Modeling and Controller Design for the Air-to-Air Missile Uncertain System

Transcription

1 Interntionl ournl of Computer (IC) ISSN (Print & Online) Globl Society of Scientific Reserch nd Reserchers Modeling nd Controller Design for the Air-to-Air Missile Uncertin System Ynjun Ling * unqi Ling b Zhongsheng Wng c School of Computer nd Informtion Engineering Anyng Norml University Anyng Chin b Generl Teching Office Shnghi Sunking Construction Mngement &Consulting Co. ltd. Shnghi Chin c Deprtment of Automtion Gungdong Polytechnic Norml University Gunghou Chin Emil: myluck0404@6.com b Emil: @qq.com c Emil: 84967@qq.com Abstrct The guidnce nd control problem of the ir-to-ir missile system is studied. A nonliner coupling dynmic model of the ir-to-ir missile with six degrees of freedom is investigted nd uncertin control system is proposed ccording to some ssumptions nd simplifictions. Then bsed on Lypunov stbility theory Lypunov function is employed nd controller is designed for the ir-to-ir missile. Numericl simultions show tht the control system proves the correctness nd hs preferbly trcking performnce nd illustrte the effectiveness of the proposed controller. Keywords: uncertin system; dynmic model; controller design; ir-to-ir missile system.. Introduction In the future ir combt the missile must hve strong mneuverbility nd off-xis emissive cpbility nd ll rnge ttck bility especilly rer hemisphere ttcking trget bility. Therefore the ir-to-ir missile in the future should hve huge off-xis cpbility nd the better mneuverbility nd gility * Corresponding uthor.

2 The common methods in the integrted design of missile guidnce nd control include sliding mode control bckstepping design feedbck linerition nd robust prmeterition. But it is difficult to get nlyticl form of the control lw using the sliding mode control method for mneuver trget nd unstble erodynmic. The complexity of the control lgorithm will increse with the order number increse shrply using bckstepping design. Feedbck linerition method needs ccurte object model. Robust prmeterition pproch must estblish complete prmetric system meeting the performnce index of control lw. Therefore these methods re limited in prcticl ppliction. Especilly for the cse of rbitrry mneuvering trget nd gust disturbnce the system is nonliner coupled nd uncertin. The bove methods re difficult to meet the system requirements. In recent yers due to the fst response insensitivity to system prmeters nd externl disturbnces simple lgorithm nd strong robustness the optiml control method hs ttrcted much ttention in the integrted design of guidnce nd control. In recent yers due to the fst response insensitivity to system prmeters nd externl disturbnces lgorithm simpleness nd strong robustness Lypunov direct method hs ttrcted much ttention in the integrted design of guidnce nd control. Shtessel nd his collegues studied the integrted guidnce nd control problem bsed on first order two order nd higher order sliding mode control [-]. Shim nd Idn nd his collegues [4-6] estblished the direct connection between the control input nd the control trget with the ero miss distnce s the sliding surfce nd design the integrted controller. Nthn nd his collegues [7-8] took the predicted collision point error s the sliding mode surfce nd use the finite time convergence of the sliding mode stte to meet the required constrints nd propose n integrted sliding mode control method. In this pper the guidnce nd control problem of the ir-to-ir missile system is studied. A nonliner coupling dynmic model of the ir-to-ir missile with six degrees of freedom is investigted nd n uncertin control system is proposed ccording to some ssumptions nd simplifictions. Then bsed on Lypunov stbility theory Lypunov function is employed nd controller is designed for the ir-to-ir missile. The numericl simultion demonstrted the control effect of the proposed controller.. Dynmicl System Modeling The reserch object of this pper is the ir-to-ir missile tht uses erodynmic lyout with erodynmic force / thrust vector composite control system nd in the ctive phse cn use thrust vector control rudder or ir rudder. Becuse the erodynmic configurtion of the missile uses norml pneumtic lyout so the erodynmic chrcteristics of the missile rudder is simple. Considering this chrcteristic the erodynmic contribution of the ir rudder is simply considered s liner function of the rudder deflection ngle. In ddition the influence of erodynmic torsion ngle on erodynmic forces cn be neglected without considering the erodynmic coupling chrcteristics t high ngles of ttck. Bsed on the bove considertions in order to mke the motion eqution of the missile with six degrees of freedom not too complex the following ssumptions should be mde: ) The elstic mode of the missile is neglected nd the missile is considered s rigid body; ) Assuming tht the thrust force of the engine is constnt nd the force provided by the thrust vector deflection is only involved in the longitudinl nd lterl motions of the missile. Thrust vector control ctutor model ssuming it thrust sie is constnt nd ssuming tht only in the pitch nd yw plne surfce deflection of thrust vector nd use two kinds of ctutor to complete the two deflection (not from the rolling control system); 4

3 ) Ignoring the influence of grvity considering only the ction force nd thrust force of the control force nd thrust vector nd the influence of grvity cn esily be compensted; 4) Due to the short time of compound control turn the missile is considered to be in short period motion nd the missile rottion inerti nd velocity re considered constnt; 5) The center of mss of missile remins unchnged. The erodynmic force / thrust vector composite control system of the missile is s follows: δ qs( Cn + Cn δ)cos ω ωx tn βcos + ω tn βsin cos β qs sin Psin PδP cos + Cx + cos β cos β cos β qs cossin β P cossin β β ωxsin + ω cos + Cx + δ β qs( C )sin sin qs( C C )cos n + Cn δ β β + δ + + PδP sinsin β PδP cos + ω x ω ω x xl δx ( mx + mx δ x) qsl ω V x x ω δ β m ω L ( m δ + m β) qsl ( x) ωω x lpδt ω + + V ω δ m ( ) ( ) ω lp L m δ + m qsl ωω δ ω + + V δ x x T () in which αβ re ttck ngle sideslip ngle nd roll ngle respectively; nd ωωω x re relevnt rottionl ngulr rtes respectively; q is dynmic hed; S is chrcteristic re L is chrcteristic length P is engine thrust force m is missile mss V is missile velocity i ( i x ) re projections of the missile inerti tensor on x erodynmic coefficients xes i δ ( i x ) re relevnt rudder deflection ngles C j re relevnt j mi re relevnt erodynmic moments. i It cn be seen from () tht the ir-to-ir missile control system model with six degrees of freedom hs complex nonliner nd coupling chrcteristics. When considering gust disturbnce it lso involves uncertinties which mkes the design of control system more difficult. In prcticl design the model needs to be simplified. The usul prctice is to ssume tht the missile does not roll during the trget pursuit nd the three-dimensionl 5

4 interception problem is decomposed into two dimensionl interception problems in the longitudinl nd lterl plnes. Bsed on the ssumptions following: ) The missile body does not roll; ) The ngle of ttck nd the sideslip ngle of the missile re smller; ) The coupling term for the rest of the chnnel is bounded nd unknown. The pproximte liner model is proposed in [9] s follows: α R 57.qSC + P ε ε + ε R mr α 57.qSC + P + ω + α qslm qsl m qslm ω α + ω + δ + α ω δ V ω () in which ε denotes the dip ngle t the very moment. Choose stte vribles for the ir-to-ir missile control system () in the following: x [ ε α ω ] T u δ y ε x () nd the system () is rewritten in the stte-spce representtion: 0 0 x 0 0 x+ 0 u+ (4) y x 0 b re bounded unknown uncertin prmeters; R represents reltive distnce between the in which missile nd trget; nd 6

5 R 57.qSC P 57.qSC P + + R mr ω δ 57.qSLm qsl m 57.qSLm V b. (5) The im of this pper is to design n pproprite controller for the uncertin control system (4) which mkes the closed loop control system (4) globlly uniformly symptotic stble nd the output of the closed loop control system (4) symptoticlly pproch ero.. Controller Design In this section we design the control lw for system (4) bsed on Lypunov stbility theory. The control lw cn be presented in the following form: u ( xx + x + x + xx + x + x ) (6) bx Theory Control lw in (6) mke the ir-to-ir missile uncertin control system (4) globlly uniformly symptotic stble. Proof Choose Lypunov function for the system (4) s following: V (7) xi i nd its derivtive long the systems (4) is s follows V xx i i i xx + xx + xx x + xx + x + x + x + x x + x + x + bu x + x 0 (8) According Lypunov stbility theory control system (4) is globlly uniformly symptotic stble. 4. Numericl Experiment To verify the effectiveness of the integrted guidnce nd control lw numericl experiment is crried out for the proposed controller. The results re given in Figure- Figure. 7

6 Figure : dip ngle rte curve Figure : ttck ngle curve Figure : pitch ngle rte curve Our im is to mke the closed loop of the ir-to-ir missile control system globlly uniformly symptotic stble nd the output of the closed loop control system symptoticlly pproch ero. It cn be seen form Figure- Figure tht the proposed controller hs the dvntges of short interception time little trget missing. The rudder deflection ngle of the missile vries smoothly throughout the flying process the vrition of the ttck ngle nd sideslip ngle is lso stble nd the mplitude of the fluctution is lso smll. Especilly in the ner impct point the missile's rudder ngle nd the ngle of ttck nd sideslip ngle without divergent trend. 8

7 Therefore the proposed controller is efficient rel-time nd robust for the ir-to-ir missile control system. 5. Conclusions In this pper the guidnce nd control problem of the ir-to-ir missile system is studied. A nonliner coupling nd uncertin dynmic model of the ir-to-ir missile with six degrees of freedom is considered. Then bsed on Lypunov stbility theory Lypunov function is employed nd controller is designed for the ir-to-ir missile. To verify the effectiveness of the integrted guidnce nd control lw we crry out its simultion nd their nlysis show preliminrily tht the integrted guidnce nd control lw cn gurntee the ccurcy of the ir-to-ir missile hitting n rbitrrily mneuvering trget nd gurntee the stbility of its ttitude. Thus it is effective for interception. Acknowledgements This work ws supported in prt by Nture Science Foundtion of Chin (No nd No. U0440) Science nd Technology Key Project of Henn Province (006) nd Nturl Science Foundtions of Henn Province Eduction Deprtment (No. A000 No. A5008 No. A5007 nd No. A00). References [] I. Shkolnikov Y. Shtessel D. Linos. Integrted guidnce-control system of homing interceptor: sliding mode pproch. AIAA Guidnce Nvigtion nd Control Conference nd Exhibit 00. [] C. Tournes Y. Shtessel. Integrted guidnce nd utopilot for dul controlled missiles using higher order sliding mode controllers nd observers. AIAA Guidnce Nvigtion nd Control Conference 008. [] Y. ShtesselC. Tournes. Integrted higher-order sliding mode guidnce nd utopilot for dulcontrol missiles. AIAA ournl of Guidnce Control nd Dynmics vol. no. pp [4] T. Shim M. Idn O. Goln. Sliding mode control for integrted missile utopilot guidnce. AIAA ournl of GuidnceControl nd Dynmics vol. 9 no. pp [5] M. Idn T. Shim. Integrted sliding mode guidnce nd control for missile with on-off ctutors. AIAA ournl of GuidnceControl nd Dynmics vol. 0 no. 4 pp [6] A. Koren M. Idn O. Goln. Integrted sliding mode utopilot-guidnce for dul-control missiles. AIAA ournl of GuidnceControl nd Dynmics vol. no. pp [7] H. Nthn S. N. Blkrishnn C. Phillips. Sliding mode integrted missile guidnce nd control. AIAA Guidnce Nvigtion nd Control Conference 00. [8] S. Sun D. Zhou. A finite time convergent vrible structure guidnce lw. ournl of Astronutics vol. 9 no. 4 pp [9] Z. Zhu P. Chen B. Tng. Designing integrted guidnce nd control lw for ir to ir missile bsed on sliding mode control. ournl of Northwestern Polytechnicl University Vol. No. pp