Research Papers

Velocity Estimation of Motion Systems Based on Low-Resolution Encoders

[+] Author and Article Information
Hongzhong Zhu

e-mail: zhu@hflab.k.u-tokyo.ac.jp

Toshiharu Sugie

e-mail: sugie@i.kyoto-u.ac.jp
Mechanical Systems Control Laboratory,
Department of Systems Science,
Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received March 23, 2011; final manuscript received April 26, 2012; published online October 30, 2012. Assoc. Editor: John R Wagner.

J. Dyn. Sys., Meas., Control 135(1), 011006 (Oct 30, 2012) (8 pages) Paper No: DS-11-1085; doi: 10.1115/1.4007065 History: Received March 23, 2011; Revised April 26, 2012; Accepted May 09, 2012

This paper proposes a new approach to estimate the velocity of mechanical system in the case where the optical incremental encoder is used as the position sensor. First, the actual angular position is reconstructed via moving horizon polynomial fitting method by taking account of quantization feature and the plant dynamics. Then, the reconstruction signal is applied to a classical observer to obtain the velocity estimation. Its robustness against the position sensor resolution and the degree of the polynomial is discussed by some numerical examples. Experiments with very low-resolution encoder in low speed range also confirm its effectiveness.

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Fig. 1

Encoder characteristic; Δ: quantization step

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Fig. 2

Modeling of mechanical system

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Fig. 3

Fitting strategy: (i) shows the p + 1 quantized measurements {θq(k-i)}i=0,1,2,…,p; (ii) shows the polynomial fitting approach: the points (τi,Yi)i=1,2,…,p are fitted by gk(τ). The quantity gk(τ1+h2) is treated as the reconstruction value of θ(k), as shown by the star ‘⋆’ in (ii).

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Fig. 4

Moving horizon output reconstruction strategy

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Fig. 5

Block diagram of state estimation from position measurements θq. The parts in the dashed line are the proposed approach.

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Fig. 6

Block diagram for simulations to evaluate the estimation error. Part (b) is used instead of the part in the dashed line in (a) when Kalman filter is implemented.

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Fig. 7

Velocity estimation errors obtained by the Kalman filter

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Fig. 8

Velocity estimation errors obtained by the proposed method

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Fig. 9

Comparison of the proposed approach (MHPFA) and KF in the case of γ = 0.2 and Δ = 2π/8. (a) Shows the comparison of the estimated velocity; (b) shows the velocity estimation error.

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Fig. 10

Experimental setup

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Fig. 11

Block diagram of dc motor control system. (b) Is the implementation of Kalman filter, which is used instead of the parts in the dashed line in (a) when it is implemented.

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Fig. 12

Velocity tracking results of the proposed approach

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Fig. 13

Velocity tracking results of the Kalman filter

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Fig. 14

Experimental results of velocity control in low speed range, including acceleration, constant speed motion, and deceleration. (a), The velocity reference; (b), the results of the Kalman filter; (c), the results of the proposed approach.

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Fig. 15

The block diagram of control system. In the first 2 s, the signal passing a difference filter and a low-pass filter is used as the feedback signal. After t = 2 s, the feedback signal is switched to the velocity signal estimated by the MHPFA.

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Fig. 16

The experimental results in the case where feedback signal is switched at t = 2 s. The dashed line shows the estimated velocity and the solid line shows the velocity reference.




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