# Pitch Channel Control of a REMUS AUV with Input Saturation and Coupling Disturbances
## 4 Results and Discussion
### Control Experiments Comparison  
In Figure 5, pitch angle, rate and control signals for L1 AC and our proposed controller are compared in the presence of model uncertainties and bounded disturbances.  
L1 AC and the proposed method can both adapt to time-varying inaccurate model parameters of vehicle, but the performance of L1 AC with AW compensator surpasses L1 AC in performance, which verifies the capability of L1 AC with AW compensator controller. It should be noted that the proposed controller can make better use of the potential of the actuator of the vehicle and reduce the fluctuation of pitch rate \(q\) and roll rate \(p\). The coupling disturbance between roll channel and pitch channel is suppressed, thus the desired set-points can be achieved at lower cost of energy.  
Figure 5: Pitch channel control in the presence of the actuator saturation for linear plant tracking \(\theta_{cmd}\) (pulse signal).  
Figure 6: Pitch channel control in the presence of the actuator saturation for REMUS six DOF model tracking \(\theta_{cmd}\) (pulse signal).  
Figure 7: Pitch channel control in the presence of the actuator saturation for REMUS six DOF model tracking \(\theta_{cmd}\) with different set-points.  
The six DOF model of REMUS vehicle is a system with strong nonlinearities. It cannot keep steady in the water due to gravity and buoyancy when the system shut down, which brings more uncertainties to the control. In the case of pitch control for REMUS vehicle, the input saturation for elevator angles is restricted from \(-20\times\pi/180+\delta_{s0}\) to \(20\times\pi/180+\delta_{s0}\)\(rad\), where \(\delta_{s0}\) is the input signal from horizontal rudders when pitch angle of REMUS vehicle is zero. In the simulation, \(\delta_{s0}\) is \(-0.2 rad\), which is extracted from the instruction database and the status measurements when underwater vehicle navigates in the water.  
In view of the battery life and overall stability of the vehicle system control, the input signal should be deliberated. As seen in Figures 6 and 7, the overall performance of L1 AC can be improved with AW compensator compared with L1 AC via exploiting the potential of propeller within the permissible range when there is an input constraint. Unexpected fluctuations in control signals, pitch angle \(\theta\) and roll rate \(p\) caused by tracking instructions, disturbances, unknown model uncertainties and system coupling effects can be weakened. It should be noted that the overall stability of L1 AC controller will not be affected by the compensator augmented according to Figures 5-7. From the viewpoint of energy conservation, the adaptive control method with a compensator can moderately suppress the coupling disturbance (i.e., roll rate) of the underwater robot and reduce the energy loss.  
Furthermore, the nonlinear six DOF model of REMUS AUV is considered to track a desired pitch angle aiming to further investigate the realistic performance of our proposed approach. As seen in Figure 8, although the roll angle fluctuation exists in the six DOF model simulation, the L1 AC controller with AW compensator can cope with actuator nonlinearities and improve the performances of control signal as well as pitch angle tracking results when the disturbance of actuator (height of Power Spectral Density (PSD) is \(2.36\times 10^{-6}\)), measurement noises (heights of PSD are \([4.66\times 10^{-7},\,8\times 10^{-6}]\)) and input time-delay (the value is 0.01 s) are considered, which reveals that the introduced control strategy  
Figure 8: Pitch channel control in the presence of the actuator saturation for REMUS six DOF model tracking \(\theta_{cmd}\) with different set-points with measurement noise, elevator disturbance and input time-delay.  
is appropriate to control the motion of vehicle with model uncertainties and actuator limitations in control practice.