Torpedo Trajectory Visual Simulation Based on Nonlinear Backstepping Control

Transcription

1 orpedo rajetory Visual Simulation Based on Nonlinear Bakstepping Control Peng Hai-jun 1, Li Hui-zhou Chen Ye 1, 1. Depart. of Weaponry Eng, Naval Univ. of Engineering, Wuhan 400, China. Depart. of Aeronautial Armament Fire Control, Naval Aeronautial Eng. Institute Qingdao Branh, Qingdao 66041, China. College of Eletroni Eng, Naval Univ. of Engineering, Wuhan 400, China Abstrat: orpedo trajetory visual simulation has great importane on produt exploitation and war field use. It s a diffiult task beause it ontains different speialties and has a omplex struture. By use of the flexible and effiient Visual C++6.0 and the speialized visual simulation platform Vega, a torpedo trajetory visual simulation system is established. Nonlinear bakstepping ontrol strategy is validated on the system. System mainframe and trajetory models are realized in VC. Senario simulation is realized in Vega. It s shown that this simulation system is favourable. It is helpful in the design and analysis of olletivity, ontrol system and homing system of torpedo. Key word: visual simulation torpedo trajetory three dimension model bakstepping ontrol 1 Introdution 1 Visual simulation is the fruit of the ombination of digital simulation and graphi display tehnology. Information from digital simulation is presented before researhers in the form of graphis and video. Its user interfae (UI) is onveniene. Its real-time three dimension (D) display tehnology is widely used in virtual training and virtual reality. In the proess of weapon system design and validation, it is not eonomial to test too muh times. he data ahieved are not enough to evaluate the weapon system ompletely and orretly. By means of simulation, we an analysis and optimize the digital model of torpedo. It s helpful to develop high quality torpedo at low ost in a relatively short term. Visual simulation an show the movement of weapon intuitively and vividly, and is onvenient for real-time mutual operation. It s shown great importane on weapon system design and validation, weapon platform development [1]. MALAB is brief for programming and graphi display, but it is ineffiient in alulation and not ompatible with senario display platform []. OpenGL graphi library is widely used for visual appliation. Although it is versatile and ready for transplanting, the programming are ompliated and ineffiient []. By ombination of the effiient programming platform, 1 Foundation Item: he National Natural Siene Foundation of China ( ) VC++6.0, and the speialized visual simulation platform, Multigen Vega, a torpedo trajetory visual simulation system is realized. On this system, nonlinear bakstepping ontrol strategy of torpedo depth trajetory is simulated and validated. his system an be used for design of torpedo trajetory, ontrol strategy and homing rules. he system is realized on PC with PIV.0G CPU, i400 video ard. Funtion of system Digital simulation of torpedo motion and ontrol strategy is arried out on the simulation system. At the same time, virtual senario is presented to researhers. Funtions of the simulation system are listed as bellow: (1) Calulation of torpedo trajetory. Data from alulation are used for real-time visual display. At the same time, these data are stored to hard disk for analysis and proessing. () Integrating with D models of torpedo and terrain, virtual senario is onstruted on visual simulation platform Vega. he movement of torpedo will demonstrate in the virtual senario. () Based on data from alulation, D movement of torpedo was presented before researhers. he mode of presentation, suh as the distane and the diretion of observation, an be ontrolled by user. (4) A favorable human-omputer interfae is established. he proess of simulation an be ontrolled SiRes.

2 through the interfae, suh as starting, suspending and terminating the simulation. Before the start of simulation, parameters of torpedo, target and environment are set in parameter dialog boxes. In the progress of simulation, researhers an inspet data through diagrams. Struture of system he simulation system is realized with VC++6.0 and Multigen Vega. VC++6.0 is an objet-oriented visual program development environment whih originated from C. It inherits the merits of high effiieny, flexibility and good ompatibility from C. Its visual integrated development environment is effiient and powerful. So it is often used for programming of ompliated software system espeially those with heavy alulation and ompliated struture [4]. he framework of the system is realized with VC Vega is a high performane software environment and toolkit for real-time simulation and virtual reality appliations. It onsists of a graphial user interfae (GUI) alled LynX, Vega libraries, C allable funtions and other tools [5]. Vega funtionality an be extended by additional speial purpose modules onveniently. MultiGen Creator produes realisti D models and terrain for use in real-time appliations. he torpedo and terrain D models are reated with Creator and imported into Vega [6]. he alulation is heavy and in real-time. In order not to affet the response speed of the interfae, the alulation is arried out in a single thread. Data from alulation are stored in publi memory to be used by Vega. here are three modules in the simulation system: (1) Main interfae module. It manages the whole simulation system, suh as setting parameters, ontrolling the progress of simulation, display graphis of motion status data. () rajetory alulation module. Aording to parameters from interfae, rules of motion, ontrol strategy, it alulates status data of torpedo. () Visual presentation module. It imports D models of torpedo and terrain and reates the environment whih the torpedo sails in. Aording to torpedo status data, it demonstrates the movement of torpedo. he struture of system is shown as figure 1: torpedo trajetory visual simulation system main interfae trajetory alulation data visual presentation data ontrol ontrol of simulation parameters input graphis dispaly parameters ontrol D models of torpedo and terrain Figure 1 Struture of torpedo trajetory visual simulation system 4 Key tehnologies 4.1 Mathemati model of torpedo motion he mathemati model mainly ontains kinematial equations and dynamial equations. Dynamial equations desribe the dynami relationship between position, attitude of torpedo and veloity, angular speed of torpedo. Kinematial equations desribe the dynami relationship between veloity, angular speed of torpedo and outside fores, outside moments. By ombining kinematial equations, dynamial equations and algebrai equations, we an get a group of equations with 15 motion status variables and rudder variables [7]. his group of equations will be soluble with the supplement of ontrol equations. In ontrol equations, rudder angles are determined by motion status variables aording to ontrol strategy. Given initial values of motion status variables, we an get the only solution. But the group of motion equations desribed above is nonlinear and too ompliated. It is an only be solved by numerial integration. Generally it was divided into horizontal motion and vertial motion. In this artile, the SiRes. 1

3 nonlinear vertial motion model is studied and the new stable zero dynami spae is found. he new input-output dynami spae was transformed into strit feedbak nonlinear form. Using the lifting veloity and pithing angular speed as virtual ontrol variables, bakstepping ontrol strategy is presented [8]. Nonlinear motion model in vertial plane is given in literature[9]: x f ( x) g( x)u (1) where x [ v y] f ( x) [ f 1 f f f4 f5] f k v k sin( k f ) 18 k 1v k v k k 4 sin( ) k 5 os( ) k6 os v f k1v kv k4 sin( k 5 os( ) k 6 os f 4 f 5 vsin g ( x) [0 k 9v k9v 0 0] u e ), denotes input ontrol variable. Meanings and typial values of these symbols an be found in appendix 1 of literature [9]. If there is a stable zero dynami spae, we need only to design ontrol strategy of input-output dynami spae. By this ontrol strategy, we an ontrol the depth of torpedo trajetory stably. It was proved that vertial motion model has a stable zero dynami spae: v k11v k18 () 0 Using depth y, lifting veloity, pithing angular speed as status variables of input-output dynami spae, this nonlinear spae an be transformed into v y standard strit feedbak nonlinear form: y vy v y θφ g θφ gu Where θ () k11 k14 k18 k1 k k4 k5 k6 φ [ v sin v os sin sin sin os os os os os ] 1 k os k k k g v k k [ v v sin( ) θ φ os( ) os ] g k9v he bakstepping ontrol strategy is designed with follow steps: (1) We assume z1 y y. It denotes the error of depth traking. Where y is depth instrution. he Lyapunov funtionv 1 is 1 V 1 z 1 (4) () We define z vy vy, where vy 1z1. denotes the virtual lifting veloity instrution. he v y V Lyapunov funtion is V 1 1 z 1 z (5) z, where () We define. denotes the virtual pithing θφ / g angular speed instrution. he Lyapunov funtion is 1 ( V z1 z z θθ θθ ) (6) (4) hen we an design nonlinear bakstepping ontrol strategy: 1 g u θφ (7) 4. D models of entities and terrain MultiGen Creator is a software pakage designed speifially for the reation of real-time D models for visual simulation. raditional D modeling software pakages emphasize the visual effet, so models take CPU a lot of time to render. hey are not suitable for real-time simulation. Creator is base on OpenFlight data format, whih was designed speifially for real-time visual appliation. OpenFlight has layered data struture and manages data with nodes. hese make real-time rendering an easy work [6]. V SiRes.

4 We reate D model of torpedo following these steps: (1) Geometri size of the torpedo was olleted. () OpenFlight database file is reated. hen unit and root node of the database is set. () Branh nodes are reated below the root node. hese nodes manage ertain parts of torpedo model separately, suh as models of body, fin, rudder and srew. (4) Light soures and materials are attahed to torpedo model, this makes the torpedo more realisti. (5) exture is applied to surfae of model to make the model vivid. rifling details are replaed by texture, so the real-time appliation will run more smoothly and use less memory. At the end, we get the torpedo model shown in figure. he struture of database is show in figure. onverted into DED files, whih an be edited by Creator. Creator has toolkits to do this work. () DED files and default parameters are loaded into Creator. hen you an selet the area your database will over. () In order to save time of proessor, some details of terrain beyond ertain distane will be onealed. Aording to the degree you oneal the details, ritial distanes are speified. (4) Feature data are added to terrain. (5) Seleting algorithm to onvert altitude data to triangle data of terrain. (6) At last, terrain database with feature data is established. D model of terrain is shown in figure 4. Struture of terrain model database is shown in figure 5. Eah bran h node represents a ertain area of terrain. Figure D model of torpedo Figure 4 D model of terrain Figure Struture of torpedo model database Weapon platform and target are modeled in the same way. Just like entity models, terrain is stored as D models. errain models are omposed of polygons too. extures and feature data are added into terrain model. hen it an be put into database and driven by real-time appliation. he proess of modeling sea floor is listed as bellow: (1) Altitude data files in all kinds of format are Figure 5 Struture of terrain model database 4. Integrating Vega with VC mainframe his simulation system is onstruted with the Doument/View mainframe of VC. But the View of mainframe is not derived from lass CView of VC [4]. A new lass zsvegaview is derived from CView, and funtions of Vega are added into zsvegaview. So zsvegaview has all funtions of CView and Vega. he SiRes. 14

5 View of mainframe is derived from zsvegaview. So this mainframe has all funtions of the one provided by VC, and an make use of Vega. It is zsvegaview that integrates Vega and VC. Its funtions are list as bellow: (1) At the beginning of simulation, zsvegaview starts Vega thread. Beause the senario needs to be refreshed ontinually and response to windows messages from users, so the job of Vega is arried out in a single thread. he all-bak of the thread is allbakvegahread ( ). () Attahing the handle of CView s window to Vega system. () Initiating Vega system and setting parameters of Vega. (4) Seleting mode of observation. In this system, the trajetory zone is very big and the torpedo is relatively rather small, so tether mode is seleted. Under this mode, observer will follow the torpedo with a ertain distane and angle. User an hange the distane and angle by mouse. (5) he mode of motion is set to user-defined. So the motion and attitude of torpedo are ompletely deided by real-time input data. (6) Refreshing the senario ontinually. 4.4 Driving the senario with data from trajetory alulation he motion of entity in Vega is managed by motion model. here are several motion models in Vega, suh as spinning model, UFO model and so on. But all these models are rather simple and diffiult to improve. here are not suitable for omplex system [5]. By seleting user-defined model, we an replae it with the mathemati model we are studying. Runge-Kutta method is adopted to solve the nonlinear motion model of torpedo. Data produed are provided to Vega for visual presentation. he approah an be divided into following steps: (1) Calulating motion status of torpedo. he alulation thread is start at the beginning of simulation. Its all-bak is allbakorpedocalhread ( ). Data produed are stored in publi memory to be used by Vega. () Implementing motion model of torpedo. First, a user-defined model is registered in Vega system. hat is, a all-bak allbakorpedomotion ( ) is registered. his all-bak takes harge of the initiating, updating of position and terminating of motion. hen the motion model is attahed to torpedo. () Aording to the proess of simulation, status data of torpedo is passed to torpedo model. Vega uses these data to refresh visual senario. Sene of simulation is shown as figure 6. 5 Result of simulation Figure 6 Sene of simulation Step length of alulation is 0.001s. Initial status is given as xe 0 0, y e0 10m, 0 0, 0 0 /s, vy0 0, v x 0 18m / s. Depth instrution y is set to -5m and -50m. Aording to motion model (Equation 1) and ontrol strategy (Equation 7), we an get urves of depth data of torpedo trajetory, as shown in figure 7. Figure 7 Curves of depth dat a of torpedo trajetory It is seen that the depth of torpedo levels off after 10s and 15s. From the result of simulation, we an find that the SiRes.

6 motion model agrees well with reality and the nonlinear bakstepping ontrol strategy is effetive. 6 Conlusions Based on VC++6.0 and visual simulation environment Vega, torpedo trajetory visual simulation system is realized. Considering the nonlinear property of torpedo vertial motion, nonlinear bakstepping ontrol strategy is presented and validated on this system. In this simulation system, motion status of torpedo is alulated in real time. At the same time virtual senario is presented to user. he simulation system haraterizes the motion and ontrol strategy of torpedo. Using effiient developing platform, the simulation system saves a lot of CPU time, whih is benefiial to extend the system. Supplemented with signal detetion model, homing model, motion model of lunh, this simulation system an be extended into full trajetory simulation system. Methods used in this artile are useful for visual simulation of other weapons and weapon platforms suh as missile, submarine, and so on [10]. Aknowledgements he authors are espeially grateful for the support and enouragement of Dr. Wang De-shi at Naval University of Engineering. Referenes [1] Kang Fen-ju, Yang Hui-zhen, Gao Li-e. ehnology and Appliation of Modern Simulation[M]. Beijing: National Defense Industry Press, 006. [] Chai Lin, Fang Qun. he Simulation of orpedo s Guidane rajetory Based on MALAB / Simulink[J]. Journal of System Simulation, 00, 15(): 1-4 [] Yuan Xu-long, Zhang Yu-wen. he Design and Implementation of Air-Drop orpedo rajetory Visual Simulation System[J]. Siene and ehnology of Vessels. 00, 4(): 4-6 [4] Bek Zaratian. Visual C++6.0 Programmer s Guide[M]. Beijing: National Defense Industry Press, [5] Wang Cheng. Real-ime Visual Simulation with Vega[M]. Huazhong University of Siene and ehnology Press, 005 [6] Meng Xiao-mei. Multigen Creator utorial[m]. Beijing: National Defense Industry Press, 005. [7] Fan Feng-tong. Dynamis of orpedo Voyage[M]. Wuhan: Naval University of Engineering Press, [8] Chen Ye, Wang De-shi. Adaptive Bakstepping Control of Nonlinear orpedo Attitude System[J]. Journal of Naval University of Engineering, 008, 0(4): [9] Xu De-min. Automati Control System of orpedo[m]. Xi an: Northwestern Polytehnial University Press, [10] Qian Xin-fang. Dynamis of Missile Aviation[M]. Beijing: Beijing Institute of ehnology Press, SiRes. 16