Feedback stabilisation of pool-boiling systems : for application in thermal management schemes

The research scope of this thesis is the stabilisation of unstable states in a pool-boiling system. Thereto, a compact mathematical model is employed. Pool-boiling systems serve as physical model for practical applications of boiling heat transfer in industry. Boiling has advantages over conventional heat-transfer methods based on air- or single-phase liquids by enabling extremely high heat-transfer rates at isothermal conditions. This o¿ers solutions to thermal issues emerging in cutting-edge technologies as semi-conductor manufacturing and electric vehicles (EVs). Continuous miniaturisation in micro-electronics is pushing heat-¿ux densities beyond the limits of standard cooling schemes and growing architecture complexity makes thermal uniformity during chip manufacturing increasingly critical. Further development of EVs may bene¿t equally from boiling heat transfer by its utilisation for actuator cooling and thermal conditioning of battery packs. A pool-boiling system consists of a heater that is submerged in a pool of boiling liquid. The theater is the to-be-cooled device (or a thermally conducting element between the device and the boiling liquid) and is heated at its bottom. On top of the heater, heat is extracted by the boiling liquid. In order to exploit boiling to its fullest e¿ciency, unstable modes need to be stabilised to avoid the formation of a thermally-insulating vapour ¿lm on the heater that causes collapse of the cooling capacity and that heralds a dangerous and ine¿cient mode of boiling. The pool-boiling model comprises a partial di¿erential equation (PDE), i.e. the well- known heat equation, and corresponding boundary conditions that represent adiabatic sidewalls, a uniform heat supply at the bottom, and a nonuniform and nonlinear heat extraction at the heater top. This nonlinear boundary condition renders the entire model nonlinear, resulting in multiple equilibria and complex and exciting dynamics. Restriction to uniform temperature distributions within the heater admits description by a model of one spatial dimension (1D). The 1D model is investigated mathematically and the results are compared with those found by the analyses of spatial-discretisations of the model. Two spatial-discretisation schemes, based on a ¿nite-di¿erence method and a spectral method, are investigated. The latter shows far better convergence properties than the former. Moreover, application of full state feedback of the spectral modes (modal control) results in signi¿cantly better properties than by regulation via standard P-control. In practical applications, the heater temperature can only be measured at the heater top. Consequently, an observer is implemented that estimates the spectral modes of the temperature within the heater, which are subsequently used in the feedback-law. The e¿ciency and performance of this controller-observer combination is examined by numerical simulations. A pool-boiling system with an electrically heated wire as heater can be represented by the model as described above, but now with two spatial dimensions (2D). The 2D model can be analysed mathematically only for uniform equilibria, i.e. the equilibria that exist also for the 1D system. For nonuniform equilibria, the mathematical analysis becomes too complex and a spatial discretisation is required to obtain results. A 1D characteristic equation on the ¿uid-heater interface can be obtained by analytical reduction of the 2D eigenvalue problem using the method of separation of variables. The system poles follow from spatially discretising this equation. Because of its outstanding performance for the 1D model, the 2D model is again stabilised by a modal controller (full state feedback) in combination with an observer. Simulations are again performed to determine the e¿ciency of the controller-observer combination. If a thermally conducting foil is considered as heater, the three-dimensional (3D) form of the model must be investigated. This involves essentially the same methodology as described above, resulting in a 2D characteristic equation on the ¿uid-heater interface. However, spatial discretisation of this equation yields large system matrices and requires excessive calculation times. Hence, the 3D system is analysed only at moderate discretisation orders. The above modal control strategy is, as before, applied in combination with an observer to stabilise unstable equilibria and the evolution of the nonlinear system is again investigated and demonstrated by way of simulations. Finally, a series of exploratory experiments, to investigate the application of pool-boiling to thermally condition battery cells in EVs, is considered. Experiments are performed to investigate the ability for thermal homogenisation of the boiling process and the ability to manipulate the boiling process via the pressure in the boiling chamber. Furthermore, the application of pool-boiling to overcome thermal issues in high-end technologies is investigated by numerical simulations

Minimal data rate stabilization of nonlinear systems over networks with large delays

Control systems over networks with a finite data rate can be conveniently modeled as hybrid (impulsive) systems. For the class of nonlinear systems in feedfoward form, we design a hybrid controller which guarantees stability, in spite of the measurement noise due to the quantization, and of an arbitrarily large delay which affects the communication channel. The rate at which feedback packets are transmitted from the sensors to the actuators is shown to be arbitrarily close to the infimal one.Comment: 16 pages; references have now been adde

Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence

Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller's estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow ($Re_\tau=100$) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl's theory of sheared turbulence

Stabilisation by adaptive feedback control for positive difference equations with applications in pest management

An adaptive feedback control scheme is proposed for stabilising a class of forced nonlinear positive difference equations. The adaptive scheme is based on so-called high-gain adaptive controllers, and contains substantial robustness with respect to model uncertainty as well as with respect to persistent forcing signals, including measurement errors. Our results take advantage of the underlying positive systems structure and ideas from input-to-state stability from nonlinear control theory. Our motivating application is to pest or weed control, and in this context the present work substantially strengthens previous work by the authors. The theory is illustrated with examples