## 외란관측기(disturbance observer)란?

## 동작원리는 무엇인가요?

## 관련 연구는 어떠한 것이 있나요?

- asd
- asd

*본 센터 소속 CDSL에서는2007년부터 DOB 관련 이론 연구를 진행해 오고 있으며, 최근 그간의 연구 결과를 모아 작성한 tutorial 논문이 있습니다.*

Yet another tutorial of disturbance observer: Robust stabilization and recovery of nominal performance

H. Shim, G. Park, Y. Joo, J. Back, and N.H. Jo

to appear at the Special Issue of Control Theory and Technology, 2016

available at http://arxiv.org/abs/1601.02075

그 외에 시간 순서로 배열된 연구 결과는 아래와 같습니다.

1. The initial result. Stability and the performance limitation of DOB for linear plants are studied in the state-space using the singular perturbation theory:

"State space analysis of disturbance observer and a robust stability condition"

H. Shim and Y.J. Joo

IEEE Conf. on Dec. and Control, pp. 2193-2198, Dec., 2007.

http://dx.doi.org/10.1109/CDC.2007.4434130

2. The above result can be more simply proved in the frequency domain, and the design procedure for the Q-filter is proposed that always guarantees the closed-loop robust stability:

"An Almost Necessary and Sufficient Condition for Robust Stability of Closed-loop Systems with Disturbance Observer"

H. Shim and N.H. Jo

Automatica, vol. 45, no. 1, pp. 296-299, 2009.

http://dx.doi.org/10.1016/j.automatica.2008.10.009

3. Although the way how to guarantee the robust stability of the closed-loop with the DOB has been revealed in the above, the question whether the DOB also guarantees the robust transient response still remains unanswered. This question turns out negative, but a simple modification of the classical DOB (using the saturation and deadzone function) is suggested which guarantees the robust transient response. This strategy is also applied to nonlinear systems. Finally, it is shown that the DOB controller intrinsically contains the high-gain observer that has been actively studied by Khalil and co-workers.

"Adding Robustness to Nominal Output Feedback Controllers for Uncertain Nonlinear Systems: A Nonlinear Version of Disturbance Observer"

J. Back and H. Shim

Automatica, vol. 44, no. 10, pp. 2528-2537, 2008.

http://dx.doi.org/10.1016/j.automatica.2008.02.024

4. The above result is refined and extended to the MIMO nonlinear systems with simpler proof in

"An Inner-loop Controller Guaranteeing Robust Transient Performance for Uncertain MIMO Nonlinear Systems"

J. Back and H. Shim

IEEE Trans. on Automatic Control, vol. 54, no. 7, pp. 1601-1607, 2009.

http://dx.doi.org/10.1109/TAC.2009.2017962

5. The paper (no.1) also pointed out that a blind application of DOB controller may degrade the performance especially when the performance output variable is different from the measurement output, and it is one of the states in the zero-dynamics. Instead, the DOB may be applicable only to a portion of the plant dynamics. An example is

"Robust Tracking and Vibration Suppression for a Two-Inertia System by Combining Backstepping Approach with Disturbance Observer"

J.S. Bang, H. Shim, S.K. Park, and J.H. Seo

IEEE Trans. on Industrial Electronics, vol. 57, no. 9, pp. 3197-3206, Sept. 2010

http://dx.doi.org/10.1109/TIE.2009.2038398

6. All the above results are limited to the minimum phase systems. A trial has been made to apply the DOB approach to non-minimum phase systems.

"A New Disturbance Observer for Non-minimum Phase Linear Systems"

H. Shim, N.H. Jo, and Y.I. Son

American Control Conference, pp. 3385-3389, Seattle, June, 2008.

http://dx.doi.org/10.1109/ACC.2008.4587015

or, its refinement:

"Disturbance Observer for Non-minimum Phase Linear Systems"

N.H. Jo, H. Shim, and Y.I. Son

Int. J. of Control, Automation, and Systems, vol. 8, no. 5, pp. 994-1002, Oct. 2010

http://dx.doi.org/10.1007/s12555-010-0508-x

7. Our stability condition has not been experimentally tested, but the following paper performed an experiment using our stability condition:

"Disturbance-Observer-Based Hysteresis Compensation for Piezoelectric Actuators"

J. Yi, S. Chang, and Y. Shen

IEEE/ASME Trans. on Mechatronics, vol. 14, no. 4, 2009

http://dx.doi.org/10.1109/TMECH.2009.2023986

8. Since the same Q-filters are found in the loop, they could be merged into one in order to reduce the dimension of the DOB controller:

"Robust Tracking by Reduced-order Disturbance Observer: Linear Case"

J. Back and H. Shim

IEEE Conf. on Dec. and Control and European Control Conf. (CDC-ECC), Orlando, pp. 3514-3519, 2011

http://dx.doi.org/10.1109/CDC.2011.6161399

"Reduced-order Implementation of Disturbance Observers for Robust Tracking of Non-linear Systems"

J. Back and H. Shim

IET Control Theory & Applications, vol. 8, no. 17, pp. 1940-1948, 2014.

http://digital-library.theiet.org/content/journals/10.1049/iet-cta.2013....

9. One of the standing assumption is to know the relative degree of the uncertain plant. But, a series of study is performed when this is not the case:

"Can a Fast Disturbance Observer Work Under Unmodeled Actuators?"

N.H. Jo, Y. Joo, and H. Shim

Int. Conf. on Control, Automation and Systems (ICCAS), pp. 561-566, Seoul, Korea, 2011

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6106423

"A Note on Disturbance Observer with Unknown Relative Degree of the Plant"

N.H. Jo, Y. Joo, H. Shim, and Y.I. Son

IEEE Conf. Dec. Control, pp. 943-948, Maui, HI, 2012

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6426142

"A Study of Disturbance Observers with Unknown Relative Degree of the Plant"

N. H. Jo, Y. Joo, and H. Shim

Automatica, vol. 50, no. 6, pp. 1730-1734, 2014

http://www.sciencedirect.com/science/article/pii/S0005109814001459

10. Disturbance rejection by DOB is an approximate one. But, by embedding some internal models, perfect rejection is possible for a class of disturbance signals.

The initial result is about polynomial-in-time disturbances:

"Rejection of Polynomial-in-time Disturbances via Disturbance Observer with Guaranteed Robust Stability"

G. Park, Y. Joo, H. Shim, and J. Back

IEEE Conf. Dec. Control, pp. 949-954, Maui, HI, 2012.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6425973&tag=1

In addition to such type of signals, sinusoidal disturbances also can be dealt with in

"Embedding Internal Model in Disturbance Observer with Robust Stability"

Y. Joo, G. Park, J. Back, and H. Shim

IEEE Trans. Autom. Control, to appear, 2016

This property is combined with the nominal performance recovery introduced in (no. 3):

"Asymptotic Rejection of Sinusoidal Disturbances with Recovered Nominal Transient Performance for Uncertain Linear Systems"

IEEE Conf. Dec. Control, pp. 4404-4409, Los Angeles, CA, 2014

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7040076

11. The conventional DOB consists of two same Q-filters, yet they play different roles for nominal performance recovery; one works for disturbance rejection, while the other is to estimate the plant's state (similar to high-gain observer as discussed in (no. 3)). This finding raises a question about stability and performance when the Q-filters have different forms. It is answered by

"Reduced Order Type-k Disturbance Observer Based on a Generalized Q-filter Design Scheme"

Y. Joo and G. Park

Int. Conf. Control, Automation, and Systems, Seoul, Korea, pp. 1211-1216, 2014.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6987743&tag=1

12. Most of the previous works on DOB has focused only on the disturbance rejection. A study on attenuating both disturbance and noise via DOB is newly introduced:

"Robust Stabilization via Disturbance Observer with Noise Reduction"

N. H. Jo and H. Shim

European Control Conf., pp. 2861-2866, Zurich, Switzerland, 2013.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6669565&tag=1

"A Simple Noise Reduction Disturbance Observer and Q-filter Design for Internal Stability"

J. Han, H. Kim, Y. Joo, N. H. Jo, and J. H. Seo

Int. Conf. of Control, Automation, and Systems, pp. 755-760, 2013

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6704014

13. While all the above results are discussed in the continuous-time domain, for implementing it into digital devices, DOB will be constructed in the discrete-time domain and be applied to a sampled-data system. At first glance, stability seems to remain guaranteed whenever a discretization of a well-designed continuous-time DOB is used with fast sampling. Interestingly, this is not the case and the sampling process may hamper stability of the DOB controlled system with the so-called sampling zeros. Some works are made to clarify this phenomenon in a theoretical sense, and to propose a new design guideline for the discrete-time DOB:

Our first trial is in

"Analysis of Discrete-time Disturbance Observer and a New Q-filter Design Using Delay Function"

C. Lee, Y. Joo, and H. Shim

Int. Conf. of Control, Automation, and Systems, pp. 556-561, 2012

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6393245

but, we don't recommend the above result because we have found better approach:

"On Robust Stability of Disturbance Observer for Sampled-data Systems Under Fast Sampling: An Almost Necessary and Sufficient Condition"

G. Park, Y. Joo, C. Lee, and H. Shim

in Proc. of IEEE Conf. Dec. Control, 2015.

http://dx.doi.org/10.1109/CDC.2014.7040076

"A Generalized Framework for Robust Stability Analysis of Discrete-time Disturbance Observer for Sampled-Data Systems: A Fast Sampling Approach"

G. Park and H. Shim

in Proc. of Int. Conf. of Control, Automation, and Systems, 2015.

http://dx.doi.org/10.1109/ICCAS.2015.7364926

The above finding also can be interpreted in the state space by using the discrete-time singular perturbation theory:

"State-space Analysis of Discrete-time Disturbance Observer for Sampled-data Control Systems"

H. Yun, G. Park, H. Shim, H. J. Chang

submitted at American Control Conf., 2016.