Kurt Chudej

Optimal Control of Load Changes for Molten Carbonate Fuel Cell Systems: a Challenge in PDE Constrained Optimization

Molten carbonate fuel cells provide a promising technology for the operation of future stationary power plants. In order to enhance service life, a detailed understanding of the dynamical behavior of such fuel cell systems is necessary. In particular, fast load changes shall be simulated, (resp., optimized) without risking material stress due to the extreme temperature differences usually accompanying fast load changes. Fast load changes are important for daily operations in order to react on varying demands. Material stress may lead to irreparable damage of the fuel cell stack. For these contradicting goals, a family of hierarchically ordered mathematical models has been developed with the aim of simulating and optimizing the temporal and spatial dynamical behavior of the gas streams, chemical reactions, and potential fields within the fuel cells. Altogether, the most complicated system, which is investigated in the present paper, results in a Pareto-optimal control problem with constraints in form of a ...

Optimal Rendezvous Path Planning to an Uncontrolled Tumbling Target

Abstract As the number of uncontrollable objects in low earth orbit is rising, the thread of collisions and thus the breakdown of working satellites becomes worth analyzing. Consequently, projects on removing objects from the important orbits are taken into account by the international space associations. This paper is about the modelling and optimal path planning of a docking maneuver to an uncontrollable tumbling target. After deriving the system dynamics, we introduce boundary conditions to ensure a safe and realizable maneuver and a general Bolza type cost functional to incorporate different optimization goals. In order to solve the resulting problem, we transform the dynamics to a set of differential algebraic equations which allow us to employ a direct optimization method while perserving the energy of the system. The concluding simulation results show the reliability and effectiveness of this approach.

Instationary Heat-Constrained Trajectory Optimization of a Hypersonic Space Vehicle by ODE–PDE-Constrained Optimal Control

During ascent and reentry of a hypersonic space vehicle into the atmosphere of any heavenly body, the space vehicle is subjected, among others, to extreme aerothermic loads. Therefore, an efficient, sophisticated and lightweight thermal protection system is determinative for the success of the entire mission. For a deeper understanding of the conductive, convective and radiative heating effects through a thermal protection system, a mathematical model is investigated which is given by an optimal control problem subject to not only the usual dynamic equations of motion and suitable control and state variable inequality constraints but also an instationary quasi-linear heat equation with nonlinear boundary conditions. By this model, the temperature of the heat shield can be limited in certain critical regions. The resulting ODE–PDE-constrained optimal control problem is solved by a second-order semi-discretization in space of the quasi-linear parabolic partial differential equation yielding a large-scale nonlinear ODE-constrained optimal control problem with additional state constraints for the heat load. Numerical results obtained by a direct collocation method are presented, which also include those for active cooling of the engine by the liquid hydrogen fuel. The aerothermic load and the fuel loss due to engine cooling can be considerably reduced by optimization.

Global state space approach for the efficient numerical solution of state-constrained trajectory optimization problems

A new approach based on a global state space form is introduced for solving trajectory optimization problems with state inequality constraints via indirect methods. The use of minimal coordinates on a boundary arc of the state constraint eliminates severe problems, which occur for standard methods and are due to the appearance of differential-algebraic boundary-value problems. Together with a hybrid approach and a careful treatment of some interior-point conditions, we obtain an efficient and reliable solution method.

Parametric Sensitivity Analysis of Fast Load Changes of a Dynamic MCFC Model

Molten carbonate fuel cells are well suited for stationary power production and heat supply. In order to enhance service lifetime, hot spots, respectively, high temperature gradients inside the fuel cell have to be avoided. In conflict with that, there is the desire to achieve faster load changes while temperature gradients stay small. For the first time, optimal fast load changes have been computed numerically, including a parametric sensitivity analysis, based on a mathematical model of Heidebrecht. The mathematical model allows for the calculation of the dynamical behavior of molar fractions, molar flow densities, temperatures in gas phases, temperature in solid phase, cell voltage, and current density distribution. The dimensionless model is based on the description of physical phenomena. The numerical procedure is based on a method of line approach via spatial discretization and the solution of the resulting very large scale optimal control problem by a nonlinear programming approach.

Suboptimal control of a 2D molten carbonate fuel cell PDAE model

Numerical results for suboptimal boundary control of an integro partial differential algebraic equation system of dimension 28 are presented. The application is a molten carbonate fuel cell power plant. The technically and economically important fast tracking of the new stationary cell voltage during a load change is optimized. The nonstandard optimal control problem s.t. degenerated PDE is discretized by the method of lines yielding a very large DAE constrained standard optimal control problem. An index analysis is performed to identify consistent initial conditions.

Optimal Ascent of a Hypersonic Space Vehicle

An ascent optimization of a hypersonic Sanger type lower stage is presented. The optimal control problem is reduced to a multipoint boundary-value problem by calculus of variations and solved by the multiple shooting method. A good first estimate of state and especially adjoint variables to start the multiple shooting algorithm is computed via a special direct collocation method. Accurate solutions including the switching structure are obtained through this hybrid approach due to Bulirsch and von Stryk.

Optimal control for a simplified 1D fuel cell model

Molten carbonate fuel cells are a promising technology for the operation of future stationary power plants. To enhance service life, a detailed knowledge of their dynamical behaviour is essential. The possibility of fast and save load changes is important for daily operation of these power plants. To predict the dynamical behaviour of fuel cells a hierachy of mathematical models has been developed in the past. Recently a systematic model reduction was applied to a 2D crossflow model. We present here the new 1D counterflow model and discuss a suitable discretization method. Accordingly we set up a method of optimal control following the first-discretize-then-optimize approach. Results are shown for simulation and optimal control in the case of load changes.

Modelling and Optimal Control of a Docking Maneuver with an Uncontrolled Satellite

Abstract Capturing disused satellites in orbit and their controlled reentry is the aim of the DEOS space mission. Satellites that ran out of fuel or got damaged pose a threat to working projects in orbit. Additionally, the reentry of such objects endangers the population as the place of impact cannot be controlled anymore. This paper demonstrates the modelling of a rendezvous szenario between a controlled service satellite and an uncontrolled target. The situation is modelled via first order ordinary differental equations where a stable target is considered. In order to prevent a collision of the two spacecrafts and to ensure both satellites are docked at the end of the maneuver, additional state constraints, box contraints for the control and a time dependent rendezvous condition for the final time are added. The problem is formulated as an optimal control problem with Bolza type cost functional and solved using a full discretization approach in AMPL/IpOpt. Last, simulation results for capturing a tumbling satellite are given.

Numerical Simulation of a Molten Carbonate Fuel Cell by Partial Differential Algebraic Equations

The dynamical behavior of a molten carbonate fuel cell (MCFC) can be modeled by systems of partial differential algebraic equations (PDEAs) based on physical and chemical laws. Mathematical models for identification and control are considered as valuable tools to increase the life time of the expensive MCFC power plants, especially to derive control strategies for avoiding high temperature gradients and hot spots. We present numerical simulation results for a load change of a new one-dimensional counterflow MCFC model consisting of 34 nonlinear partial and ordinary differential algebraic-equations (PDEAs) based on physical and chemical laws. The PDAE system is discretized by the method of lines (MOL) based on forward, backward, and central difference formulae, and the resulting large system of semi-explicit differential-algebraic equations is subsequently integrated by an implicit DAE solver.