This work shows a linearization for a AUV-Cormoran
dynamic mathematical model with the aim of designing linear
controllers for trajectory control. The model is developed under 3
degrees of freedom and the whole system has been simulated in
Matlab Simulink environment. The linearization model is based on
understanding the dynamics of the vehicle under different operating
speeds, which present a different behavior, yet to be controlled
by a single linear controller. For the linear control has raised the PD
control that allows eliminate the position error, performing simulations
of different trajectories and comparing its results in stability.Peer ReviewedPostprint (published version

Benezra, Andreina

Gomáriz Castro, Spartacus

González Agudelo, Julián

Manuel Lázaro, Antonio

English

UPCommons. Portal del coneixement obert de la UPC

LINEAR CONTROL DESIGN FOR A PATH PLANNING OF AUV-COR-MORANJulián González, Andreína Benezra, Spartacus Gomáriz, Antoni Mànuel SARTI Research Group. Electronics Dept.. Universitat Politècnica de Catalunya (UPC). Rambla Exposició 24, 08800 Vilanova i la Geltrú, Spain. Phone: +(34) 938967200, Fax: +(34) 938967201Abstract- This work shows a linearization for a AUV-Cormoran dynamic mathematical model with the aim of designing linear controllers for trajectory control. The model is developed under 3 degrees of freedom and the whole system has been simulated in Matlab Simulink environment. The linearization model is based on understanding the dynamics of the vehicle under different operat-ing speeds, which present a different behavior, yet to be controlled by a single linear controller. For the linear control has raised the PD control that allows eliminate the position error, performing simula-tions of different trajectories and comparing its results in stability.IntroductionThe Cormoran is a low-cost vehicle for ocean observing, is a hybrid of the AUV (Autonomous Underwater Vehicles) and ASV (Autonomous Surface Vehicles) which was built in the Mediter-ranean Institute of Advanced Studies (IMEDEA), from Mallorca (Spain), for a group of Oceanography, in collaboration with the University of the Balearic Islands. Figure 1 shows a picture of the vehicle.The vehicle was designed to sail just below the water surface along a predetermined path following way-points, in which it sinks vertically and obtains samples of the water column. Then it emerges also vertically and transmits by GSM messages with the most relevant data (temperature, salinity, depth and posi-tion, given by a GPS on board).Afterwards, it moves to a new way-point repeating the process, and so on until a mission is completed [1]. Vehicle Model in 3DOFDue to the movements of the vehicle described above, the heave, roll and pitch can be neglected, so that the characteriza-tion of the vehicle can be achieved through a 3-DOF model for the advance ( ), lateral movement ( ) and yaw angle ( ) [2]. Vec-tors position, speed and strength can be expressed as shown in (2.1).Figure 1. AUV CormoranII-A. Vehicle Dynamics Equation (2.2) is the nonlinear dynamic equation of an under-water vehicle,(2,1)(2,2)where,MRE is the mass and inertia matrix.CRE is the centripetal and Coriolis matrix.tRE is the hydrodynamic force and moment general vector (pro-duced by movement of the hull in the water, forces due to the control surfaces, the forces generated by the propulsion system and the forces due to environmental perturbations). n is the velocity vector. Taking into account the dynamic equation of the vehicle in (2.2), and making an assessment of forces and moments of terms, the equations can be expressed describing the nonlinear model of the vehicle as Cormoran shows in (2.3). In the same equation, combine the terms of the rigid body dynamics, the added mass, the damping terms, and the terms of the thrust (see Figure 2 for the block diagram of this dynamic).LinearizationTo design a linear control system, first it is necessary obtain a linear model of the system to which these techniques will be ap-plied. The model is linearized respect the forward speed u, ne-glecting the velocities v and r, because they are small compared with u; similar approaches were carried out work on the vehicle REMUS [3], as well as in the Infante AUV [4]. Consequently, the operating point on which we will work is (u,v,r) = (un 0,0).Applying Taylor series approximations [5] to (2.3), produce the linear vehicle model expressed in matrix form, equation (3.1). For this model, the propulsion motor  Xnrnnand the rudder angle d are considered the system inputs.(2,3)Instrumental Viewpoint / 10 / Winter 25Figure 2. Block diagram of vehicle dynamics(3,1)(4,1)(4,2)III-A. Analysis of poles and zeros Following the linearization of (3.1) are calculated the transfer function   of yaw with respect to the rudder angle, for different speeds advance from   to  . These transfer functions   have a pole and a zero that are very close between them, so it was decided to cancel them to simplify the transfer function.Figure 3 shows these poles in closed loop with negative gain (due of the opposite relationship between the yaw angle and rudder angle) so that the system is stable. It is important to know that while increases the speed, the system response be-coming faster, and at the same time maintains the overshoot.Control DesignThe tracking of requirements focus on designing a controller that takes the whole nonlinear system to a desired dynamic area. This dynamic area will be defined as desired specifications are achieved, such the time in (4.1).In Figure 4, the dynamic target zone is delimited for the vehicle showed in (4.1)Figure 3. Closed loop Poles in yaw with gain k=-1 for differents uIV-A. PD Control For the controller design, it is sufficient to implement a PD con-trol in the system linearization to eliminate the position error and reach the target zone stated in (4.1).When the system is at a rate of 3.3m/s, the desired dynamic is already accomplished by simply applying a proportional control with gain k = -1, as shown in Figure 3; for other linearization it is necessary to move the poles with a PD control.A zero to the plant has been added applying linear control tech-niques, so to move the system poles at a speed of 0.3m/s to the target dynamic area, matching the system poles for the speed 3.3m/s in closed loop with gain k = -1. The result was a zero at s = -5.44, with a gain k = -22.25.Similarly, it was the same PD control design for the linearized system at the other speeds, resulting in different PD controls, each of them to bringing the poles to the desired dynamic area.However, making a comparison between different PD controls design, it was concluded that it was only necessary to create one PD control to move the system poles for the different lineal-izations to the target zone.ResultsFollowing the study shown above, the same linear PD control was applied throughout the plant. In this case, the control that was used is the designed for the first speed (4.2). The outcome was represented in the S-plane, showing all the modified poles for the different speeds, Figure 4 shows these poles for differ-ent linearizations between 0.3m/s and 0.6m /s, which show that as speed increases, the conditions significantly improve the de-sign.V-A. Position Error This PD control has been applied to the nonlinear model operat-ing at different speeds. Figure 5 shows their responses to a step input. It is evident that as the speed increases the settling time decreases, as well as the maximum on impulse (and that going Instrumentation Viewpoint / 10 / Winter26to increase the speed the system tends to be first order).ConclusionsIn this study was created a nonlinear model for the Cormoran vehicle with 3 degrees of freedom, this model has been linear-ized by taking one constant speed.For the control action, it has a single PD controller designed for the entire system, showing that it is possible to define a target dynamic area eliminating the position error at steady state. It Figure 4. closed loop poles applying the PD controlFigure 5. Responses to step input for different speeds using PD con-trolalso showed that when the vehicle is at higher speeds the re-sponse is even better, and therefore it is sufficient to design a single PD.References[1] D. Roig Broman, M. Martínez Ledesma, B. Garau Pujol, A. Alva-rez Díaz, J. Tintoré Subirana. “A Low-Cost Autonomous Vehicles For Coastal Sea Monitoring”. Mediterranean Institute of Advanced Studies (CSIC – UIB). Autumn 2005.[2] Thor I. Fossen. “Marine Control Systems”.[3] Timothy Prestero. “Verification of a six degree of freedom simu-lation model for the REMUS autonomous underwater vehicle. Mas-ter’s thesis, September 2001.[4] A. Pascoal, C. Silvestre. “Depth control for the infante auv using gain-scheduled reduced order output feedback”. Science Direct, pages 883-895, 2007.[5] K. Ogata. “Ingeniería de control moderna”. 3º edition.[6] Xin-quian Bian Jia-jia Zhou Xiang-quin Cheng, Zhe-ping Yan. “Application of linearization via state feedback to heading control for autonomous underwater vehicle”. IEEE International Confer-ence on Mechatronics and Automation, 2008.CONSIDERATIONS ON THE ELECTRONIC CONTROL SYSTEM FOR AUTONOMOUS UNDERWATER VEHICLEI.Masmitja, G. Masmitja, J. González, S. Gomáriz,SARTI Research Group. Electronics Dept.. Universitat Politècnica de Catalunya (UPC).Rambla de l’Exposició, 61-69. Neàpolis Building.  08800 Vilanova i la Geltrú. Barcelona. Spain.Abstract—This work proposes the development of a control system for an autonomous underwater vehicle dedicated to the observa-tion of the oceans. The vehicle, a hybrid between Autonomous Un-derwater Vehicles (AUVs) and Autonomous Surface Vehicles (ASV), moves on the surface of the sea and makes vertical immersions to obtain profiles of a water column, according to a pre-established plan. The displacement of the vehicle on the surface allows the navigation through GPS and telemetry communication by radio-modem. The vehicle is 2300mm long by 320mm wide. It weighs 85kg and reaches a maximum depth of 30m. A control system based on an embedded computer is designed and developed for this vehicle that allows a vehicle’s autonomous navigation. This control system has been divided into navigation, propulsion, safety and data acquisition subsystems.IntroductionTraditionally, oceanographic vessels have been and are the most important observation platforms where multidisciplinary oceanographic studies are carried out. The high cost of using them prevents to get data with spatial and temporal resolution required. A recent alternative way, which allows ocean observa-tions with good spatial and temporal resolution simultaneously and with lower costs are the Gliders, the Autonomous Under-water Vehicles (AUVs) and Autonomous Surface Vehicles (ASVs) [1] [2].There is a type of hybrid vehicle in underwater observation that lies between the AUVs and ASVs, ie moving along the surface of the sea and makes vertical immersions to obtain profiles of water column. [3] [4]. The vehicle control system developed belongs to the latter group [5] [6]. It has a double hull structure where the outer hull, Instrumental Viewpoint / 10 / Winter 27

Linear control design for a path planning of AUV-Cormoran

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Linear control design for a path planning of AUV-Cormoran

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