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Research Papers

Restructuring Controllers to Accommodate Plant Nonlinearities

[+] Author and Article Information
William G. La Cava

Department of Mechanical and
Industrial Engineering,
University of Massachusetts,
Amherst, MA 01003
e-mail: wlacava@umass.edu

Kushal Sahare

Department of Mechanical and
Industrial Engineering,
University of Massachusetts,
Amherst, MA 01003
e-mail: ksahare@umass.edu

Kourosh Danai

Professor
Fellow ASME
Department of Mechanical and
Industrial Engineering,
University of Massachusetts,
Amherst, MA 01003
e-mail: danai@umass.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 30, 2016; final manuscript received January 17, 2017; published online May 17, 2017. Assoc. Editor: Sergey Nersesov.

J. Dyn. Sys., Meas., Control 139(8), 081004 (May 17, 2017) (10 pages) Paper No: DS-16-1277; doi: 10.1115/1.4035870 History: Received May 30, 2016; Revised January 17, 2017

A method of controller restructuring is introduced for improved closed-loop control of nonlinear plants. In this method, an initial controller, potentially the linear controller designed according to the linearized model of the plant, is expanded into several candidate nonlinear control structures that are subsequently shaped to achieve a desired closed-loop response. The salient feature of the proposed method is a metric for quantifying structural perturbations to the controllers, which it uses to scale the structural Jacobian for improving its condition number. This improved Jacobian underlies shaping of candidate controllers through gradient-based search. Results obtained from three case studies indicate the success of the proposed restructuring method in finding nonlinear controllers that improve not only the closed-loop response of the nonlinear plant but also its robustness to modeling uncertainty.

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Figures

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Fig. 1

Schematic of restructured controller adaptation by MSAM

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Fig. 2

Illustration of the two adaptation stages by MSAM, candidate model selection in the round robin stage, followed by further adaptation of the selected model in the second stage, as represented by the inverse of the fitness value for each model

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Fig. 3

Block diagram of the first platform, consisting of a linear plant actuated by a nonlinear valve (Adapted from [2])

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Fig. 4

Step responses and control efforts of the closed-loop customized solution in Fig.3 at different reference magnitudes

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Fig. 5

Effect of modeling inaccuracy on the step responses and control efforts of the closed-loop solution in Fig. 3

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Fig. 6

Inverted pendulum on a cart used as the plant in the second study platform

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Fig. 7

Closed-loop impulse responses (y = θ) and control efforts of the inverted pendulum on a cart controlled by linear state feedback. Impulse magnitudes are in newton.

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Fig. 8

Step responses and control efforts of the restructured and initial (PI) controllers from the first platform shown with the desired response used for controller restructuring

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Fig. 9

Step responses of the initial and restructured controllers and their control efforts from the first platform at different reference magnitudes as well as those of the customized controller in Fig. 3

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Fig. 10

Impulse responses and control efforts of the linear and restructured controllers from the inverted pendulum on a cart (second platform) shown with the desired response used for controller restructuring

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Fig. 11

Impulse responses and control efforts of the linear and restructured controllers from the inverted pendulum on a cart at impulse magnitudes of 15–20

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Fig. 12

Stabilizing responses of the inverted pendulum (third platform) and the corresponding control efforts by the initial (linear), feedback linearized, and restructured controllers to an initial displacement shown with the desired response used for restructuring

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Fig. 13

Closed-loop step response and control effort ranges of the first platform by restructured and customized controllers in presence of additive band-limited measurement noise at the approximate signal-to-noise ratios of 18 at r = 1–33 at r = 5

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Fig. 14

Closed-loop responses and control efforts of the first platform by restructured and customized controllers to unit step disturbances before G0(s) in Fig. 3 (at time 100) and after G0(s) (at time 200)

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Fig. 15

Closed-loop responses and control efforts of the first platform by restructured and customized controllers at higher step sizes (6–15) than those (1–5) used for restructuring

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Fig. 16

Closed-loop impulse responses and control efforts of the inverted pendulum on a cart (second platform) by the restructured controller (obtained at the impulse magnitude of 20) at impulse magnitudes of 27–33 that are beyond the capacity of the linear controller

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Fig. 17

Stabilizing responses and control efforts of the linear, restructured and feedback linearized controllers for the inverted pendulum (third platform) to a higher initial displacement than used for restructuring

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Fig. 18

Step responses and control efforts of the first platform by restructured and customized controllers (Fig. 3) as affected by inaccurate actuator nonlinearities

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Fig. 19

Closed-loop impulse responses and control efforts of the restructured and linear controllers for the inverted pendulum on a cart with inaccuracies of 0%, 10%, 20%, and 30% in the pendulum mass

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Fig. 20

Components of the control efforts of the linear and restructured controllers with the two forms in Table 6 for the nonlinear actuator in response to step of magnitudes of 1–5

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Fig. 21

Components of the control efforts of the linear and restructured controllers with the three forms in Table 6 for the inverted pendulum in response to impulse magnitudes of 15–22

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