# Control Design and Validation for Floating Piston Electro-Pneumatic Gearbox Actuator
## 3 Model-Based Controller Development  
The control goal is to achieve gear change by controlling the position of the Main Piston. There are four possible requests: Low to Neutral (L2N), Neutral to Low (N2L), High to Neutral (H2N), and Neutral to High (N2H). Theoretically, High to Low and Low to High requests would also be possible, though this request can be divided into two subsequent requests. As there is no continuous reference signal to follow (the change in the requested position is always a step function), the position control of the actuator could be relatively easy. Yet, the nonlinear behavior of the system and the contradictory requirements make it difficult:  
* Maximum 80 ms shift time, 25-40 ms expected
* Maximum measurement and control frequency is 1 kHz
* Maximum 0.2 m/s impact velocity at reaching the end positions of the cylinder
* Maximum 1 mm (around 10%) overshoot and amplitude when reaching neutral state
* Maximum 6 solenoid valve actuation \begin{table}
\begin{tabular}{l c c c c} \hline  & **N2H** & **H2N** & **N2L** & **L2N** \\ \hline Chamber 1 pressure [\%] & 1.45 & 2.96 & 1.84 & 2.28 \\ \hline Chamber 2 pressure [\%] & 1.02 & 4.49 & 1.91 & 4.57 \\ \hline Main piston position [\%] & 3.13 & 3.38 & 2.40 & 2.69 \\ \hline \end{tabular}
\end{table} 
Table 1: Euclidean norms of the error signals. Figure 3: Validation test case—Neutral-to-High gear change. The time interval of gear change shall be minimized, as it interrupts the power flow to the wheels; therefore, it negatively affects both the vehicle's performance and the passenger's comfort. A typical gear change contains the disengagement of the clutch, synchronization if needed, gear shift, and the engagement of the clutch, and it takes approximately 0.5-1 s for a human driver, most of which is needed to operate the clutch. As automated transmission systems expected to have at least the same level of performance as a human driver, the shift time must be lower than 80-100 ms. The capacity of the ECU limits the maximum measurement and control frequency. Both the impact velocity and the maximum valve switch constraints aim to increase the expected lifetime of the system. Too high impact velocity (or kinetic energy during a collision) would damage either the housing or the pistons, which is usually determined by finite-element modeling and lifetime calculations. Solenoid valves have a limited lifetime, which, together with the expected lifetime of the actuator and the expected number of gear changes during its lifetime, determines the maximum valve actuations for a gear change. Naturally, this is a less strict criteria, as a slight difference from this limit can be accepted if its average for all gear changes meets the requirements; however, it highly limits the applicable methods. On the other hand, the overshoot limit is a stricter requirement both quantitatively and in importance, as the actuator shall operate on different gearboxes, where the position of the shifted gear can change and accidental gear changes caused by overshoot must be avoided to ensure safe operation. It is also able to improve a part of performances such as the reduction of shift time or the collision speed; moreover, the overshoot can be eliminated. However, in these cases other performances can be violated as requirements are in contradiction each other. The industrial trade-off prefers low impact in this case, and deals with the wearing of the components through the mechanical design of the elements. All the requirements and main characteristics of the system has to be taken into consideration to decide which control method to implement. It can be seen that the system is only stable at its fixed positions, where its stability is guaranteed by the housing, floating piston, and detent mechanism. Besides, discrete control signals are required to control the solenoid valves. A Pulse-Width Modulation-based method could be an obvious choice, but it would undoubtedly violate the requirement regarding the maximum number of solenoid valve activations.