Heat absorption control equation and its application of cool-wall cooling system in mines

In order to solve the heat damages in deep mines, a cool-wall cooling technology and its working model are proposed based on the principles of heat absorption and insulation in this paper. During this process, the differential equation of thermal equilibrium for roadway control unit is built, and the heat adsorption control equation of cool-wall cooling system is derived by an integral method, so as to obtain the quantitative relationship among the heat absorption capacity of cooling system, the heat dissipating capacity of surrounding rock and air temperature change. Then, the heat absorption capacity required by air temperature less than the standard value for safety is figured out by section iterative method with the simultaneous solution of heat absorption control equation and the heat dissipation density equation of surrounding rock. Finally, the results show that as the air temperature at the inlet of roadway is 25 ℃, the roadway wall is covered by heat-absorbing plate up to 39% of the area, as well as the cold water is injected into the heat-absorbing plate with a temperature of 20 ℃ and a mass flow of 113.6 kg/s, the air flow temperature rise per kilometer in the roadway can be less than 3 ℃.

Bending analysis and control of rolled plate during snake hot rolling

In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate' and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.

Boundary Control of Coupled Nonlinear Three Dimensional Marine Risers

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.

Computing Open-Loop Optimal Control of the q-Profile in Ramp-Up Tokamak Plasmas Using the Minimal-Surface Theory

The q-profile control problem in the ramp-up phase of plasma discharges is consid- ered in this work. The magnetic diffusion partial differential equation （PDE） models the dynamics of the poloidal magnetic flux profile, which is used in this work to formulate a PDE-constrained op-timization problem under a quasi-static assumption. The minimum surface theory and constrained numeric optimization are then applied to achieve suboptimal solutions. Since the transient dy- namics is pre-given by the minimum surface theory, then this method can dramatically accelerate the solution process. In order to be robust under external uncertainties in real implementations, PID （proportional-integral-derivative） controllers are used to force the actuators to follow the computational input trajectories. It has the potential to implement in real-time for long time discharges by combining this method with the magnetic equilibrium update.

Fast Solvers of Fredholm Optimal Control Problems

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

MOTION VELOCITY SMOOTH LINK IN HIGH SPEED MACHINING

To deal with over-shooting and gouging in high speed machining, a novel approach for velocity smooth link is proposed. Considering discrete tool path, cubic spline curve fitting is used to find dangerous points, and according to spatial geometric properties of tool path and the kinematics theory, maximum optimal velocities at dangerous points are obtained. Based on method of velocity control characteristics stored in control system, a fast algorithm for velocity smooth link is analyzed and formulated. On-line implementation results show that the proposed approach makes velocity changing more smoothly compared with traditional velocity control methods and improves productivity greatly.

VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY PARABOLIC EQUATIONS

This paper considers the variational discretization for the constrained optimal control problem governed by linear parabolic equations.The state and co-state are approximated by RaviartThomas mixed finite element spaces,and the authors do not discretize the space of admissible control but implicitly utilize the relation between co-state and control for the discretization of the control.A priori error estimates are derived for the state,the co-state,and the control.Some numerical examples are presented to confirm the theoretical investigations.

Exact Boundary Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls

In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.

Computer simulation to arc spraying

The arc spraying process is divided into two stages: the first stage is atomization-spraying stream (ASS) and the second one is spraying deposition (SD). Then study status is described of both stages’ physical model and corresponding controlling-equation. Based on the analysis of study status, the conclusion as follows is got. The heat and mass transfer models with two or three dimensions in ASS stage should be established to far deeply analyses the dynamical and thermal behavior of the overheat droplet. The statistics law of overheated droplets should be further studied by connecting simulation with experiments. More proper validation experiments should be designed for flattening simulation to modify the models in SD stage.

INVESTIGATION ON THE APPLICATION OF THE BOUNDARY ELEMENT METHOD TO THE SPILL GROOVED THRUST BEARING

An application of the boundary element method (BEM) is presented to calculate the behaviors of a spiral grooved thrust bearing (SGTB). The basic reason is that the SGTB has very complex boundary conditions that can hinder the effective or sufficient applications of the finite difference method (FDM) and the finite element method (FEM), despite some existing work based on the FDM and the FEM. In other to apply the BEM, the pressure control equation, i. e., Reynolds' equation, is first transformed into Laplace's and Poisson's form of the equations. Discretization of the SGTB with a set of boundary elements is thus explained in detail, which also includes the handling of boundary conditions. The Archimedean SGTB is chosen as an example of the application Of BEM, and the relationship between the behaviors and structure parameters of the bearing are found and discussed through this calculation. The obtained results lay a solid foundation for a further work of the design of the SGTB.

Null Controllability for Some Systems of Two Backward Stochastic Heat Equations with One Control Force

Abstract The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.

Common Fixed Point Theorems and Q-property for Quasi-contractive Mappings under c-distance on TVS-valued Cone Metric Spaces without the Normality

In this paper, we derive the stochastic maximum principle for optimal control problems of the forward-backward Markovian regime-switching system. The control system is described by an anticipated forward-backward stochastic pantograph equation and modulated by a continuous-time finite-state Markov chain. By virtue of classical variational approach, duality method, and convex analysis, we obtain a stochastic maximum principle for the optimal control.

On the quantum master equation under feedback control

The nature of the quantum trajectories, described by stochastic master equations, may be jump-like or diffusive, depending upon different measurement processes. There are many different unravelings corresponding to different types of stochastic master equations for a given master equation. In this paper, we study the relationship between the quantum stochastic master equations and the quantum master equations in the Markovian case under feedback control. We show that the corresponding unraveling no longer exists when we further consider feedback control besides measurement. It is due to the fact that the information gained by the measurement plays an important role in the control process. The master equation governing the evolution of ensemble average cannot be restored simply by eliminating the noise term unlike the case without a control term. By establishing a fundamental limit on performance of the master equation with feedback control, we demonstrate the differences between the stochastic master equation and the master equation via theoretical proof and simulation, and show the superiority of the stochastic master equation for feedback control.

Plate Shape Control Theory and Experiment for 20-high Mill

Roll flattening theory is an important part of plate shape control theories for 20-high mill. In order to improve the accuracy of roll flattening calculation for 20-high mill, a new and more accurate roll flattening model was proposed. In this model, the roll barrel was considered as a finite length semi-infinite body. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distributed force was obtained and an accurate roll flattening model was established. Coupled with roll bending model and strip plastic deformation, a new and more accurate plate control model for 20-high mill was established. Moreover, the effects of the first intermediate roll taper angle and taper length were analyzed. The tension distribution calculated by analytical model was consistent with the experimental results.

BOUNDARY FEEDBACK CONTROL OF ELASTIC BEAM EQUATION WITH STRUCTURAL DAMPING AND STABILITY

In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential stability for this elastic system by using a theorem whichbelongs to F. L.Huang; finally, we discuss the distribution and multiplicity of the spectrum of this system. Theseresults are very important and useful in practical applications.

H_2/H_∞ CONTROL PROBLEMS OF BACKWARD STOCHASTIC SYSTEMS

This paper is concerned with the mixed H_2/H_∞ control problem for a new class of stochastic systems with exogenous disturbance signal.The most distinguishing feature,compared with the existing literatures,is that the systems are described by linear backward stochastic differential equations(BSDEs).The solution to this problem is obtained completely and explicitly by using an approach which is based primarily on the completion-of-squares technique.Two equivalent expressions for the H_2/H_∞ control are presented.Contrary to forward deterministic and stochastic cases,the solution to the backward stochastic H_2/H_∞ control is no longer feedback of the current state;rather,it is feedback of the entire history of the state.

Numerical investigation on jet interaction with a compression ramp

A numerical investigation on jet interaction in supersonic laminar flow with a compres- sion ramp is performed utilizing the AUSMDV scheme and a parallel solver. Several parameters dominating the interference flowfield are studied after defining the relative increment of normal force and the jet amplification factor as the evaluation criterion of jet control performance. The computational results show that most features of the interaction flowfield between the transverse jet and the ramp are similar to those between a jet and a flat plate, except that the flow structures are more complicated and the low-pressure region behind the jet is less extensive. The relative force increment and the jet amplification factor both increase with the distance between the jet and the ramp shortening till quintuple jet diameters. Inconspicuous difference is observed between the jet-before-ramp and jet-on-ramp cases. The variation of the injection angle changes the extent of the separation region, the plateau pressure, and the peak pressure near the jet. In the present computational conditions, 120 is indicated relatively optimal among all the injection angles studied. For cold gas simulations, although little influence of the jet temperature on the pressure distribution near the jet is observed under the computation model and the flow parameters studied, reducing jet temperature somehow benefits the improvement of the normal force and the jet efficiency. When the pressure ratio of jet to freestream is fixed, the relative force increment varies little when increasing the freestream Mach number, while the jet amplification factor increases.

Optimal Transportation for Generalized Lagrangian

This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.