# Pitch Channel Control of a REMUS AUV with Input Saturation and Coupling Disturbances
## 1 Introduction  
Underwater vehicle has been widely used in applications such as underwater oil and gas extraction, resource exploration, and monitoring operations, which bring practical challenges for developing underwater systems with better performance. Underwater vehicle working system is prone to be affected by many factors including system dynamics, navigation, motion control and path planning [1]. Among these, a variety of concerns have been focused on the controller designed for vehicle considering actuator nonlinearities and model uncertainties. The controller is required to have the ability to deal with fundamental problems such as actuator saturation, adaptation to changes in model parameters along with the vibrations caused by coupling motions [1; 2; 3]. To achieve this, appropriate control techniques are necessary to be adopted. In practice, PID (Proportional-Integral-Derivative) control with simple structure regarded as model free control has been widely used in the attitude and position control of autonomous vehicles operating underwater or flying in the air. Unfortunately, the realization of PID controller is at the cost of plenty of parameter tuning [4]. In addition, the accuracy of the tasks performed and the complexity of underwater environments, as well as dynamic nonlinearities of model and measurement errors caused by sensors, make adaptive control a better solution [5; 6; 7; 8; 9]. The key to adaptive control of underwater vehicle is to approach the challenges arising from nonlinearities of actuator, uncertainties and inherent coupling disturbances in vehicle system [4; 6; 10; 11]. Adaptive control is investigated to pursue the potential of required robustness, stability and response speed in the presence of unmodeled dynamics and time-varying parameters [7]. To tackle the stability problem of adaptive depth control of Remotely Operated Vehicle (ROV), direct Model Reference Adaptive Control (MRAC) is used to deal with the time-varying buoyancy and gravity problem by updating parameters of controller [12]. Although direct MRAC can track desired depth via computing adaption law, it is time consuming to adjust controller parameters. Several adaptive controllers based on MRAC approaches have been employed in autonomous vehicle, and multiple neural network and fuzzy logic techniques were presented to update controller parameters [9; 11; 13; 14]. Integral feedback MRAC with input saturation was developed to investigate the yaw and pitch angle adaptive control to confront with the practical actuator nonlinearity when vehicle tracks desired commands under different working status [15]. MRAC method has attracted many researchers to solve the coupling problem between rate of adaption and robustness, but the modification attempt still requires sacrificing robust performance such as response speed. Besides, the controller parameters and reference models should be treated carefully. To solve the coupling issue between response speed and robustness of the adaptive controller, L1 AC strategy has been proposed by [PERSON] and [PERSON] [16; 17; 18]. \(L_{1}\) adaptive controller has novelly decoupled the problem of adaption, robustness and convergence speed, where the superiority of the method compared to MRAC is demonstrated. L1 AC can guarantee robustness and fast adaption to uncertainties. The L1 AC architecture is recently implemented to control the depth and pitch of an underwater inspection vehicle named AC-ROV with success in [19; 20; 21]. \(L_{1}\) adaptive control is an effective method to deal with the general system dynamic uncertainties and disturbances. However, the effect of disturbances control on transient dynamics is not prominent. The disturbances in the system should be reduced in controller design stage, especially disturbances from transient dynamics caused by actuator or vehicle nonlinearities, such as input saturation [22; 23; 24].