeros BAT, adpated from Ref. [1]

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Fig. 2

Machine learning variant of nested plant and controller codesign using batch Bayesian optimization

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Fig. 3

Clarification of iteration versus time in the proposed framework

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Fig. 4

Ground-fixed and body-fixed coordinates plus the key variables used in deriving Euler–Lagrangian dynamics

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Fig. 5

Block diagram of closed-loop flight controller for the BAT. zsp denotes a constant altitude set-point. We choose pc=θsp and pp=[xcm−xcb AH]T in our case study results.

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Fig. 6

Water channel experimental setup at UNC Charlotte

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Fig. 7

Convergence of plant parameters, control parameter, and integral cost function for 1, 3, and 4 batch sizes (from upper left to lower right)

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Fig. 8

Sample evolution of control parameter (i.e., trim pitch angle) and actual pitch angle in inner loop over the time

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Fig. 9

(Zoomed) roll tracking error before and after the optimization

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Fig. 10

(Zoomed) heading tracking error before and after the optimization

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Fig. 11

Zenith angle before and after the optimization

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Fig. 12

1/100-scale BAT model

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