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Research Papers

Design and Experimental Investigation of Rotational Angle-Based Tracking Control

[+] Author and Article Information
Meng Yang

Mechanical Engineering Department,
University of Minnesota,
Minneapolis, MN 55455

Xingyong Song

Dwight Look College of Engineering,
Department of Engineering Technology and
Industrial Distribution;
Department of Mechanical Engineering
(Joint Appointment),
Texas A&M University,
College Station, TX 77840

Zongxuan Sun

Mechanical Engineering Department,
University of Minnesota,
Minneapolis, MN 55455
e-mail: zsun@umn.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 7, 2014; final manuscript received March 30, 2016; published online May 10, 2016. Assoc. Editor: Gregory Shaver.

J. Dyn. Sys., Meas., Control 138(7), 071005 (May 10, 2016) (8 pages) Paper No: DS-14-1462; doi: 10.1115/1.4033317 History: Received November 07, 2014; Revised March 30, 2016

This paper investigates tracking control in the rotational angle domain based on the time-varying internal model principle. The objective is to enable precise, reliable, and computationally efficient output tracking of signals that are dependent on angular displacement. To achieve desired performance, existing approaches based on internal model principle require a large number of samples per revolution, which significantly increases the controller order and also poses challenges for the transient performance. To address those issues, a varying sampling interval approach is proposed, where the angular sampling locations are not fixed but optimized based on tracking errors between sampling points so that desired performance can be achieved without increasing the number of samples. Meanwhile, to improve the convergence rate of the tracking error, additional linear matrix inequalities (LMI) constraints are added to the existing stabilizer synthesis. Through experimental study on a camless engine valve actuation system, the effectiveness of the proposed approaches is demonstrated. It is shown that, compared with the fixed interval sampling, the varying sampling approach can reduce the tracking error by over 50%.

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References

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Figures

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Fig. 1

Signal profile in the angle domain (top) and the time domain (bottom)

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Fig. 2

Block diagram of the internal model-based control system

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Fig. 3

Comparison of convergence rate for system with different internal model order

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Fig. 4

Comparison of fixed and variable interval sampling

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Fig. 5

Block diagram of the iterative approach to search the optimal sampling interval for the internal model-based system

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Fig. 6

Initialize sampling intervals for the reference profile

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Fig. 7

Flowchart of the iterative approach to search the desired sampling interval

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Fig. 8

Camless engine valve actuation system experimental setup

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Fig. 9

Schematic of camless engine valve actuation system

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Fig. 10

Reference profile

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Fig. 11

Experimental tracking results with 12-point fixed interval sampling [5–9 Hz at 0.2 Hz/s] using stabilizer design in Refs. [13] and [14]

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Fig. 12

Experimental tracking results with 12-point fixed interval sampling [5–9 Hz at 0.2 Hz/s] using the convergence-regulating stabilizer

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Fig. 13

Experimental tracking results with 12-point variable interval sampling [5–9 Hz at 0.2 Hz/s] with convergence-regulating stabilizer

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Fig. 14

Comparison of the tracking performance achieved using different internal model unit during 8–9 Hz

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Fig. 15

Maximum task execution time for internal model controllers of different order

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Fig. 16

Experimental tracking results with eight-point variable interval sampling [5–9 Hz at 0.2 Hz/s] with the convergence-regulating stabilizer

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Fig. 17

Experimental tracking results with eight-point variable interval sampling [5–20 Hz at 1 Hz/s] with the convergence-regulating stabilizer

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