Research Papers

Optimal Decoupled Disturbance Observers for Dual-Input Single-Output Systems

[+] Author and Article Information
Xu Chen

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: maxchen@me.berkeley.edu and xuchen@cal.berkeley.edu

Masayoshi Tomizuka

Department of Mechanical Engineering,
University of California,
Berkeley, CA 94720
e-mail: tomizuka@me.berkeley.edu

For the sake of brevity, the index (z−1) is omitted here. This simplification of notation will be adopted for long equations in the remainder of the paper.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 5, 2012; final manuscript received March 20, 2014; published online July 9, 2014. Assoc. Editor: Evangelos Papadopoulos.

J. Dyn. Sys., Meas., Control 136(5), 051018 (Jul 09, 2014) (11 pages) Paper No: DS-12-1410; doi: 10.1115/1.4027282 History: Received December 05, 2012; Revised March 20, 2014

The disturbance observer (DOB) has been a popular robust control approach for servo enhancement in single-input single-output systems. This paper presents a new extension of the DOB idea to dual- and multi-input single-output systems, and discusses an optimal filter design technique for the related loop-shaping. The proposed decoupled disturbance observer (DDOB) provides the flexibility to use the most suitable actuators for compensating disturbances with different spectral characteristics. Such a generalization is helpful, e.g., for modern dual-stage hard disk drives, where enhanced servo design is becoming more and more essential in the presence of vibration disturbances.

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Fig. 1

Mechanical structure of a dual-stage HDD

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Fig. 2

Block diagram of DDOB for P2(z−1)

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Fig. 3

Block diagram of DDOB for P1(z−1)

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Fig. 4

DDOB for general MISO systems

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Fig. 5

Closed-loop structure with DDOB for P2(z−1)

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Fig. 6

An equivalent form of the system in Fig. 5

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Fig. 7

Block diagram transformation for Fig. 5

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Fig. 8

Block diagram transformation for Fig. 7: DDOB is decomposed to series and parallel modules

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Fig. 9

Q design example: BP denotes band-pass filter; the standard BP equals 1 − Fnf(z−1); the causal BP is from Sec. 6.1; and the optimal BP comes from Eqs. (25) to (27)

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Fig. 10

Block diagram of the closed-loop system with DDOB and decoupled sensitivity control

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Fig. 11

A reduced-order implementation of Fig. 10

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Fig. 12

Frequency responses of the plant models

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Fig. 13

P∧1(z-1) for DDOB in VCM actuator

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Fig. 14

Magnitude responses of the sensitivity functions with different Q-filter configurations

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Fig. 15

Practical plant perturbations

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Fig. 16

Perturbed sensitivity functions with and without DDOBs

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Fig. 17

Values of μ from robust-stability analysis

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Fig. 18

Spectra of the PES using a projected disturbance profile

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Fig. 19

Time traces of the PES signals in Fig. 18

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Fig. 20

General closed-loop for perturbed DISO plants

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Fig. 21

Generalized block diagram of Fig. 20



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