Plasma stabilization on the base of Model Predictive Control with the linear closed-loop system stability

The problem of plasma current, position and shape stabilization systems design for modern tokamaks in the frame of model predictive control approach (MPC) is considered. New control algorithm, which is based on the ideas of MPC and modal parametric optimization, is proposed. This algorithm allows to stabilize control plant in the neighborhood of the plasma equilibrium position. Within the suggested framework linear closed-loop system eigenvalues are placed in the specific desired areas on the complex plane at each time instant. Such areas are located inside the unit circle and reflect specific requirements and constraints imposed on closed-loop system stability and oscillations. The real-time implementation of the proposed algorithm requires the solution of the nonlinear programming problem at each time instant. To decrease computational consumptions, a special method is proposed with the theoretical support in the form of three proven theorems. The working capacity and effectiveness of the proposed modal-MPC algorithm is demonstrated by the example of ITER plasma stabilization.