Real Time Hybrid Model Predictive Control for the Current Profile of the Tokamak à Configuration Variable (TCV)

Abstract

Plasma stability is one of the obstacles in the path to the successful operation of fusion devices. Numerical control-oriented codes as it is the case of the widely accepted RZIp may be used within Tokamak simulations. The novelty of this article relies in the hierarchical development of a dynamic control loop. It is based on a current profile Model Predictive Control (MPC) algorithm within a multiloop structure, where a MPC is developed at each step so as to improve the Proportional Integral Derivative (PID) global scheme. The inner control loop is composed of a PID-based controller that acts over the Multiple Input Multiple Output (MIMO) system resulting from the RZIp plasma model of the Tokamak à Configuration Variable (TCV). The coefficients of this PID controller are initially tuned using an eigenmode reduction over the passive structure model. The control action corresponding to the state of interest is then optimized in the outer MPC loop. For the sake of comparison, both the traditionally used PID global controller as well as the multiloop enhanced MPC are applied to the same TCV shot. The results show that the proposed control algorithm presents a superior performance over the conventional PID algorithm in terms of convergence. Furthermore, this enhanced MPC algorithm contributes to extend the discharge length and to overcome the limited power availability restrictions that hinder the performance of advanced tokamaks.

A Variable Structure Control Scheme Proposal for the Tokamak à Configuration Variable

“…One of the main issues to overcome in the path to commercialization is the instabilities [15][16][17][18][19][20][21][22][23][24]. These instabilities cause disruptions, limiting the maximal achievable time for plasma confinement and making indispensable an optimal control system.…”

“…The TCV is simulated by the RZIp model [15], which considers a rigid plasma radial and vertical displacement. The RZIp model is widely used for simulation purposes and design of real time controllers [19][20][21][22][23][24].…”

Energy Conservation in an Office Building Using an Enhanced Blind System Control

“…A definition of the physical power limits of the HVAC and of the comfort bounds is also necessary, as shown in Equations (12)- (14). Moreover, the weather conditions may force the system outside of the comfort bounds, which can provoke problems when looking for an optimum within the given constrains.…”

“…Provided with the state-space model of the building, the MPC uses measured and predicted disturbances that influence the system to calculate the control action. The minimization of a cost function for the u vector is a typical constrained quadratic programming problem represented by Equation (11) with a prediction horizon Np subject to the constraints given by Equations (12)- (14). The solution of the minimization provides the minimum action the HVAC system needs to guarantee the thermal comfort in the building.…”

State-space Coil Modelling in Plasma Magnetic Confinement Devices

“…In turn, current is controlled indirectly through voltage, as these signals are dependent each other. There exist different control approaches for this purpose, being the most used traditional PID-based schemes, robust (sliding-mode) schemes and MPC schemes [11][12][13][14][15][16][17][18][19][20][21][22][23]. In particular, when dealing with fusion devices where the available energy is limited, MPC is especially interesting due to its ability to ensure that both the control action and the solution error are minimal [9].…”