Systematic design of a sawtooth period feedback controller using a Kadomtsev–Porcelli sawtooth model

Abstract

A systematic methodology for structured design of feedback controllers for the sawtooth period is presented, based on dedicated identification of the sawtooth dynamics. Therefore, a combined Kadomtsev–Porcelli model of a sawtoothing plasma actuated by an electron cyclotron current drive system has been set-up. This is used to derive the linearized input–output relations (transfer functions) from the varying deposition location of the electron cyclotron waves (ECW) to the sawtooth period. These transfer functions are derived around a large collection of operating points. Assessment of these control-relevant transfer functions shows that a sawtooth period controller requires an integral (I) action to guarantee closed-loop stability with zero steady-state error. Additional proportional-integral (PI) action can be applied to further increase the closed-loop performance. The parameters of both the I and PII controllers have been optimized in terms of stability, performance and robustness. Moreover, the effect of the mechanical ECW launcher on the closed-loop performance is studied for realistic cases. It is shown that the launcher dynamics seriously affects the achievable closed-loop performance in present-day experiments.

Real-time wavelet detection of crashes in limit cycles of non-stationary fusion plasmas

“…Other possibilities are to estimate the signals noise by use of automatic variance estimators, which are present in most signal processing software. The threshold T min in (12) defines the absolute lower bound on the wavelet coefficients due to noise and (13) determines what the maximum amplitude of the wavelet coefficients due to noise are for every scale.…”

“…Some control experiments and simulations for the sawteeth period have been presented in the literature [3][4][5][10][11][12][13]. Most of the above-mentioned experiments were carried out in open-loop and some in closed-loop, but a systematic optimization of the overall control loops (which includes the sensor) has not been presented.…”

“…Although real-time applicable, this method lacks robustness, and fails in noisy signal environments. The noise-sensitivity can be improved by applying a band-pass filter such that part of the noise is suppressed [4], but this reduces the accuracy and generally introduces significant signal delays, which are detrimental for the performance of any control-loop [13]. Furthermore, various types of time-frequency methods based on Fourier analysis have been used, such as the Short Time Fourier Transform (STFT) [14]; the Morlet Wavelet for sawteeth [15,16], and for ELMs [17][18][19]; and instantaneous frequency methods [20,21].…”

“…Witvoet et al [13] show the detrimental effect of the latency of the sawtooth period detection on the controller. This motivates the development of an algorithm for high-fidelity, low latency identification of the limit cycles for closed-loop control.…”

Robust adaptive control of the sawtooth instability in nuclear fusion

“…In [12], it is shown that the sawtooth period controller is stable for small period sawteeth, and is actually unstable for larger period sawteeth, where the controller introduces heavy oscillations in the launcher angle. This stability problem is addressed in [15], where the dynamics of a sawtooth model with constant plasma parameters is identified in a selected region of the operating range by specifying limits on the launcher angle. A stabilizing linear feedback controller is designed, and the tracking of sawtooth period references is demonstrated.…”