Study on Global Particle Balance Model for Plasma Density Feedback Control in KSTAR

Abstract

한국초전도핵융합연구장치(Korea Superconducting Tokamak Advanced Research, 이하 KSTAR)와 같은 장시간운전이 가능한 장치에서는 지속적인 플라 즈마 밀도의 실시간 되먹임 제어가 반드시 필요하다. 제어기 설계를 효율적으 로진행하기위해서는플라즈마의상태를적절하게기술하는모델이필요한데 특히 플라즈마의 밀도 반응의 경우는 플라즈마 전하들의 재활용 (recycling, 이 하리사이클링)의효과가큰영향을미친다.따라서밀도변화의모델링은이러 한 리사이클링 혹은 플라즈마와 내벽간의 반응을 올바르게 기술하여야 한다. 이를위해최근에Maddison에의해제안된중수소분자의리사이클까지고려한 모델을바탕으로KSTAR의실험결과를재현하였다.이때KSTAR와같은수초 이상의 장시간 운전의 경우 기존 모델에서 적절한 결과를 도출할 수 없었는데 이에 대한 문제는 중수소 분자의 지체탈착시간 (τw)을 도입함으로써 해결이 가능하다. 이를 통해 방전 전류가 지속적으로 유지되는 전체 기간동안 핵융합 플라즈마의밀도를 정량적으로재현할 수있는 모델을처음으로 설립하였다. 이러한모델에서도출한파라미터는각각의영향이완벽히독립적이지않 기때문에일정량의불확실성을가지는데특히플라즈마밀도의가둠시간인τi 와 중수소 분자의 즉각적인 재방출이 되는 정도를 의미하는 δD 의 경우 그에 대한 영향을 직접적으로 구분하는 것이 매우 힘들다. 따라서 기존의 밀도 데이 터 이 외에 다른 진단 데이터를 활용하여 이를 구분하여야 하는데 본 연구의 경우 정전탐침법을 활용한 이온입자속을 모델의 데이터와 비교함으로써 가능 하였다.기존의밀도데이터만활용하였을경우수치적으로가능한τi의범위가 10-120ms에 달하는 반면, 이온입자속을 함께 고려한 경우 약 15ms-35ms의 범 위로한정되는것을확인하였다.이를유럽연합의공동핵융합연구장치인JET 147 에서 도출된 결과와 비교하면 약 18-37ms의 경우로 예측되므로 서로 일치하는 결과를 얻을수 있었다. 이렇게 얻어낸 인자들을 모델기반 제어기 설계를 위하여 선형화된 전달 함수를 구할 수 있다. 전달함수에서 도출되는 특성값인 zero와 pole을 제어파 라미터인 τI , τP를 활용하여 삭제할 경우 되먹임제어의 동작 결과를 여러 플라 즈마 인자의 범위에 대해서 원하는 범위 내로 구할 수 있다. 예를 들어 오버슛 (Overshoot) 20% 이내와 안정시간 (settlement time) 1초 이내의 반응도를 얻을 수있음을 확인하였다. 결론적으로장시간운전에대한플라즈마밀도변화를정량적으로모사할 수 있는 물리적인 모델을 최초로 도출하고 이로부터 여러 플라즈마 인자의 변 화에 대해 안정적으로 원하는 반응도를 얻을 수 있는 모델기반 되먹임제어기 설계를달성하였다.

Real-time control of plasma density is of particular importance in achieving not only steady-state operation but machine efficiency for various scientific researches with less time and resource. A global particle model has been established for the model based controller design in Korea Superconducting Tokamak Advanced Research or KSTAR. The model is based on one of the most comprehensive model, proposed by Maddison and validated in Mega-Ampere Spherical Torus or MAST, which however cannot be directly applicable for KSTAR experiment. The is mainly due to much longer pulse of KSTAR compared with MAST. For the long pulse discharges, such as KSTAR, the delayed recycling of retained fuels in the wall needs to be included for successful modeling, which is evident from the particular observation of density sustainment without any external fueling injection. By the improved i model, both dynamic response and equilibrium states of density waveform are reproduced in an excellent agreement with the gas modulation experiments, less than 5% average squared error for the entire Ip flattop period. The quantified reproduction of long pulse discharges from the particle balance model is accomplished for the first time in fusion plasmas. However, some of the model parameters are under large uncertainties inherently due to the superposed effect between different parameters such as τi and δD since the pure transport loss in τi is hardly measurable without compensation of recycling effect from δD. Thus another constraint needs to be participated in the modeling such as ion saturation current I+ sat measurements from electric probe diagnostics. With the diagnostic constraint, automatic tuning algorithm that minimizes errors of the model from the experiments yield τi about 15−35ms for 0.3MA circular ohmic plasmas which was originally obtained within 10−120ms. The refined range of τi is consistent with ohmic limiter plasma scaling law, proposed in Joint European Tokamak or JET, yielding 18−37ms. Remaining parameters can be also specified with fixed τi at 25ms : core fueling efficiency fc, immediate molecular desorption coefficient δD and particle residence time in the wall or delayed molecular desorption τw. In the particular KSTAR experiments, they are individually determined as 33%, 0.44, and 0.72s respectively. The obtained parameters produce density waveform in excellent agreement with both feedforward and feedback control experiments, provided similar wall condition. From the global particle balance model, a equivalent transfer function is evaluated for designing robust PID controllers in various plasma and wall conditions. For the purpose, gas injection algorithm is proposed to be changed from voltagerequested control to flow-requested control in order to eliminate such large nonlinii earity that stems from gas puffing rate upon operating piezo-valve voltage. As bypassing the critical nonlinearity with direct flow control, designed controller with its control parameters, proportional and integral gains GP and GI , and their characteristic times τP and τI are able to cancel two zeros and a pole, provided the parameters remain as same as previously determined. Designed controller with root-locus method, performs feedback action in good quality in terms of transient responses such as 20% overshoot and 1s settlement time in wide range of parameter variation, confirming robustness of the PI controller. If the plasma parameters alter by conditions of plasma and wall, as moving zeros and poles subsequently to different positions, the performance of the controller turns out to still remain successful, proved with both time-domain solution of transfer function and direct numerical simulation of global particle balance model. In conclusion, a comprehensive global particle balance has been established with delayed molecular desorption effect for relatively long pulse discharges in KSTAR yielding excellent accuracy of the model compared with density waveform both in gas modulation and feedback control. This is the first time achievement for fusion plasmas in long pulse discharges of plasma density with quantitative accuracy. The feedback control system can be linearized with direct flow-request control instead of original voltage-request control scheme of plasma control system or PCS of KSTAR. Thus the equivalent transfer function becomes valid, and root-locus method with the model-based transfer function enables robust control of plasmas by canceling out some zeros and poles with controller variables. The designed controller results in desired performance for example 20% overshoot with 1s settlement time for various iii plasma and wall conditions.