Claes Breitholtz

Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model

Active feedback stabilization of pressure-driven modes in tokamaks is studied computationally in toroidal geometry. The stability problem is formulated in terms of open-loop transfer functions for fluxes in sensor coils resulting from currents in feedback coils. The transfer functions are computed by an extended version of the MARS stability code [A. Bondeson et al., Phys. Fluids B 4, 1889 (1992)] and can be accurately modeled by low order rational functions. In the present paper stability is analyzed for a system with an ideal amplifier (current control). It is shown that feedback with modest gain, and a single coil array poloidally, gives substantial stabilization for a range of coil shapes. Optimum design uses sensors for the poloidal field, located inside the resistive wall, in combination with rather wide feedback coils outside the wall. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. A future companion paper [C. M. Fransson et al., Phys. Plasmas (ac...

High-Level Scheduling of Energy Optimal Trajectories

The reduction of energy consumption is today addressed with great effort in manufacturing industry. In this paper, we improve upon a previously presented method for robotic system scheduling. By applying dynamic programming to existing trajectories, we generate new energy optimal trajectories that follow the same path but in a different execution time frame. With this new method, it is possible to solve the optimization problem for a range of execution times for the individual operations, based on one simulation only. The minimum energy trajectories can then be used to derive a globally energy optimal schedule. A case study of a cell comprised of four six-link manipulators is presented, in which energy optimal dynamic time scaling is compared to linear time scaling. The results show that a significant decrease in energy consumption can be achieved for any given cycle time.

Wall average heat transfer in CFB-boilers

Abstract The purpose of this work is to find a correlation for heat transfer to walls in circulating fluidized bed (CFB) boilers. Heat transfer and suspension density data from six boilers in the range from 12 to 300 MWth form the basis of the correlation. The data were averaged over the entire height of the heat-receiving wall to facilitate application to boilers. Averaging also reduces uncertainties in the measured data. The correlation of heat transfer coefficient (HTC) and average suspension density represents the measured heat transfer coefficients within 15%. An attempt to separate radiation and convection was made in order to account for variations in wall and bed temperatures. The improvement due to the separate treatment is not significant compared to the uncertainty in the experimental data, but the influence of temperature on the heat transfer coefficient is explicitly represented.

Physics and control of resistive wall modes

Active feedback stabilization of resistive wall modes in tokamaks is studied both analytically, using large aspect ratio theory, and by means of toroidal computations. Extensive studies show that robust stabilization, with respect to variations in plasma current, pressure and flow velocity, can be achieved with a simple control system using poloidal sensors inside the first wall. The required coil voltages are modest, even for the two-wall structure of a tokamak reactor.

Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. II. Control analysis

Active feedback of nonaxisymmetric resistive wall modes in tokamaks is investigated using control theory. Control systems are designed to stabilize the resistive wall mode of toroidal mode number n=1 and meet certain performance specifications for a set of test equilibria. The response of the plasma and resistive wall is described by low order rational functions from an electromagnetic model [Y. Q. Liu et al., Phys. Plasmas 7, 3681 (2000)]. Simple coil arrangements are assumed, both for the sensor and feedback coil arrays, and the sensors detect the perturbed poloidal field. The active coils are modeled both as broad strips and as thin wires, and several different controllers: P (proportional), PD (proportional plus derivative) and H∞ are investigated. An important parameter is the ratio, τ, of control system response time to the resistive wall time, and the analysis shows the restrictions on this ratio for acceptable performance. For an equilibrium that exceeds the no-wall beta limit by 63%, good control...

Steady-state solution of a two-species biofilm problem

Through a thorough investigation of the boundary conditions for a general two‐species biofilm model, a simple and fast method for solving the steady‐state case is developed and presented. The methods used may be extended to biofilm models in which more than two species are considered. Four different sets of boundary conditions are possible for the two‐species biofilm model. Each set is shown to be asymptotically stable. A biofilm model describing the competition between autotrophic and heterotrophic bacteria and a biofilm model considering only Nitrosomonas and Nitrobacter are used for illustration. A parameter Lcrit, critical film thickness for bacterial coexistence, is introduced from which criteria on the bulk concentrations for coexistence are derived. From these criteria it is seen that the thinner the biofilm, the more restrictive the conditions are for steady‐state coexistence. For thin biofilms there may, in many cases, be no point in considering more than one species in the biofilm model. Furthermore, the gradients of the bacterial concentrations are in many cases negligible in thin biofilms, and the biofilm may then be assumed to be homogeneous. The criteria on the bulk concentrations together with the four sets of boundary conditions provide the necessary information for a direct solution of the steady‐state two‐species biofilm model by means of an ordinary differential and algebraic equation solver.

Active feedback stabilization of high beta modes in advanced tokamaks

Active feedback of non-axisymmetric external modes in tokamaks is studied by means of combined MHD and control analysis. The MARS code for toroidal MHD stability analysis has been extended to compute transfer functions for the electromagnetic response of the plasma, the coils and the resistive wall. These transfer functions are used for controller design. The controller is designed to allow for the longest possible response time of the amplifier-feedback coil circuit, such that certain predetermined performance criteria are satisfied. Calculations are presented for high beta advanced tokamak equilibria with ITER-FEAT shape. With an array of feedback coils that has only one coil in the poloidal direction, and assuming a single resistive wall, control of modes with toroidal mode number n = 1 is found to be possible for βN up to 5, or twice the no-wall limit. Sensors for the poloidal field are superior to sensors for the radial field. Feedback coils with a rather broad cross-section have significant advantages over thin-wire coils. The controller needs to have significant derivative action, but the requirements on the time constant of the amplifier-feedback coil circuit are moderate. This time needs to be less than a few resistive wall times, and broad strips allow an even longer time constant.

On the analysis of the dc dynamics of multi-terminal VSC-HVDC systems using small signal modeling

In this paper, an analysis of the dc dynamics of multiterminal VSC-HVDC systems using the small signal modeling method is presented. Usually, the VSC controllers are designed under the consideration that they operate independently of each other. However, the possible interactions among them and the dc grid should be studied, especially in multi-terminal topologies. In this paper, three VSC-HVDC systems are modeled and, after linearization, the eigenvalues of the system are calculated for different loading conditions. The results from this analysis are compared to those obtained from more detailed models using PSCAD. It is shown that the operating point, the gains of the direct-voltage controller and the cable dynamics have an impact on the system performance.

LPV-based gain scheduling technique applied to a turbo fan engine model

Linear parameter varying (LPV) system based gain scheduling design is applied to a nonlinear jet engine model. A major shortcoming of LPV based gain scheduling techniques is the transformation step of the nonlinear system into an LPV system. It is crucial to have an accurate LPV model to design a controller meeting the performance specifications. Here, the nonlinear model is transformed into an LPV system using velocity based linearization. The derived state feedback controller has, under the assumption of a correct transformation, a guaranteed L/sub 2/ performance for the considered operating range. The performance of the controller is illustrated by simulations of the closed loop system.

Nyquist Stability Analysis of an AC-Grid Connected VSC-HVDC System Using a Distributed Parameter DC Cable Model

In this paper, a two-terminal VSC-HVDC system embedded in a weak grid ac environment is considered, emphasizing modeling, controller design, and small-signal stability analysis. Traditionally, the dc cable is modeled by Π-sections, implying that care has to be taken when using the model for higher frequencies or in cases of higher cable impedance density, such as submarine cables. Here, a distributed parameter cable model is used to overcome this problem. The VSC-HVDC system can be described as two cascaded blocks. The first block is a transfer function that will differ depending on what input and output variables are considered, but which is in all realistic cases stable. The second block is a feedback loop, where the forward path is a rational function and the return path is a dissipative infinite dimensional function, remaining the same in all cases. The stability is then analyzed, using the Nyquist criterion, in a straightforward manner. Numerical examples are given by the use of MATLAB. The result is that if the VSC-HVDC system using a single Π-section cable model is stable, so is the VSC-HVDC system using a distributed parameter cable model.