# Control Design and Validation for Floating Piston Electro-Pneumatic Gearbox Actuator
## 1 Introduction
In [21], an SMC is presented for an electro-pneumatic clutch actuator, then a controller reduction possibility is proposed. In [22], a cascaded tracking controller is performed by combining sliding-mode and Lyapunov techniques based on a nonlinear state-space representation. A similar method is presented in [23]. However, instead of SMC, a model-based backstepping controller is used. The authors of [24] show a dual-mode controller for an electro-pneumatic clutch actuator, which is a combination of a local and a global switched controller. In [25], a switched backstepping control of an electro-pneumatic clutch actuator is presented, showing better performance than PWM-based methods and also using less solenoid valve switches. The authors of [26] propose a Fuzzy Backstepping Controller for a PAM, where three fuzzy sets are used: one for inflation, one for deflation, and one for the transition region. In [27], an adaptive robust neural network controller is proposed for a pneumatic actuator, which can achieve high tracking accuracy without knowing the bounds of the parameters and disturbances. In [28], the position control problem of an electro-pneumatic clutch actuator is formulated as a robust asymptotic tracking control problem, which is solved through a constructive robust stability algorithm using Simulated Annealing Algorithm. The authors of [29] present a Ho controller, which is used to achieve high reference tracking performance and meet stability specifications, then proposes [PERSON] singular value-based model order reduction. Most of these methods perform well in their given applications, which are mainly PAMs using proportional valves or electro-pneumatic clutches. Proportional valves can be used to achieve constant mass flow rates, thus the control problem significantly differs, while in the latter case, the actuator must hold the clutch in the requested position, therefore it has to utilize a diaphragm spring, which has a highly nonlinear and hysteretic force characteristic. In this regard, the position control of a clutch actuator is more difficult, but there are further differences between these systems. In essence, clutch actuators are single-acting cylinders with 2-way 2-position solenoid valves, which means there are distinct valves to load and to exhaust the chamber, thus it is also possible to hold the chamber at constant pressure. On the other hand, gearbox actuators mostly are double-acting cylinders with a single 3-way 2-position solenoid valve connected to each chamber. Therefore, it is not possible to achieve constant chamber pressure during a gear change. There is also a difference in the average actuating speed, gearbox actuators have an actuation speed higher by a factor of around 3-5, than that of a typical clutch actuator. This paper aims to present and compare two control methods, which can achieve the high-quality position control of an electro-pneumatic gearbox actuator. The quality of the gear change has a considerable impact on the vehicle comfort and the expected lifetime of the actuator. Using a high number of solenoid valve activations or achieving too fast gear changes with high impact velocity decreases the expected lifetime of the system and increases its noise. At the same time, too slow gear changes harm the torque flow. Thus they can reduce passenger comfort and debase the vehicle dynamics. In addition to the qualitative requirements, the closed-loop system should be robust to the changes of the supply pressure, as it can be decreased due to failure when the controller should also be able to reach a safe state, which is the neutral position of the actuator. Besides, if the controllers can operate reliably with different supply pressures, the same system could be used for different vehicles, decreasing production and development costs. In an optimal case, the robustness analysis of a system should provide mathematical evidence and guarantees.