Bram de Jager

Modeling of Surge in Free-Spool Centrifugal Compressors: Experimental Validation

The derivation of a compressor characteristic, and the experimental validation of a dynamic model for a variable speed centrifugal compressor using this characteristic, are presented. The dynamic compressor model of Fink et al. is used, and a variable speed compressor characteristic is derived by the use of energy transfer and loss analysis. It is demonstrated that taking into account the losses due to friction, incidence, mixing, and blade loading results in compressor characteristics that closely match the measured characteristics. The simulated response of the dynamic model was found to be in excellent agreement with the experimental results, both for set point changes using fuel flow and blow off and for surge oscillations. Analysis of the power spectrum of the in-surge rotational speed and pressure oscillations reveal that the simulated nonlinear oscillations match experimental values up to the third harmonic, both with respect to frequency and amplitude.

Energy management in hybrid electric vehicles: benefit of prediction

Hybrid vehicles require a supervisory algorithm, often referred to as energy management strategy, which governs the drivetrain components. In general the energy management strategy objective is to minimize the fuel consumption subject to constraints on the components, vehicle performance and driver comfort. Typically, we have to deal with two difficulties in the design of an energy management strategy. Firstly, the nonlinear behavior of the components results in a nonconvex cost function, complicating the use of optimization methods. Different approaches to deal with the nonconvexity are discussed. Secondly, the future power and velocity trajectories are unknown. Prediction of the future trajectories, based upon either past or predicted vehicle velocity and road grade trajectories, could help in obtaining a solution close to optimal. The benefit of prediction, compared to a heuristic and an optimal control strategy that uses only actual vehicle data, is shown with an example of a hybrid truck at a highway trajectory in a hilly environment. Results indicate that prediction has benefits only when the slopes have sufficient grade and length, such that the battery state-of-charge boundaries are reached.

An Adaptive Sub-Optimal Energy Management Strategy for Hybrid Drive-Trains

A method and apparatus for interfacing a bus with a plurality of input/output (I/O) devices includes steps for handling transactions to and from the I/O devices. Transactions from the I/O devices includes processing that begins by receiving the transactions, where each transaction is received at a rate corresponding to the providing I/O device. The processing continues by identifying, for each transaction, a corresponding section of memory for temporarily storing the transaction. The particular section of memory is identified based on the type of transaction and/or the identity of the I/O device. The processing then continues by storing each transaction in the identified section of memory when the section has an available entry. When the bus is available and a transaction has been selected, the selected transaction is provided to the bus at the rate of the bus. Processing of transactions directed towards the I/O devices includes steps for monitoring the bus during non-I/O bus intervals for transactions relating to one of the I/O devices. When a transaction is directed towards an I/O device, the transaction is interpreted to identify the particular I/O controller that supports the particular I/O device. The processing then continues by storing, at the bus rate, the transaction in the section of memory corresponding with the I/O device. Once stored in memory, the transaction is provided to an associated I/O controller, which processes the transaction at the rate of the corresponding I/O device.

Optimal trajectories for vehicles with energy recovery options

Abstract The fuel optimal control of modern vehicles involves the control of several components: the automated manual transmission, power split between the engine and secondary power converter, vehicle velocity, clutch position and motor start-stop. These controls are often optimized separate from each other, which leads to suboptimal results. In this paper we focus on the combined optimization of hybrid system use, gearbox and vehicle velocity. A novel cost function description is used which describes the influence of the automated manual transmission, the potential of brake energy recovery, and the vehicle velocity with one control signal, and, therefore, reduces the computational complexity. The cost is modeled using a piecewise affine continuous function, which has the advantage of the control appearing affine in the Hamiltonian. Besides the standard optimal control solution for systems with an affine cost function, non-smooth optimal control theory is involved to obtain a sequence of subarcs that fulfills the necessary conditions of optimality. Since the length and cost of each subarc, that fulfills the necessary conditions of optimality, in travel time and fuel consumption, can analytically be expressed in its initial and end velocity, the fuel optimal control of a vehicle with energy recovery options is rewritten as a nonlinear optimization problem.

Heat exchanger modeling and identification for control of Waste Heat Recovery systems in diesel engines

To meet future CO2 emission targets, Waste Heat Recovery systems have recently attracted much attention for automotive applications, especially for long haul trucks. This paper focuses on the development of a dynamic counter-flow heat exchanger model for control purposes. The model captures the dynamic phenomena of two-phase fluid flow using the mass and energy balance equations. While most of the studies use chemical libraries to retrieve the working fluid properties, in this model mathematical equations are derived. Compared to other evaporator models, the proposed model is validated on data from a complete engine platform. Experiments are done on a state-of-the-art Euro-VI heavy-duty diesel engine, which is equipped with a Waste Heat Recovery system. For transient conditions over a wide range of operating points, simulation results show good agreement in comparison with experimental data. This makes the model suitable for real-time simulations, diagnostics and control algorithm designs.

Implementation of an optimal control energy management strategy in a hybrid truck

Energy Management Strategies for hybrid powertrains control the power split, between the engine and electric motor, of a hybrid vehicle, with fuel consumption or emission minimization as objective. Optimal control theory can be applied to rewrite the optimization problem to an optimization independent of time. Estimation of the Lagrange parameter, e.g., by feedback on the battery State-Of-Charge (SOC), can be used to arrive at a real-time implementable strategy. Nevertheless, it is still required to solve a nonconvex optimization problem with limited onboard computational power. This paper suggests to solve this optimization problem, offline, for different values of the Lagrange parameter, crankshaft rotational speed, and torque request. The resulting strategy is evaluated with simulations of a hybrid distribution truck on two different velocity trajectories. The influence of several control parameters is investigated also.

Symbolic stiffness optimization of planar tensegrity structures

During the design of mechanical systems one normally exploits numerical analysis and optimization tools. We make a plea for symbolic computation and give an example where structural displacements under load are computed symbolically. Geometrical design parameters enter in this computation. The set of equilibrium conditions, linear in the displacements, but nonlinear in the design parameters, is solved symbolically. The resulting expressions reveal the geometry which yield optimal properties for stiffness or stiffnessto-mass. This technique is applied to a class of repetitive mechanical systems, namely tensegrity structures. A large scale example with 1533 degrees-of-freedom is computed successfully. The results make it possible to optimize the structure with respect to stiffness properties, not only by appropriately selecting (continuous) design parameters, influencing geometry, but also by selecting the number of stages used to build up the structure (a discrete design parameter), influencing topology.

Optimal topology and geometry for controllable tensegrity systems

This paper demonstrates a procedure to design an optimal mass to stiffness ratio tensegrity structure. Starting from an initial layout of the structure that defines an allowed set of element connections, the procedure defines positions of the nodal points of the structure, volumes of the elements and their rest lengths yielding a tensegrity structure having smaller compliance for a given load applied then an initial design. To satisfy design requirements strength constraint for all the elements of the structure, buckling constraint for bar elements as well as constraint on geometry of the structure are imposed yielding a nonconvex nonlinear constrained optimization problem. Structural static response is computed using complete nonlinear large displacement model. Examples showing optimal layout of a 2D and 3D structure are shown.

One-Sided Control of Surge in a Centrifugal Compressor System

Active surge control is studied in a centrifugal compressor system. To stabilize surge, a bleed valve is applied which is nominally closed and only opens to stabilize the system around the desired operating point. This bleed valve is controlled using a linear output feedback controller based on plenum pressure measurements. In this study, the practical limitations of this one-sided surge controller are examined. Experiments show that the performance of the controller is affected by measurement noise and the desired equilibrium point in the controller, which is not accurately known in the unstable operating region. Fully-developed surge is stabilized with relatively small stationary bleed valve mass flow using the proposed controller in combination with a small band-pass filter. Measurements are compared with the results of the Greitzer model. This model shows qualitative agreement with experiments. For the examined compressor system, a 3.5% extension of the stable operating region is obtained using the one-sided surge controller.Copyright

Improving pushbelt continuously variable transmission efficiency via extremum seeking control

The control design for the variator in a pushbelt continuously variable transmission (CVT) is investigated. The variator enables a stepless variation of the transmission ratio within a finite range. A conventional control design for the variator is typically obtained by the use of a variator model, which incorporates large uncertainties and, therefore, limits the variator efficiency. In this paper, a control design for the variator is discussed, which improves the variator efficiency and limits the number of sensors. The relation between inputs and outputs of the variator is investigated, from which one input-output map is identified, which exhibits a maximum. This maximum indicates performance in terms of the variator efficiency. For this reason, this input-output map is maximized by means of extremum seeking control (ESC), which omits the use of a variator model. Experiments illustrate that the approach is feasible and show that a conventional control design for the variator is outperformed.