The aim of this paper is the optimization of velocity trajectories for electrical railway vehicles with the focus on total energy consumption. On the basis of four fundamental operating modes—acceleration, cruising, coasting, and braking—energy-optimal trajectories are determined by optimizing the sequence of the operating modes as well as the corresponding switching points. The optimization approach is carried out in two consecutive steps. The first step ensures compliance with the given timetable, regarding both time and position constraints. In the second step, the influence of different operating strategies, such as load distribution and the switch-off of traction components during low loads, are analyzed to investigate the characteristics of the energy-optimal velocity trajectory. A detailed simulation model has been developed to carry out the analysis, including an assessment of its capabilities and advantages. The results suggest that the application of load-distribution techniques, either by a switch-off of parallel traction units or by a load-distribution between active units, can affect the energy-optimal driving style.

This paper deals with the optimization of velocity trajectories for electrically driven railway vehicles w.r.t. the total energy consumption between two successive stops. First, a quasi-static model of the complete power train of a standard railway vehicle is described. Based on four principle operating regimes-acceleration, cruising, coasting, and braking-energy-optimal trajectories are computed by determining the optimal regime sequence. For the optimization of the switching points between these operating states, particle swarm optimization (PSO) is used. The benefits of this approach are pointed out by simulation results using validated train models.

This paper deals with the optimization of velocity trajectories for railway vehicles w.r.t. the total energy consumption between two successive stops. Based on four principle operating modes - acceleration, cruising, coasting, and braking - energy-optimal trajectories are computed by optimizing the sequence of operating modes as well as the corresponding switching points. The optimization involves two consecutive steps: As a basic technique in the first step, a multimodal optimization, namely the Firefly Algorithm (FFA), is utilized to determine the boundaries defined by the timetable request regarding both time and position constraints. In a second step, the energy-optimal solution will be determined within the remaining parameter space reduced by the first step. The advantages of this approach are pointed out by detailed simulation results.

This paper presents a model-based approach to an energy-optimal speed control of a centrifugal pump that is used within heating systems for buildings. The pump operating strategy is based on two main pillars. The first pillar is represented by a module that provides an estimation of the unknown flow resistances in the hydraulic circuit of the heating system. The second pillar is given by a detailed model-based analysis of the pump characteristic in combination with an optimization approach regarding the energy-efficiency to determine the optimal angular velocity of the hydraulic pump. The resulting control strategy is applied to a validated detailed simulation model, which addresses a generic but typical heating scenario. It becomes obvious that a significant improvement w.r.t. the state-of-the-art is achieved.

In previous work, it has been shown that sensitivity-based procedures can be employed effectively for the design of predictive control strategies, for the implementation of state estimators as well as for the offline and online identification of system parameters. These procedures were used, on the one hand, for control of dynamic processes which perform a certain task only once and, on the other hand, also for the control of systems that are operated in a repetitive manner. The latter class of applications is hence closely related to the design of iterative learning control strategies. A common feature of all sensitivity-based approaches implemented so far by the authors is that the control signals are piecewise constant on an equidistant time discretization mesh. However, this assumption may make the computation of differential sensitivities inefficient if long control horizons are taken into account for learning-type controllers of processes with a fast dynamics. Therefore, this assumption is removed in the current paper, both by a control parameterization using polynomial ansatz functions and by a computation of optimal switching points for piecewise constant control signals. The adaptive discretization scheme of the latter approach allows for obeying predefined performance constraints with a minimum memory demand. These procedures are demonstrated by simulations for a prototypical high-speed rack feeder system.