$$\mathscr{H}_2$$ optimal control techniques for resistive wall mode feedback in tokamaks
Abstract
DIIID experiments show that a new, advanced algorithm improves resistive wall mode (RWM) stability control in high performance discharges using external coils. DIIID can excite strong, locked or nearly locked external kink modes whose rotation frequencies and growth rates are on the order of the magnetic ux di usion time of the vacuum vessel wall. The VALEN RWM model has been used to gauge the e ectiveness of RWM control algorithms in tokamaks. Simulations and experiments have shown that modern control techniques like Linear Quadratic Gaussian (LQG) control will perform better, using 77% less current, than classical techniques when using control coils external to DIIID's vacuum vessel. Experiments were conducted to develop control of a rotating n = 1 perturbation using an LQG controller derived from VALEN and external coils. Feedback using this LQG algorithm outperformed a proportional gain only controller in these perturbation experiments over a range of frequencies. Results from high N experiments also show that advanced feedback techniques using external control coils may be as e ective as internal control coil feedback using classical control techniques.
 Authors:
 Univ. of California, San Diego, CA (United States); columb
 Columbia Univ., New York, NY (United States)
 Publication Date:
 Research Org.:
 USDOE
 Sponsoring Org.:
 USDOE Office of Nuclear Energy (NE)
 OSTI Identifier:
 1425033
 Grant/Contract Number:
 FC0204ER54698
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Nuclear Fusion
 Additional Journal Information:
 Journal Volume: 58; Journal Issue: 4; Journal ID: ISSN 00295515
 Publisher:
 IOP Science
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Clement, Mitchell, Hanson, Jeremy, Bialek, Jim, and Navratil, Gerald. $\mathscr{H}_2$ optimal control techniques for resistive wall mode feedback in tokamaks. United States: N. p., 2018.
Web. doi:10.1088/17414326/aaaecd.
Clement, Mitchell, Hanson, Jeremy, Bialek, Jim, & Navratil, Gerald. $\mathscr{H}_2$ optimal control techniques for resistive wall mode feedback in tokamaks. United States. doi:10.1088/17414326/aaaecd.
Clement, Mitchell, Hanson, Jeremy, Bialek, Jim, and Navratil, Gerald. 2018.
"$\mathscr{H}_2$ optimal control techniques for resistive wall mode feedback in tokamaks". United States.
doi:10.1088/17414326/aaaecd.
@article{osti_1425033,
title = {$\mathscr{H}_2$ optimal control techniques for resistive wall mode feedback in tokamaks},
author = {Clement, Mitchell and Hanson, Jeremy and Bialek, Jim and Navratil, Gerald},
abstractNote = {DIIID experiments show that a new, advanced algorithm improves resistive wall mode (RWM) stability control in high performance discharges using external coils. DIIID can excite strong, locked or nearly locked external kink modes whose rotation frequencies and growth rates are on the order of the magnetic ux di usion time of the vacuum vessel wall. The VALEN RWM model has been used to gauge the e ectiveness of RWM control algorithms in tokamaks. Simulations and experiments have shown that modern control techniques like Linear Quadratic Gaussian (LQG) control will perform better, using 77% less current, than classical techniques when using control coils external to DIIID's vacuum vessel. Experiments were conducted to develop control of a rotating n = 1 perturbation using an LQG controller derived from VALEN and external coils. Feedback using this LQG algorithm outperformed a proportional gain only controller in these perturbation experiments over a range of frequencies. Results from high N experiments also show that advanced feedback techniques using external control coils may be as e ective as internal control coil feedback using classical control techniques.},
doi = {10.1088/17414326/aaaecd},
journal = {Nuclear Fusion},
number = 4,
volume = 58,
place = {United States},
year = 2018,
month = 2
}

An adaptive optimal stochastic state feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The extended leastsquare method with exponential forgetting factor and covariance resetting is used to identify (experimentally determine) the timevarying stochastic system model. A Kalman filter is used to estimate the system states. The estimated system states are passed on to an optimal state feedback controller to construct control inputs. The Kalman filter and the optimal state feedback controller are periodically redesigned online based on the identified system model. This adaptive controller can stabilize the timedependent RWM in a slowly evolving tokamakmore »

Adaptive stochastic output feedback control of resistive wall modes in tokamaks
An adaptive optimal stochastic output feedback control is developed to stabilize the resistive wall mode (RWM) instability in tokamaks. The system dynamics is experimentally determined via the extended least square method with an exponential forgetting factor and covariance resetting. The optimal output feedback controller is redesigned online periodically based on the system identification. The output measurements and past control inputs are used to construct new control inputs. The adaptive output controller can stabilize the time dependent RWM in a slowly evolving tokamak discharge. This is accomplished within a time delay of roughly three times the inverse of the growth rate.more » 
Conceptual design of an active feedback system for the control of the resistive shell mode in tokamaks
A quadratic dispersion relation is derived which governs the feedbackmodified stability of the resistive shell mode in a largeaspect ratio, low{beta} tokamak plasma. The effectiveness of a given feedback scheme is determined by a single parameter, {alpha}{sub 0}, which measures the coupling of different poloidal harmonics due to the nonsinusoidal nature of the feedback currents. Feedback fails when this parameter becomes either too positive or too negative. Feedback schemes can be classified into three groups, depending on the relative values of the poloidal mode number, m{sub 0}, of the intrinsically unstable resistive shell mode, and the number, M, of feedbackmore » 
Stabilization of the external kink and control of the resistive wall mode in tokamaks
One promising approach to maintaining stability of high beta tokamak plasmas is the use of a conducting wall near the plasma to stabilize low{ital n} ideal magnetohydrodynamic instabilities. However, with a resistive wall, either plasma rotation or active feedback control is required to stabilize the more slowly growing resistive wall modes (RWMs). Previous experiments have demonstrated that plasmas with a nearby conducting wall can remain stable to the n=1 ideal external kink above the beta limit predicted with the wall at infinity. Recently, extension of the wall stabilized lifetime {tau}{sub L} to more than 30 times the resistive wall timemore »