외란 관측기 기반 제어 시스템의 강인 안정성을 위한 Q-필터의 최소 대역폭 계산

학위논문 (석사) -- 서울대학교 대학원 : 공과대학 전기·정보공학부, 2021. 2. 심형보.As the disturbance observer (DOB)-based controller has been widely applied in practice, various aspects of the disturbance observer have been theoretically studied. In particular, robust stability of the linear closed-loop system with single-input single-output (SISO) Q-filter-based DOB has been rigorously analyzed, and finally, a necessary and sufficient condition for robust stability was obtained under the premise that the bandwidth of Q-filter is large. However, even the most recent study about the design of Q-filter-based DOB for robust stability does not offer a practical method for the determination of the Q-filter's bandwidth. In this thesis, we present several lemmas regarding the determination of the bandwidth, from which a procedure is developed that can exactly compute the threshold of the bandwidth, so that robust stability (against parametric variations of the plant within a prescribed range) is lost if the bandwidth of the Q-filter becomes lower than that. The proposed procedure is implemented in a MATLAB toolbox named DO-DAT, which is now available at https://do-dat.github.io.외란 관측기가 널리 활용됨에 따라 외란 관측기가 가지는 다양한 측면이 이론적으로 연구되어 왔다. 특히, Q-필터를 기반으로 하는 단일 입출력 외란 관측기를 포함하는 선형 폐루프 시스템의 강인 안정성에 대해 많은 연구가 이루어졌으며 결국 폐 루프 시스템의 강인 안정성에 대한 필요 충분 조건이 제안된 바 있다. 그러나 제안된 필요 충분 조건은 충분히 큰 Q-필터의 대역폭을 전제하는데, 폐 루프 시스템의 강인 안정성을 보장하기 위해 필요한 Q-필터의 최소 대역폭을 정확히 알아내는 방법은 제시된 바 없다. 본 학위논문에서는 몇 가지 보조정리와 함께 Q-필터 기반 외란 관측기가 포함된 폐 루프 시스템의 강인 안정성을 보장하는 Q-필터의 최소 대역폭을 정확히 계산할 수 있는 방법론을 제안한다. 본 학위논문에서 제안하는 방법론은 DO-DAT이라는 이름의 MATLAB 툴박스로 구현되어 있으며 관련 내용은 https://do-dat.github.io에서 확인할 수 있다.ABSTRACT i List of Figures vii Notation and Symbols ix 1 Introduction 1 1.1 Overview of Q-filter-based Disturbance Observer . . . . . . . . . . 3 1.2 Necessary and Sufficient Condition for Robust Stability . . . . . . 4 2 Lemmas on Robust Stability of Closed-loop System 7 2.1 Observations on Characteristic Polynomial . . . . . . . . . . . . . . 7 2.2 Application of Edge theorem and Bialas' theorem . . . . . . . . . . 11 3 Computation of Minimum Bandwidth of Q-filter for Robust Stability 15 3.1 Procedure for Computing τ . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Examples and Simulations . . . . . . . . . . . . . . . . . . . . . . . 17 4 DO-DAT: a MATLAB Toolbox for Design and Analysis of Disturbance Observer 21 4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.1.1 setup_sys.m . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2 Design of Coefficients of Q-filter . . . . . . . . . . . . . . . . . . . . 23 4.2.1 gen_Qcanon.m . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2.2 isFastDynamicsStable.m . . . . . . . . . . . . . . . . . . . . 24 4.3 Determination of Bandwidth of Q-filter . . . . . . . . . . . . . . . . 25 4.3.1 isValidTau.m . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.3.2 get_supTau.m . . . . . . . . . . . . . . . . . . . . . . . . . 27 5 Conclusion 29 APPENDIX 31 A.1 Edge theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A.2 Bialas' theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A.3 Routh-Hurwitz Stability Criterion . . . . . . . . . . . . . . . . . . . 32 A.4 Sturm's theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 BIBLIOGRAPHY 35 국문초록 39Maste

Yet Another Tutorial of Disturbance Observer: Robust Stabilization and Recovery of Nominal Performance

This paper presents a tutorial-style review on the recent results about the disturbance observer (DOB) in view of robust stabilization and recovery of the nominal performance. The analysis is based on the case when the bandwidth of Q-filter is large, and it is explained in a pedagogical manner that, even in the presence of plant uncertainties and disturbances, the behavior of real uncertain plant can be made almost similar to that of disturbance-free nominal system both in the transient and in the steady-state. The conventional DOB is interpreted in a new perspective, and its restrictions and extensions are discussed

Vibration suppression using fractional-order disturbance observer based adaptive grey predictive controller

A novel control strategy is proposed for vibration suppression using an integration of a fractional-order disturbance observer (FDOB) and an adaptive grey predictive controller (AGPC). AGPC is utilized to realize outer loop control for better transient performance by predicting system outputs ahead with metabolic GM(1,1) model, and an adaptive step switching module is adopted for the grey predictor in AGPC. FDOB is used to obtain disturbance estimate and generate compensation signal, and as the order of Q-filter is expanded to real-number domain, FDOB has a wider range to select a suitable tradeoff between robustness and vibration suppression. For implementation of the fractional order Q-filter, broken-line approximation method is introduced. The proposed control strategy is simple in control-law derivation, and its effectiveness is validated by numerical simulations

A Glueball- qqˉq\bar{q} Filter in Central Hadron Production

We have stumbled upon a remarkable empirical feature of central meson production which separates established $q\bar{q}$ mesons from glueball candidates. This does not appear to have been noted previously and we have no simple explanation for it. We suggest that glueballs and $q\bar{q}$ of the same $J^{PC}$ are distinguishable due to their boson versus fermion internal structure and that this leads to a different topology for central production of glueballs and $q\bar{q}$. Upon application of this test to data from the WA102 experiment we find that the $f_0(1500)$ and the $f_{2}(1900)$ show behaviour consistent with glueballs and opposite to that exhibited by established $q\bar{q}$ states.Comment: Latex file. 5 figs including 2 from WA102 CERN report "A kinematical selection of glueball candidates in central production

A CMOS Q-Enhancement Bandpass-Filter For Use In Paging Receivers

Paging receivers often have to work in a dense\ud signal environment. This poses high demands on the preselection\ud filter. One of the most difficult aspects is the large\ud image rejection demand, which only can be satisfied by use\ud of a narrow-band or high-Q filter. The practical restrictions\ud for possible filter implementations are the low cost, low\ud power and the small size of the pager. By use of positive feedback\ud around a cheap off-chip low-Q inductor we obtain an\ud enhanced quality factor. We are therefore able to construct\ud selective filters using cheap small-size inductors. The price\ud paid for Q-enhancement is a larger noise and higher sensitivity\ud to component variations. The higher noise influence\ud is eliminated using a high gain in the preceding LNA-stage,\ud which is considered a part of the filter. Simulated results\ud are: Q enhanced from 30 to 100, Image-rejection = 48dB,\ud f0 = 280MHz, Voltage-gain = 20dB, Noise- figure = 2.4dB,\ud IMFDR = 66dB, IDD = 1mA, VDD = 2V. The original contribution\ud of this work is the application of the enhancement\ud principle to off-chip components, which benefits the minimization\ud of size and cost

H∞BASEDOBSERVER FOR DISTURBANCE COMPENSATION IN DECOUPLED TRMS USING LMI OPTIMIZATION

Twin Rotor MIMO System is a laboratory model of helicopter. In this paper, the problem of disturbance rejection in TRMS is dealt with. Using disturbance observers, without any additional sensors is an attractive method to attenuate the effects of disturbances as they are highly cost effective. This method uses a simple form of DOBs, which does not need to solve the plant model inverse, and uses H∞control method using LMIs to design the Q-filter in the DOB. The estimation capability of DOB is verified using simulation results in frequency domain as well as in time domain

Data-driven optimal ILC for multivariable systems : removing the need for L and Q filter design

Many iterative learning control algorithms rely on a model of the system. Although only approximate model knowledge is required, the model quality determines the convergence and performance properties of the learning control algorithm. The aim of this paper is to remove the need for a model for a class of multivariable ILC algorithms. The main idea is to replace the model by dedicated experiments on the system. Convergence criteria are developed and the results are illustrated with a simulation on a multi-axis flatbed printer

Spin-to-Orbital Angular Momentum Conversion and Spin-Polarization Filtering in Electron Beams

We propose the design of a space-variant Wien filter for electron beams that induces a spin half-turn and converts the corresponding spin angular momentum variation into orbital angular momentum of the beam itself by exploiting a geometrical phase arising in the spin manipulation. When applied to a spatially coherent input spin-polarized electron beam, such a device can generate an electron vortex beam, carrying orbital angular momentum. When applied to an unpolarized input beam, the proposed device, in combination with a suitable diffraction element, can act as a very effective spin-polarization filter. The same approach can also be applied to neutron or atom beams.Comment: 9 pages, 5 figure