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

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.