2010 Conference on Control and Fault Tolerant Systems Nice, France, October 6-8,2010 FrB1.1 Control of Airship in Case of Unpredictable Environment Conditions Wojciech Adamski, Przemyslaw Hennan, Yasmina Bestaoui and Krzysztof Kozlowski Abstract-The article demonstrates how to generate the trajectory, taking into account the concept of the tunnel of error that ensures route trace with an error no greater than assumed, even in dificult to predict environmental conditions. The mathematical model of kinematics and dynamics using spatial vectors is presented in short. The theoretical assumptions are tested by simulation. The model used in the simulations takes into account the structure of the drives in the form of two engines placed symmetrically on the sides of the object. I. INTRODUCTION Airships are flying objects which, thanks to buoyancy need small amount of energy to keep in the air. Thus they are an interesting alternative to existing transport platforms. One of the most promising applications is monitoring, especially open large or widespread objects, such as construction sites, stadiums, forests, roads, pipelines, etc. Observation of the terestrial objects task can be conside red as tracking a given route task. The key issue determining the usefulness of such solution is reliability of path tracking to be realized with the assumed error, in practice this error is deined, for example, by a range of monitoring equipment. Ensuring such feature is difficult even for objects operating in an environment of low variation of conditions. Airships move in the atmosphere, so they are exposed to chaotic disturbances, which values may be higher than the maximum value of control signals. Such environment makes a task of path tracking with error lower than assumed extremely dificult. This article presents a proposal for solving this problem by introducing concepts of the temporary eror tunnel (TET) and the main error tunnel (MET). The advantages of such solution are: • sureness about pass a given route with position error lower that assumed in each point of main trajectory, • high resistance to wind gusts which temporarily excess acceptable limits of used control algorithm, • increased resistance to not optimal parameters of con troller, • low level of complexity of control algorithm. Apart from concept of errors' tunnels, presented solution is distinguished by implementation of control algorithm in three dimensional space and using only the engines as control effectors. In contrast to many works devoted to this topic This work was supported by Partenariat Hubert-Curien Polonium Wojciech Adamski, Przemyslaw Herman and Krzysztof Kozlowski are with Faculty of Computer Sciences, Poznan Univeristy of Technology, 60- 965 Poznan, Poland wojciech.adamski@put.poznan.pl Yasmina Bestaoui is with Laboratoire IBISC and Department of Electrical Engineering, Universite d'Evry, 91020 Evry, France bestaoui@iup.univ-evry.fr Fig. l. Schematic model of the airship with description of coordinate systems [1], [2], [3], [4], [5], [6], [7], [8], [9] there is no separation of altitude adjustment and control of motion in horizontal plane. Treating tail control surfaces only as stabilizers was dictated by intention to maximize simplification of eventual implementation of proposed solution in reality. II. TRAJECTORY GENERATOR The model of the airship considered in this paper is presented in Fig. 1. Computer simulations use the three dimensional generator of 3rd order polynomial trajectory with erors' tunnel algorithm which is taken into account. The erors' tunnel algorithm divides control tasks to main and curent parts. The main task is to track segment AB in three dimensional space with position error less than OM (Fig. 2). This eror is deined as a cylinder with height IABI and radius OM, called the main eror tunnel (ET). The current task is to track so-called temporary trajectory which determines the time-dependent spatial curve described by equations in the form of the 3rd order polynomials. The temporary trajectory is also surrounded by an errors' tunnel n this case called "temporary"with a radius of OT. Moreover, when the maximum curvature of temporary trajectory exceeds a specified level, which is dependent on the airship maneuvering capabilities, the transitional point D is generated and a new temporary trajectory passes through it. The trajectory generator is shown in Fig. 2. At the moment t = 0 the first temporary trajectory is generated. The begin ning of each temporary trajectory To, T1, T2, T3 is deined by the actual position, orientation and speed of the object. The end of the first temporary trajectory A is also the beginning of the main trajectory. When the airship flies through the base of MET it is generated a new temporary trajectory with 978-1-4244-8154-5/101$26.00 ©2010 IEEE 843