# Control Design and Validation for Floating Piston Electro-Pneumatic Gearbox Actuator
## 1 Introduction  
In recent years, the main trends of the automotive industry, such as automated driving and electric mobility, have reached the heavy-duty vehicle market. Advanced driver assistance systems (ADAS) and autonomous functions, such as platooning [1], automated highway driving [2], and autonomous yard maneuvering [3], are expected to increase fuel efficiency, decrease emission [4], and also enhance safety [5]. As a consequence of the continuous development in the field of electric mobility, the application of electric actuators already started to expand. They provide a more viable alternative to pneumatic systems in pure electric vehicles, but at present, in diesel and diesel hybrid trucks, pneumatic actuators are indispensable. They have many advantages over equivalent electro-mechanic and hydraulic actuators, such as the unlimited supply of air, high operational safety, and easy maintainability. Still, their nonlinear behavior makes modeling and controlling them difficult. Despite having an already extensive literature and prior knowledge, the continuously tightening qualitative requirements and increased functionality caused by the more and more automated system generates a need for further research. Besides the application of single- and double-acting pneumatic cylinders in heavy-duty vehicles, pneumatic systems are also widely used in robotics, and Pneumatic Artificial Muscles (PAM) represent one of the most promising solutions for interactions between robots and humans. In both applications, one of the most widely researched areas is the modeling of the hysteretic aspects of pneumatic linear actuators. Proposed methods contain the Preisach model [6], the Maxwell-slip model [7], the generalized Bouc-Wen model [8], and empirical approaches, such as the method presented in [9]. There are many approaches in the literature to achieve the position control of pneumatic linear actuators, such as linear controllers, for instance, Linear-Quadratic Regulators (LQR) and Proportional-Integral-Derivative (PID) -type controllers with their robustness enhanced with different types of compensations. In [10], a Linear Quadratic servo control is presented to control a single-piston pneumatic gearbox actuator. Many PID-based solutions exist to achieve the position control of a PAM. In [11], a fuzzy PID control is presented, where fuzzy models are used to provide dynamic feedback, which cancels the nonlinear effects; therefore, a PID controller can be used effectively. In [12], a novel Neural Network based PID controller is presented, which proves to be more robust than a conventional PID controller. The authors of [13] show an adaptive fuzzy PD controller combined with a non-fuzzy integral branch, where a fuzzy inverse model dynamically adjusts the PD part. In [14], an active model-based, advanced nonlinear PID controller is presented to reduce the errors of the simplified dynamics model and improve the performance of the controller. The authors of [15] present a two-degree-of-freedom nonlinear PID controller to compensate for the nonlinear hysteretic phenomena of the PAM and to increase its disturbance rejection. Model Predictive Controllers (MPC) are also proposed to control PAMs and clutch actuators, such as in [16; 17], where a discrete-valued MPC controller is developed to control a hybrid pneumatic-electric actuator. Moreover, the authors of [18] present an explicit MPC method using Pulse-Width Modulation (PWM). Nonlinear methods, such as sliding-mode control (SMC) and backstepping controllers, are also used. The authors of [19] present an Extended Proxy-Based Sliding Mode Controller through the application of a PAM to solve the \"chattering\" problem of a traditional Sliding Mode Controller. The authors of [20] present an analytic control design model of PWM-based pneumatic systems, which serves to transform a discontinuous switching model into a continuous model, then develops an SMC controller for such a system.