Lyapunov-based Current-Profile Feedback Control in Tokamaks with Nonsymmetric Individual Actuator Saturation∗

Advanced tokamak scenarios can achieve optimal tokamak operation by shaping the plasma internal profiles through the use of noninductive heating and current sources. As a result of the dynamic complexities, active control of the power of each noninductive heating and current source, a non-negative value, may be necessary to achieve the desired tokamak performance. However, due to the inherent physical limitations, arbitrary power prescription by the controller may saturate the heating and current drives. Therefore, it is highly desirable to develop a class of active control algorithms that account for the saturation limits of these actuators. A Lyapunov-based nonlinear feedback control algorithm that intrinsically accounts for saturation limits is proposed in this work to regulate the spatial distribution of the toroidal current density in the tokamak. The controller does not rely on constrained optimization techniques, which can be computationally expensive for real-time implementation. Furthermore, the controller can handle nonsymmetric saturation limits, i.e., the absolute values of the upper and lower saturation limits do not have to be equal. The effectiveness of the control algorithm is demonstrated for a DIII-D tokamak scenario in nonlinear simulations.