Anders Fröberg

Optimal Operation of a Turbocharged Diesel Engine during Transients

Recent development has renewed the interest in drivetrain concepts which give a higher degree of freedom by disconnecting the engine and vehicle speeds. This freedom raises the demand for active control, which especially during transients is not trivial but of which the quality is crucial for the success of the drivetrain concept. In this work the fuel optimal solution for a turbocharged diesel engine connected to a load which does not restrict the engine speed is derived, analysed and utilized for finding a suboptimal operating point trajectory. We use a Willan s efficiency model for the engine, expanded with a first order delay dependent torque reduction representing the turbocharger pressure, and study different output power transients. The analysis is made with dynamic programming, Pontryagin’s maximum principle and a suboptimal strategy based on the static optimal operating points. We present a method for using Pontryagin’s maximum principle for deriving the optimal operating point trajectory. The time needed for computation was reduced a factor >100 compared to dynamic programming, but this method is only applicable to load cases with steps between different high output powers. We also present a suboptimal method which shows a 1000 compared to dynamic programming.

Optimized engine transients

Recent development has renewed the interest in drivetrain concepts which give a higher degree of freedom by disconnecting the engine and vehicle speeds. This freedom raises the demand for active control, which especially during transients is not trivial but of which the quality is crucial for the success of the drivetrain concept. This work attempts to analyze and explain the fuel optimal solution for the simplest drivetrain setup, which is an engine connected to a load which does not restrict the engine speed. This is made by using a Willans model for the engine and deriving the fuel optimal solution during output power transients. The analysis is made with dynamic programming, Pontryagins maximum principle and backward simulation under a static optimal line restriction. The analysis show that the optimal transients can be explained, visualized and, in simple cases, derived from phase planes of the engine speed and the Lagrange multiplier. In these cases the time needed for computation was reduced a factor > 1000 compared to dynamic programming. Restricting the engine to the static optimal line turns out to be very close to optimal, even during highly transient operation, while reducing the time needed for computation a factor ≫ 1000.

Modeling and optimal control of a wheel loader in the lift-transport section of the short loading cycle

Abstract Optimal control of a wheel loader operating in the short loading cycle is studied in order to investigate the potentials for fuel consumption reduction while maintaining acceptable production rates. The wheel loader is modeled as a system with five states and three control inputs including torque converter nonlinearities. The torque converter is modeled with no lockup enabling power transmission in both directions. The geometry of the wheel loader boom and the demanded force in the lift cylinders during lifting are used to ensure that the in-cylinder pressure remains below components limits. The lift-transport section of the short loading cycle is divided into four phases due to discontinuities in the gearbox ratios and fuel consumption is calculated in each phase. Time optimal and fuel optimal transients of the system and the power consumption in each and every component is presented showing the dominance of the torque converter losses compared to the other components especially in the time optimal solutions. It is shown that introducing path constraints on the maximum lifting speed of the bucket due to limitations in hydraulic pumping speed moves the diesel engine operation towards higher speeds in order to maintain the lifting speed. Trade-off between fuel optimal and time optimal transients is calculated which is found to be in agreement with the results of experimental studies.

Fuel potential and prediction sensitivity of a power-split CVT in a wheel loader

Wheel loader transmissions are commonly based on a torque converter and an automatic gearbox. This solution is mechanically robust and well suited for the typical operation of the machine, but the fuel efficiency is low at some modes of operation. One proposed improvement is to replace the present transmission with a multi-mode power-split CVT (MM-CVT). This paper compares the fuel saving potential of the MM-CVT to the potential of the present transmission under different assumptions on the prediction of future loads. A load cycle with a probability distribution is created from a measurement including 34 short loading cycles. Trajectory optimization is performed both against this, probabilistic, and three deterministic load cycles with the two concepts. The optimization shows that the MM-CVT transmission has at least 15% better fuel saving potential than the present transmission, and that this difference is not sensitive to the quality of the prediction or the smoothness or length of the load case.

Fuel and time minimization in a CVT wheel loader application

Abstract A method is developed for the minimization of time and fuel required for performing a short loading cycle with a CVT wheel loader. A factor β is used for weighing time to fuel in the optimization. Dynamic programming is used as optimization algorithm, and the developed method is based on the change of independent variable, from time to distance driven. It is shown that a change of states from speeds to kinetic energies in the internal simulations is essential. A driving cycle, derived from measurements, representing a short loading cycle is introduced. Optimization is performed against this cycle according to the method presented, using two different values on the time to fuel weighing parameter. It is shown that this parameter can be used to find optimal solutions directed toward short time or low fuel consumption.

Using Stochastic Dynamic Programming for look-ahead control of a Wheel Loader Diesel Electric Transmission

Three Stochastic Dynamic Programming (SDP) implementations are developed for control of a diesel-electric wheel loader transmission. The implementations each use a stochastic description of the loa ...

On the use of stochastic dynamic programming for evaluating a power-split CVT in a wheel loader

Complex transmission concepts may enable high fuel efficiency but require much effort in controller development. This effort should only be spent if the potential of the concept if high, a potential which can be determined using optimization techniques. This paper examine the use of stochastic dynamic programming for transmission potential evaluation, applied on a wheel loader. The concepts evaluated is the present automatic gearbox and a multi-mode CVT (MM-CVT). A probabilistic driving cycle is created from a measurement including 34 loading cycles. Trajectory optimization is performed both against probabilistic and deterministic cycles. The paper shows that the introduction of a probabilistic load highly affect the application of optimization. It is also shown that the MM-CVT has approximately 20% lower minimum fuel requirement than the present transmission, and that this number is not sensitive to the quality of the prediction.

Optimal transient control of power generation in hybrid construction equipment

Optimal energy management and power generation control in hybrid construction machines is presented. Power demand is often highly transient for construction equipment. The influence of the transient demand is studied by introducing powertrain speed dynamics in addition to energy storage dynamics in the optimal control problem. Solutions to the optimal control problem are derived and an approximate solution is proposed that can be used for on-line control. The well known equivalent consumption minimization strategy is extended and the new method introduces a new control parameter, fuel equivalent kinetic energy. Simulations of the on-line control strategy are presented and it is shown that they approximate the optimal control solutions well.