# Target State Optimization: Drivability Improvement for Vehicles with Dual Clutch Transmissions
## 2 Optimization Problem and Objective Functions
### Customer Objectives
#### 2.1.1 Acceleration Peak and Acceleration Build-Up Objective  
Humans cannot perceive speed but can perceive acceleration and jerk [45]. The perception of the driver is therefore influenced by the acceleration and the acceleration build-up during launch, since the aim of a vehicle launch is to increase speed from standstill. The maximal acceleration and the acceleration build-up are varied in the test subject study by [PERSON] et al. [7] to investigate the influence on the evaluation criteria: sportiness, comfort, and jerkiness. An example of an acceleration profile is shown in Figure 1.  
The test subject study of [PERSON] et al. [7] is introduced to identify the EDTs of the acceleration for sportiness and comfort. The EDT for sportiness is depending on the intensity of the maximal acceleration. It is lower than 0.5 m/s\({}^{2}\) when the maximal acceleration is lower than 3 m/s\({}^{2}\). The EDT is between 0.5 m/s\({}^{2}\) and 1 m/s\({}^{2}\) as the maximal acceleration continues to rise. The EDT for comfort is between 0.5 m/s\({}^{2}\) and 1 m/s\({}^{2}\) for all the tested maximal accelerations. It is observable that the EDT for sportiness is more sensitive to the stimulus intensity than the EDT for comfort due to the fact that the EDT for sportiness tends to be lower than the EDT for comfort (for lower maximal accelerations). To determine the concrete EDTs, more test subject studies need to be conducted. However, the maximal acceleration does not influence the evaluation of jerkiness significantly. In the test subject study by [PERSON] et al. [7], the acceleration build-up refers only to the mean jerk during the rise of the acceleration. The mean jerk is determined starting from 15% and ending at 85% of the maximal acceleration [6], so that the transitions from standstill to a steady growing acceleration, and further the transition to the maximal acceleration, are excluded from the calculation of the mean jerk. The starting and ending points are marked in Figure 1 in red. The results indicate a logarithmically changing EDT of the acceleration build-up, which matches the Weber-Fechner law [11]. The EDTs of the acceleration build-up for the criteria of sportiness, comfort, and jerkiness, are greater than 2 m/s\({}^{3}\), while the acceleration build-up is smaller than 7 m/s\({}^{3}\). As the acceleration build-up increases, the thresholds for the three criteria become smaller than 2 m/s\({}^{3}\). The influence of the acceleration build-up for jerkiness and comfort are contrary. The higher the maximal acceleration and the acceleration build-up, the more jerky and the less comfortable the launches are [7]. Within the study by [PERSON] et al. [7] a regression analysis was carried out to identify the borderline between negative and positive evaluations. The borderline represents a combination of the maximal acceleration and the acceleration build-up. Negative launch behaviors (e.g., discomfort) are marked in blue. It is observable that for the borderline the maximal acceleration and the acceleration build-up influence each other mutually for any of the three criteria. When, for example, the acceleration is increasing the acceleration, build-up is decreasing. The results are shown in Figure 2.  
The demands for a sporty and a comfortable launch are conflicting [20]. Minimizing the maximal acceleration and the acceleration build-up is improving the passengers comfort [46]. High accelerations and mean jerks (shorter build-up times) in contrast tend to be sportier [2]. Obviously, to increase the speed of a vehicle the maximal acceleration and further the mean jerk must be greater than zero, but they also should not be too high  
Figure 1: Acceleration profile of a launch [7]. Figure 2: Borderlines for the criteria of: (**a**) sportiness, (**b**) comfort, and (**c**) jerkiness, the blue fields represent the negative evaluation areas [7]. either.