Gianmaria De Tommasi

ABSTRACT In this paper we investigate the stochastic finite-time stability (SFTS) problem for linear time-varying systems. The system under consideration is described by an Itô type differential equation and the Itô differentiation rule is exploited to derive conditions for SFTS. The main contribution of the paper is that we use an approach based on time-varying quadratic Lyapunov functions, which allow us to obtain less conservative conditions than the time-invariant Lyapunov functions commonly used in the literature. More specifically, we obtain a sufficient condition based on the solution of a generalized Lyapunov differential equation (GLDE) and a sufficient condition requiring the solution of a feasibility problem involving a differential LMIs (DLMI) constraint. We shall show that the DLMI based condition is less conservative and is useful to develop a sufficient condition for stochastic finite-time stabilizability via state feedback; on the other hand the GLDE condition is more efficient from the computational point of view. Numerical examples illustrate that the proposed approach attains less conservative results than those obtainable with the existing literature.

ABSTRACT In recent years, a number of papers have treated the problem of the finite-time stability and stabilization of impulsive (or, more in general, switching) dynamical linear systems. Generally, these works assume that the sequence of switching (in the following resetting) times is a priori known. In this paper, we remove such (strong) assumption, so making the technique more appealing from the practical control engineering point of view. A first result provided in this work is a sufficient condition for finite-time stability when the resetting times are known with a certain degree of uncertainty. Such condition requires the solution of a suitable feasibility problem based on coupled difference/differential LMIs. We show that as the uncertainty intervals reduce in size, our condition becomes less conservative, becoming necessary and sufficient in the certain case (i.e., the resetting instants are perfectly known). Eventually, we consider the conceptually different situation in which the resetting times are totally unknown, namely, the arbitrary switching case. The analysis results are then used to derive sufficient conditions for the existence of state-feedback controllers that finite time stabilizes the closed-loop system in the three cases mentioned earlier. A nontrivial example, considering the finite-time control of the liquid levels into three interconnected reservoirs, shows the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.

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

ABSTRACT In this study, the problem of input??output finite-time stabilisation of linear time-varying systems is dealt with. The classical definition of input-output finite-time stability (IO-FTS) is extended to that one of structured IO-FTS, which allows to incorporate, in the definition of the stabilisation problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilisation are provided in the case of L∞ and L2 inputs, respectively. Such conditions require the existence of a solution to a certain differential linear matrix inequality. The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model.

Abstract The concept of Bounded-Input Bounded-Output (BIBO) stability arises when one wants to focus on the study of the the input-output behavior of a dynamical system, as opposed to the classical Lyapunov stability. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS. A system is said to be IO finite time stable if, assigned a bounded input class and some boundaries in the output signal space, the output never exceeds such boundaries over a ...

Abstract Bounded-Input Bounded-Output (BIBO) stability is usually studied when only the input-output behavior of a dynamical system is of interest. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS (IO-FTS). FTS has been already investigated in several papers in terms of state boundedness, whereas in this work we deal with the characterization of the input-output behavior. A system is said to be input-output finite time stable if, assigned a class of input ...

ABSTRACT 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 has been designed and implemented. This paper presents the experimental results achieved at JET during the 2012 campaigns using the XSC.

ABSTRACT The scientific goal of the Ignitor experiment is to approach, for the first time, the ignition conditions of a magnetically confined D-T plasma. The IGNIR collaboration between Italy and Russia is centred on the construction of the core of the Ignitor machine in Italy and its installation and operation within the Triniti site (Troitsk). A parallel initiative has developed that integrates this programme, involving the study of plasmas in which high-energy populations are present, with ongoing research in high-energy astrophysics, with a theory effort involving the National Institute for High Mathematics, and with INFN and the University of Pisa for the development of relevant nuclear and optical diagnostics. The construction of the main components of the machine core has been fully funded by the Italian Government. Therefore, considerable attention has been devoted towards identifying the industrial groups having the facilities necessary to build these components. An important step for the Ignitor programme is the adoption of the superconducting MgB2 material for the largest poloidal field coils (P14) that is compatible with the He-gas cooling system designed for the entire machine. The progress made in the construction of these coils is described. An important advance has been made in the reconfiguration of the cooling channels of the toroidal magnet that can double the machine duty cycle. A facility has been constructed to test the most important components of the ICRH system at full scale, and the main results of the tests carried out are presented. The main physics issues that the Ignitor experiment is expected to face are analysed considering the most recent developments in both experimental observations and theory for weakly collisional plasma regimes. Of special interest is the I-regime that has been investigated in depth only recently and combines advanced confinement properties with a high degree of plasma purity. This is a promising alternative to the high-density L-regime that had been observed by the Alcator experiment and whose features motivated the Ignitor project. The provisions that are incorporated in the machine design, in that of the plasma chamber in particular, and the relevant analyses in order to withstand or prevent the development of macroscopic instabilities with deleterious amplitudes are presented.

This paper deals with the stabilization of Impulsive Dynamical Systems (IDSs) which represent a subclass of hybrid systems. The IDSs considered here are described by a continuous-time dynamics defined by a nonlinear quadratic system and exhibit discrete jumps in the state trajectory. In this paper we provide sufficient conditions for the design of both static state-and dynamical output-feedback controllers. The proposed conditions guarantee, for the closed-loop system, the local asymptotic stability of the zero equilibrium ...

ABSTRACT Several alternative plasma control schemes using the same plasma current and shape controller (SC) with different plasma vertical stabilisation (VS) controllers are explored, assessing their efficiency in the suppression of plasma shape transients after vertical displacement event (VDE) disturbances and their robustness to changes of the local dynamics. We attempt to decrease the settling time and the overshoot peaks while maintaining robustness to changes of local dynamics, by speeding up the controller response to disturbances. For VS, static output feedback (SOF) and linear-quadratic-Gaussian (LQG) control are considered. Both SOF and LQG are further augmented with an additional intermediate-level control loop that attempts to bring the system back to the origin after a VDE event faster than the SC normally does.

ABSTRACT Since the ITER-like wall in JET (JET-ILW) came into operation, dedicated ITER-like plasma current (I p) ramp-up (RU) and ramp-down (RD) experiments have been performed and matched to similar discharges with the carbon wall (JET-C). The experiments show that access to H-mode early in the I p RU phase and maintaining H-mode in the I p RD as long as possible are instrumental to achieve low internal plasma inductance (l i) and to minimize flux consumption. In JET-ILW, at a given current rise rate similar variations in l i (0.7–0.9) are obtained as in JET-C. In most discharges no strong W accumulation is observed. However, in some low density cases during the early phase of the I p &${\rm RU}(n_{\rm e}/n_{\rm e}^{\rm Gw} \sim 0.2)$ ; strong core radiation due to W influx led to hollow electron temperature (T e) profiles. In JET-ILW Z eff is significantly lower than in JET-C. W significantly disturbs the discharge evolution when the W concentration approaches 10−4; this threshold is confirmed by predictive transport modelling using the CRONOS code. I p RD experiments in JET-ILW confirm the result of JET-C that sustained H-mode and elongation reduction are both instrumental in controlling l i.

ABSTRACT The oPtImal Measurement Probes Allocation (PIMPA) tool has been recently proposed in [1] to maximize the reliability of a tokamak diagnostic system against the failure of one or more of the processing nodes. PIMPA is based on the solution of integer linear programming (ILP) problems, and it minimizes the effect of the failure of a data acquisition component. The first formulation of the PIMPA model did not support the concept of individual slots. This work presents an improved ILP model that addresses the above mentioned problem, by taking into account all the individual probes.

ABSTRACT The JET Shape Controller (SC) uses nine distinct circuits, powering the JET poloidal field coils, to control in real time the coil currents, and the plasma shape, current and position. The control scheme presently used [1] is based on a Multiple Input Multiple Output (MIMO) controller, which is designed to decouple the inductive coupling of the different coils. Achieving such a decoupling, the SC allows the user to tune independently the time response of each circuit. As a matter of fact the intended decoupling algorithm has been incorrectly coded in the JET SC system. This paper describes the modelling and experimental activities performed to correct the code error, and to improve the performance on a subset of the controlled parameters.

ABSTRACT Tokamak control systems have to deal with different kinds of instabilities related to the presence of a resistive wall that surrounds the plasma. These instabilities are known as Resistive Wall Modes and are both axisymmetric and non-axisymmetric; they can occur during normal operation of the tokamak, and therefore suitable feedback controllers need to be designed and implemented. In this paper we propose a control architecture able to deal with the two main instabilities: the axisymmetric vertical instability and the non-axisymmetric kink instability. With reference to the case of the international thermonuclear experimental reactor ITER, we design a controller consisting of two separate loops, one for the vertical stabilization and the other one for the stabilization of the kink instability. The two loops are designed in such a way to minimize the control effort and the interaction between them. The effectiveness of the approach is shown in simulation on an appropriate ITER configuration.

ABSTRACT In a tokamak, the accurate estimation of the plasma boundary is essential to maximise the fusion performance and is also the first line of defence for the physical integrity of the device. In particular, the first wall components might get severely damaged if over-exposed to a high plasma thermal load.

Abstract 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.

Abstract Tokamaks are the most promising approach for nuclear fusion on earth. They are toroidal machines where the plasma is heated in a ring-shaped vessel and kept away from the vessel by applied magnetic fields. To achieve high performance in tokamaks, plasmas with elongated poloidal cross-section are needed. Such elongated plasmas are vertically unstable, hence position control on a fast time scale is clearly an essential feature for all tokamak devices. In this context the Plasma Control Upgrade project was aimed at ...

ABSTRACT In this work we explore advanced control algorithms for the vertical stabilization of plasma in the ITER tokamak for the case where a combination of ohmic in-vessel and superconducting poloidal actuators is used for effective response to disturbances subject to thermal constraints. We apply constrained linear-quadratic optimal control, which is a hybrid between conventional linear quadratic optimal control and model predictive control (MPC). We discuss the issues of practical implementation in the form of explicit MPC, which allows application to fast processes by avoiding the use of on-line optimization.

ABSTRACT Tokamak control systems have to deal with different kinds of instabilities related to the presence of a resistive wall that surrounds the plasma. These instabilities are known as Resistive Wall Modes and are both axisymmetric and non-axisymmetric; they can occur during normal operation of the tokamak, and therefore suitable feedback controllers need to be designed and implemented. In this paper we propose a control architecture able to deal with the two main instabilities: the axisymmetric vertical instability and the non-axisymmetric kink instability. With reference to the case of the ITER tokamak, we design a controller consisting of two separate loops, one for the vertical stabilization and the other one for the stabilization of the kink instability. The two loops are designed in such a way to minimize the control effort and the interaction between them. The effectiveness of the approach is shown in simulation on an appropriate ITER configuration.

The avoidance and mitigation of plasma disruptions plays an important role in the safe operation of IGNITOR, the high field compact machine designed for the investigation of fusion burning plasmas at or close to ignition. The plasma control system is designed to obtain stable closed loop plasma configurations with an assigned plasma shape and current. This accurate and integrated control of plasma position, shape and current can be indeed an effective aid for disruption avoidance and mitigation. In some cases, the PF coil ...

UniSim is a graphic tool that can be used to develop and validate portable automation software, which fully complies with the IEC 61131-3 standard. UniSim is based on a graphical editor and on a simulation engine which allows to perform off-line validation of the automation software. Its simulation engine can also be interfaced with off-the-shelf I/O boards, in order to fast prototype automation systems by using a personal computer. Hardware-in-the-loop validation can be performed interfacing the prototype with the real plant or with an emulator. Furthermore, UniSim adopts the new XML Formats for IEC 61131-3, which provides an open interface for data exchange among different systems. Thanks to this choice the code developed with UniSim can be easily ported among different commercial platforms, increasing software reusability. Although the current release of UniSim is a work in progress version, it is already available and it can be effectively used to develop small and medium automation size projects.