Gianluca Varano

Brief paper: Nonlinear dynamic allocator for optimal input/output performance trade-off: Application to the JET tokamak shape controller

In this paper, we revisit the dynamic allocation scheme for input redundant plants proposed in Zaccarian (2009). within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow us to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. We also establish here desirable convergence properties of the allocator, which were only addressed for the linear case in Zaccarian (2009). In particular, we design the allocator dynamics as the gradient of a cost function and establish its convergence to the minimum of the cost function under some mild conditions. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom.

On linear over-actuated regulation using input allocation

We present in this paper preliminary results and research directions concerning the output regulation problem for over-actuated linear systems. The focus of the paper is on the characterization of the solution of the full-information regulator problem for systems which are right-invertible but not left-invertible, where the input operator is injective. The intrinsic redundancy in the plant model is exploited by parameterizing all solutions of the ensuing regulator equations and performing a static or dynamic optimization on the space of solutions. This approach effectively shapes the non-unique steady-state of the system so that the long-term behavior optimizes a given performance index. In particular, nonlinear cost functions that account for constraints on the inputs are considered. Examples are given to illustrate and validate the proposed methodology.

On input allocation-based regulation for linear over-actuated systems

Results concerning the output regulation problem for over-actuated linear systems are presented in this paper. The focus is on the characterization of the solution of the full-information regulator problem for systems which are right-invertible (but not left-invertible) and the input operator is injective. The intrinsic redundancy in the plant model is exploited by parameterizing all solutions of the regulator equations and performing a static or dynamic optimization on the space of solutions. This approach effectively shapes the non-unique steady-state of the system so that the long-term behavior optimizes a given performance index. In particular, nonlinear cost functions that account for constraints on the inputs are considered, within the general form of a hybrid system assumed for the allocation mechanism. An example is given to illustrate the proposed methodology.

Plasma Position and Elongation Regulation at FTU Using Dynamic Input Allocation

In this paper we employ and extend the dynamic allocation theory first presented in a recent work by the last author, L. Zuccarian, to guarantee asymptotic tracking of a prescribed elongation of the plasma cross section in the Frascati Tokamak Upgrade (FTU). This task is hard to accomplish because it can only be achieved using the so-called poloidal coil, a high bandwidth actuator needed to perform high performance horizontal plasma position regulation. Another actuator, the poloidal coil, could be used for this positioning task, but its bandwidth is insufficient. Using dynamic input allocation it is possible to hierarchically achieve the two goals above by way of a nonlinear scheme suitably exploiting the two actuators: the high priority (fast) goal is the horizontal position regulation task, while the low priority (slow) goal is the elongation regulation. We present theoretical results supporting the proposed scheme, as well as simulations and experiments showing the effectiveness of the proposed solution.

Trading output performance for input allocation: application to the JET tokamak shape controller

In this paper we revisit the dynamic allocation scheme for input redundant plants proposed in [12] within a set-point regulation setting and propose generalizations that apply to cases where the plant under consideration is not input redundant but the control specifications allow to modify the set-point regulation within certain bounds. In this case, the input allocator is extended to the nonredundant case by allowing it to improve the input allocation selection at the price of some output regulation error. Similar to [12], the allocator behaves according to some dynamics that converges to the minimum of a certain cost function. The allocation scheme is applied to the JET tokamak shape controller by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom. The allocator behavior is illustrated by simulation on the JET tokamak both in off-line operation (in open loop during the pulse planning phase) and in on-line operation (in closed loop during the pulse).

A Software Tool for the Design of the Current Limit Avoidance System at the JET Tokamak

A current limit avoidance (CLA) system has been proposed to avoid current saturation in the poloidal field (PF) coils of the Joint European Torus tokamak when the eXtreme Shape Controller is used to control the plasma shape. CLA uses the redundancy of the PF coil system to automatically obtain almost the same plasma shape with a different combination of control currents. This paper describes the set of graphic tools that has been recently developed to aid the design of the CLA parameters by nonexpert users.

Results on plasma position and elongation regulation at FTU using dynamic input allocation

In this paper we employ and extend the dynamic allocation theory first presented in [8] to guarantee asymptotic tracking of a prescribed plasma elongation on the Frascati Tokamak Upgrade (FTU). This task is hard to accomplish because it can only be achieved using the so-called F poloidal coil, a high bandwidth actuator needed to perform high performance horizontal plasma position regulation. Another actuator, the V poloidal coil, is available for horizontal position regulation but its bandwidth is insufficient to suitably perform the horizontal position regulation task. Via the dynamic allocation technique it is possible to hyerarchically achieve the two goals using the two actuators: the high priority (fast) goal is the horizontal position regulation task, while the low priority (slow) goal is the elongation regulation. We present theoretical results supporting the proposed scheme, as well as simulations and experiments showing the effectiveness of the proposed solution.

On dynamic input allocation for set-point regulation of the JET tokamak plasma shape

In this paper we propose a solution to the input saturation avoidance problem in the JET tokamak shape control by illustrating its capabilities to enforce coil currents selections that tend to move away from the saturation limits within the allowable degrees of freedom. The proposed solution revisits the dynamic allocation scheme first proposed in [10] for input redundant plants and generalized in [6] and [9] for not input redundant ones. In particular we propose a different scheme for the input allocation, more suitable within a set-point regulation setting, and prove its convergence properties. We also present simulation results to assess the steady-state and transient performances obtained with the novel scheme, as compared to the previous approaches.

Shape control with the XSC during plasma current ramp-up and ramp-down at the JET tokamak

The eXtreme Shape Controller (XSC) has been originally designed to control the plasma shape at JET during the flat-top phase, when the plasma current has a constant value. During the JET 2012 experimental campaigns, the XSC has been used to improve the shape control during the transient phases of plasma current ramp-up and ramp-down. In order to avoid the saturation of the actuators with these transient phases, a Current Limit Avoidance system (CLA) has been designed and implemented. This paper discusses the CLA algorithm and presents the experimental results achieved at JET during the 2012 campaigns using the XSC.