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Research Papers

A Guide to Design Disturbance Observer

[+] Author and Article Information
Emre Sariyildiz

Department of System Design Engineering,
Keio University,
Yokohama, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama,
Kanagawa 223-8522, Japan
e-mail: emre@sum.sd.keio.ac.jp

Kouhei Ohnishi

Department of System Design Engineering,
Keio University,
Yokohama, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama,
Kanagawa 223-8522, Japan
e-mail: ohnishi@sd.keio.ac.jp

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 8, 2012; final manuscript received September 19, 2013; published online December 9, 2013. Assoc. Editor: Luis Alvarez.

J. Dyn. Sys., Meas., Control 136(2), 021011 (Dec 09, 2013) (10 pages) Paper No: DS-12-1414; doi: 10.1115/1.4025801 History: Received December 08, 2012; Revised September 19, 2013

The goal of this paper is to clarify the robustness and performance constraints in the design of control systems based on disturbance observer (DOB). Although the bandwidth constraints of a DOB have long been very well-known by experiences and observations, they have not been formulated and clearly reported yet. In this regard, the Bode and Poisson integral formulas are utilized in the robustness analysis so that the bandwidth constraints of a DOB are derived analytically. In this paper, it is shown that the bandwidth of a DOB has upper and lower bounds to obtain a good robustness if the plant has nonminimum phase zero(s) and pole(s), respectively. Besides that the performance of a system can be improved by using a higher order disturbance observer (HODOB); however, the robustness may deteriorate, and the bandwidth constraints become more severe. New analysis and design methods, which provide good robustness and predefined performance criteria, are proposed for the DOB based robust control systems. The validity of the proposals is verified by simulation results.

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Figures

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Fig. 1

A block diagram for a two-degrees-of-freedom DOB based robust control system

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Fig. 2

Nyquist plot of inner-loop when a plant has time-delay and DOB is first order

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Fig. 3

A block diagram of a DOB based robust control system when a plant is unstable

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Fig. 4

Frequency responses of the inner-loop sensitivity and co-sensitivity transfer functions when the bandwidth of DOB is 100 rad/s

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Fig. 5

Frequency responses of the inner-loop sensitivity and co-sensitivity transfer functions when a 2nd order DOB is used

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Fig. 6

Frequency responses of the inner-loop sensitivity and co-sensitivity transfer functions when the order of DOB is one

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Fig. 7

Frequency responses of the inner-loop sensitivity and co-sensitivity transfer functions when the order of DOB is one

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Fig. 8

Frequency responses of the outer-loop sensitivity and co-sensitivity transfer functions when the order of DOB is two

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Fig. 9

Step responses of the unstable plant when it is controlled by using the proposed robust controller

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Fig. 10

A general frequency response of a sensitivity function

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