SKC IISc Performance Analysis Laboratory ECE IISc

Document Sample
SKC IISc Performance Analysis Laboratory ECE IISc Powered By Docstoc
					Mathematical Engineering
           in
 Avionics Applications
        Dr. SK Chaudhuri
                    Sc. ‘H’
      Associate Director, RCI



       9th June 2007, IISc Bangalore
    FUNCTIONAL BLOCK DIAGRAM OF MAJOR MISSILE SUBSYSTEMS



                                        Reference
                                        Generation
                                         System
                                                       Guidance                            Acceleration
                                                       Command                             Rates
         Target                                                           
                      Knowledge                                           ~
         Trajectory
                                        Decision               Action         Airframe &
                      Gathering                                                                   Kinematics
                                        Process                Process        Propulsion
                       system
                                  X
                                  ~
                                  Vx
                                  ~
                                  
                                   ~   M/T
                                                     Missile Trajectory



KNOWLEDGE GATHERING SYSTEM:
Navigation process for position, velocity and attitude etc.

DECISION PROCESS:
Missile guidance system based on available knowledge and stored guidance (if required)

ACTION PROCESS:
Flight control system with sensors, actuators
                          Engine Bay
                Control                                                                              Radome
                Surface                                           Electronic Bay
                                              Wing                                       Nose Cone


                                                                 Guidance &
                                                                   Control             Warhead
                                          Propellant Tank
                                                                   System




                          MISSILE CONFIGURATION

                            Reference
                            Generation
                             system
                                                                                    Rates &
                                                        ~
             Navigation       Guidance                      Actuation     Airframe & Acceleration
                                            Autopilot
             Computer          System                        System       Propulsion




                                                             Sensors


                                          Inertial
                                          Sensors
Target
Trajectory     RF/IR
                                             Kinematics
             Sensors         Missile
                             Trajectory
MATHEMATICAL ENGINEERING INVOLVED MISSILE SUBSYSTEMS

                    Estimation Theory                                                         Dynamic Eqn.s with
                   Random & Stochastic Process                                                 Newton’s laws of motion
                    State space Methods                                                       Fluid dynamics
                    Matrix algebra                                                            Nonlinear Time varying
                    Iteration Techniques                                                       differential Eqn.s
                    Interpolation                                                             Numerical Integration
                   Optimization Tech.                                                          (Euler & RK4)
                                                                                               Interpolation
                                                          Laplace Transforms                  Flexibility dynamics
 Quaternion algebra                                                                            in terms of generalized
 Matrix algebra                                          Z-Transforms
                                                          State space Methods                  coordinates
 Integration techniques
 Solid geometry with                                     Optimization Tech.
 Geodetic, Geocentric                                     Robust Design
 and 3D representation


                                                                                              Rates &
                             Navigation   Guidance                  Actuation
                                                                   ~             Airframe &   Acceleration
                                                         Autopilot
                             Computer      System                     System     Propulsion

 Fast Fourier Transforms                                                                                     Curve Fitting
 Signal Processing                                                   Sensors                                 Filtering techniques.
 Filtering techniques.
                                                       Inertial
                                                       Sensors

                Target         RF/IR
                Trajectory   Sensors      Missile        Kinematics
                                          Trajectory                                               Kinematic Equations
                                                                                                   Linear and Matrix Algebra
                                                                                                   Integrations techniques
                   Mathematical Modelling And Simulation

                                       ACTUAL SYSTEM




                                    COMPARISON
         MATH MODEL                                              COMPUTER SIMULATION
                                    VERIFICATION

                         System, Model & Simulation Correlation
BASIC TECH. COMPONENTS :
1.   Requirements which final Simulation must satisfy.
2.   Equations for representing actual system.
3.   Program Equations for Simulation.
4.   Compare Simulation Program to the Model and modify the mistakes.
5.   Compare Simulation result with actual results.

VERIFICATION :
     Process to determine that a program causes computer to operate as intended by the software designer
     (i.e. Equations are programmed correctly).

VALIDATION :
     Process to determine that computer simulation behaves like actual system in all pertinent respects.
                 ROTATIONAL AND TRANSLATIONAL LOOP JOB
                  ALLOCATION IN REAL TIME MISSILE 6DOF

                                                                           axs
                                          axs = (Tx-Dx)/ M                 ays
                                                                  
                                          ays = Y /M+Yy /M +cr
                                                                          azs
                                         azs = Z /M+Zp /M -cq


                                                                       
                                                                      p            p
                                      
                                      p = Lpp/Ixx+LRR /Ixx+ClQs/Ixx q            q    INCREMENTAL
                                                                                        ANGLES AND
                                      q = M /Iyy+Mp /Iyy                        r    VELOCITIES
                                                                      
                                     r = N /Izz+Ny /Izz           r




                 A/D &                             U                      VX                    1-3
ENGINE                               =tan-1(W/U)
             INERTIAL                                            R T
                                                                                 NAV. Qm QUAT
THRUST                              =tan-1(V/U)   V   VB=([DCM] S) VR          FUNC
             PARAMET                                                       DCM
                                                                                        UPDATE
                                 VM=(U2+V2+W2 ) W
                  ERS
                                                                                                 VB1-3
             t   Vm      Z
                            TWD EFFECTS IN 6-DOF MODEL




Undue Roll oscillations due to low damping introduced by gimballed
 engines, thrust frame and hardware actuator compliance
             MISSILE AUTOPILOT WITH FLEXIBILITY




Unstable Autopilot Response   Modified Stable Autopilot Response
                                TRANSFER ALIGNMENT (TA) SCHEME FOR SHIP LAUNCHED MISSILE
                                                                                                                     GPS/DGPS     LOG


                                                                                                        S : System
                                                                                                                                                           Slave Accn

                                                                                                                                        Master Vel,
                                                                                                               Master INS                Lat, Long                   F update

                                                                                                                                                          Meas & Noise
                                                                                                                                                                         ^           States
                                                             Ship 100/s                                 Process Noise
                                                                                                                                                      -
                                                                                                                                                                         s
                                                                                         SS                                                           +                    AKF
                                                            S curve  0.15 m/s 2                                                                            Fdbks        (Adaptive
                                                                                                                                                                          Kalman
                                                                                                                                                                          Filter)
                                                                                        Missile                Slave INS
                                                                                        q, r 1.2 0/s           (SDINS)                 Slave Vel,
                                                                                                                                        Lat, Long




                                                                                                                                                                    Feed back
                                                                                                                                 Conversion to
                                                                                                              Alignment                                             Controller
                                                                                                             corrections        Error quaternion

                                             PII-06 Results (Psi Error, Del Vn
                                    PII-06 Launch T.A Launch TA Results Plots)
                      50
                                                                                                 Demonstrated 7-state AKF based TA           for SSMs
                                                                                                  launched from Moving Platform.
Psi Error(arc min)




                       0

                      -50           Blue = Optically measured
                                  blue = Optically measured psi error syi error                  Fdbk gains are selected using Linear Quadratic
                                                                                                  Gaussian Regulator and offline Matrix Riccati
                     -100       red = AKF estimated psi error error
                                  red = AKF estimated syi
                                                                                                  equation solution.
                     -150                                                                        Integrated the above with EKF based GPS-INS data
                                                                                                  fusion for Dhanush extended range missions.
                     -200                                                                        Validated through Van, Aircraft, Ship & Flight trials.
                            0     100       200       300         400      500    600     700
                                                     Time (sec)
                                    GPS-INS DATA FUSION SCHEME FOR EXT. RANGE PRITHVI MISSION

                                                                                                                                                   LC


                                                                                                                                                        Nominal
                                                                                                           PURE         Quat, Pos, Vel                  Trajectory
                                                                                                        NAVIGATION

                                                                                             Rates                           Pos, Vel                  GUIDANCE
                                                                                   IMU
                                                                                             Accln                                                      MODULE

                                                                                                                          Corrections
                                                                                                           FUSED                          Quaternion
                                                                                                                                                                      Guidance
                                                                                                         NAVIGATION                                                   Commands

                                                                                                                    Pos, Vel, DCM


                                                                                                                                                 TVC                 ADC




                                                                                                                                                        Defln         Defln
                                                                                                             GPS Data              KF
                                              Position corrections                                     GPS
                    30                                                                                                           MODULE
                                                                                    X corr
                                                                                    Y corr
                    20                                                              Z corr


                    10

                                                                                                                                               CONTROL ACTUATION
Position corr (m)




                     0
                                                                                                                                                    SYSTEM
                    -10


                    -20
                                                                                                     Demonstrated 17-state Extended Kalman Filter (EKF)
                    -30
                                                                                                      based GPS-INS Data Fusion in OBC for extended
                    -40
                                                                                                      range Prithvi missions.
                          0   500   1000   1500   2000 2500          3000   3500    4000     4500
                                                   time (secs)
                         EMBEDDED ONBOARD PROCESSORS                                  GUIDANCE SYSTEM ENGINEERING




                                                                              1 Km
PROCESSOR CLASS




                                                             CEP of Prithvi
                                                                                       With Strapdown Inertial Implicit Guidance (CEP < 1 Km)
                                            System On Chip

                              •Pentium Class
                              •Power PC
                              •COTS
                              •Multi Protocol
                               Connectivity                                   40 m            With TA & GPS-INS data fusion (CEP < 40 m)

                           80486                                                                   Inertial, Radar & Seeker fused Guidance (CEP < 10 m)
                  8086
                                                                              1m                            Inertial & Seeker Guided PGMs (CEP < 1 m)

                                                                                                                                      Year
                  1985     2000     2005         2010                                1990 2003 2006           2010
                                    Year
                                      NUMBER OF FLIGHT TRIALS OF PRITHVI


                                      64       Prithvi
                                  (Planned)

                                  No. of
                                  Flight
                                  Trials




                                      38
                                  (Planned)



                                       12
                                    (Actual)

                                           0
                                            1984 1988    1996     2004
                                                    Year

 Requirement of number of flight trials is reduced because of HILS.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:44
posted:3/25/2011
language:English
pages:13