# Control Design and Validation for Floating Piston Electro-Pneumatic Gearbox Actuator
## 2 System Description  
### Electro-Pneumatic Actuator  
The controlled system is the shift actuator of an automated manual transmission (AMT) of a heavy-duty vehicle. To optimize the fuel consumption of these vehicles with a relatively low number of gear pairs, heavy-duty gearboxes usually have three gearbox stages: split gear, range gear, and the main gearbox. Both the split and range gears have two gear pairs, and in most cases, they do not have a neutral position. Thus, the neutral of the whole gearbox is achieved through the main gearbox. The main gearbox has either two or three parallel shift actuators, or a shift and a select actuator. In case of the latter, which is similar to manual transmissions, the gear shift is divided into two parts according to the H-pattern: the first phase is the lane selection along the horizontal axes of the pattern, for example, selecting the lane of 1 st-Neutral-2 nd gears, or the lane of 3 rd-Neutral-4 th gears, which is achieved by the select actuator. The second step, the gear shift is the function of the shift actuator: it moves the gear stick along the vertical axes of the shift pattern as it shifts the gearbox to neutral or to a requested gear within a previously selected lane, by using a floating piston actuator to enable three stable positions. During a gear change, the proper gearwheel must be connected to its shaft in a shape-locking connection by a face-dog clutch to achieve power-flow. Before engaging a gear, the speed difference between the elements must be reduced, which is achieved either by internal or central synchronization. In the case of internal synchronization, a synchromesh mechanism is also the part of the dog clutch. It decreases the speed difference between the shaft and the gear through friction and also prevents the connection until synchronization occurs. In the case of central synchronization, the speed difference is reduced to a partially synchronized state either by the countershaft brake or by modifying the input shaft speed through the engine control. In this paper, central synchronization is assumed. Therefore, there is no need to consider the angular velocities of the shafts and gear wheels. The pneumatic cylinder is driven by 3-way 2-position solenoid valves, which connect the supply pressure to the chambers in energized state, and in released state, they connect the chambers to the environment. A simplified layout of the system can be seen in Figure 1. The actuator contains two pistons (Main piston and Floating piston), which, together with the step-like change in the internal diameter of the actuator, divide the cylinder into three chambers. Both Chamber 1 and Chamber 2 are connected to a single solenoid valve, which serves both inflow and outflow purposes. In Chamber 3, nearly constant, ambient pressure is guaranteed by an air release port; however, in case of too fast movement, its pressure increases, thus the chamber acts as an air spring between the cylinder housing and the floating piston. The gear shift is achieved by moving the main piston within the cylinder by increasing the corresponding chamber pressures. As the main piston moves, it actuates the connected elements of the gearbox (such as the shift finger and the synchronizer sleeve), therefore it connects the proper gear to the corresponding shaft. The actuator has three dedicated positions: two gears (the High (H) and Low (L) end-positions of the piston) and the Neutral (N) position. The detent mechanism is used to fixate the pistons in these positions and to prevent their unintentional movement. The movement of the floating piston is limited to the High-Neutral section of the cylinder. Its function is to either help or act against the movement of the main piston through collision in the upper half of the cylinder.