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.