ati professional development technical training short course on missile autopilots
DESCRIPTION
ATI Professional Development Technical Training Short Course on Missile AutopilotsTRANSCRIPT
Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805 Vol. 94 – 31
November 17-20, 2008Columbia, Maryland
$1795 (8:30am - 4:00pm)
"Register 3 or More & Receive $10000 eachOff The Course Tuition."
SummaryThis applications-oriented course provides a
comprehensive overview of missile autopilots. Thecourse begins with an overview of the missileequations of motion and aerodynamic models,followed by a review of linear system theoryincluding frequency response and Bode plots, rootlocus, stability criteria, and compensator design.This introductory material is followed by detaileddiscussion of modern missile autopilot design topicsincluding hardware and hardware modeling,autopilot design requirements, and autopilot designexamples. The remainder of the course focuses on'real world' issues such as nonlinearities, gainscheduling, discretization, pitch-yaw-roll autopilotdesign, and other advanced concepts. Examplesare included throughout the course.
InstructorsPaul Jackson is the supervisor of the
Engineering and DevelopmentSection of the Guidance and ControlGroup at the Applied PhysicsLaboratory (APL) and is the APL Leadfor Standard Missile-2 Guidance andControl. Since joining the staff of APLin 1988, he has worked as an analyston missile guidance and control
systems, particularly for the US Navy Tomahawkand Standard missiles. His early contributions cameas a member of the APL team that was among thefirst to demonstrate the application of modern robustcontrol techniques such as H-Infinity Control andMu-Synthesis to the missile autopilot designproblem. Subsequent experience includes thedesign, analysis, and simulation of missile autopilotand guidance algorithms and hardware. Mr.Jackson has presented papers at AIAA and the IEEEconferences and is a former member of the AIAAGuidance, Navigation and Control TechnicalCommittee.
Course Outline1. Overview of Missile Autopilots. Definitions,
Types of Autopilots, Example Applications2. Equations of Motion. Coordinate Systems,
Transformations, Euler Angles, Force Equations,Moment Equations, Aerodynamic Variables,Linearization, Aerodynamics
3. Linear Systems. State Variables, BlockDiagrams, Laplace Transforms, Transfer Functions,Impulse Response, Step Response, Stability, SecondOrder Systems, Frequency Response, Root Locus,Nyquist Stability Theory
4. Feedback Control. Need for Feedback, DesignCriteria, Types of Feedback, Compensator Design viaRoot Locus, Compensator Design via FrequencyResponse
5. Autopilot Hardware. Actuators, Principles of theGyro, Gyro Modeling, Principles of Accelerometers,Accelerometer Modeling
6. Pitch Autopilot Design. Time DomainRequirements, Frequency Domain Requirements,Acceleration Feedback, Acceleration and RateFeedback, Pitch Over Autopilot, Three-Loop Autopilot
7. Implementation Issues. Body Modes, ActuatorSaturation, Integrator Windup, Gain Scheduling,Discretization
8. Pitch-Yaw-Roll Autopilot Design. ClassicalApproach, Skid-to-Turn, Bank-to-Turn, DesignExamples
9. Advanced Concepts. Multivariable StabilityAnalysis, LQR Optimal Control, Modern Robust ControlDesign Techniques
Missile Autopilots
What You Will Learn• The underlying physics governing missile dynamics.• Theory and applications for autopilot design and
optimization.• Autopilot requirements and design tradeoffs between
performance and robustness.• Choosing autopilot implementation approaches.• Applications to real-world missile systems.• Fundamentals for autopilot design and analysis with
emphasis on linear systems.• Missile dynamics including aerodynamic modeling.• Feedback, feedback design criteria, types of
feedback, compensator design. • Autopilot hardware modeling including actuators,
gyros, and accelerometers.• Pitch Autopilot Design.• Pitch-Yaw-Roll Autopilot Design.• Advanced Design and Analysis Techniques.
“We went from theory toadvanced design & analysistechniques ... all with real worldissues.”
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© 1998 Paul Jackson
Autopilot Definition
An Autopilot is a System of Equations that Takes Commands and Missile State Measurements as Inputs and Computes a Control Command that Stabilizes the Missile and Forces the Missile State to Track the Command
Command Autopilot Actuator Airframe
Sensors
The Combination of Autopilot, Actuator, Airframe, and Sensors is Sometimes Called the "Autopilot." Meaning Should be Clear from Context.
1/3
© 1998 Paul Jackson
Autopilot Components
AutopilotMathematical System of Equations
Implemented Digital or AnalogExternal Command and Measurements are InputsControl Command is Output
ActuatorMechanical Device that Effects a Variable Force and Moment on Airframe
Fin, Nozzle, ...Airframe
Missile Body Including Fixed Aerodynamic SurfacesExperiences Aerodynamic Lift and Moment
SensorMechanical Device to Sense Missile Motion
Accelerometer, Gyroscope, ...
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© 1998 Paul Jackson
Example Applications
Acceleration AutopilotControl Missile Acceleration Perpendicular to AirframeInterceptors
Altitude AutopilotControl Missile AltitudeCruise Missiles
Terrain FollowingControl Missile Clearance Relative to TerrainCruise Missiles
Pitchover AutopilotControl Missile AttitudeMissile Boost Phase
Others
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© 1998 Paul Jackson
Day 1
Equations of MotionLinear SystemsFrequency ResponseAerodynamicsFeedback Control
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© 1998 Paul Jackson
Day 2
Nyquist Stability CriterionRoot LocusCompensator DesignHardwareAutopilot Design RequirementsAcceleration AutopilotThree Loop AutopilotRoll Control
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© 1998 Paul Jackson
Day 3
Altitude ControlPitch Over AutopilotFlexible ModesGain SchedulingDiscretizationHardware NonlinearitiesSkid-to-Turn AutopilotBank-to-Turn Autopilot
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© 1998 Paul Jackson
Day 4
Airframe Design Trade StudyLinear Quadratic RegulatorMultivariable StabilityH-Infinity Control
1/9
© 1998 Paul Jackson
Aerodynamic Stability
Missile is Aerodynamically Stable at a Given Trim Condition if it Tends to Maintain its Trim Condition when Excited by External Disturbances
Consider the Previous Plots. At the Trim Condition a Positive Perturbation to α Results in a Negative Moment on the Airframe that Tends to Restore the Airframe to the Trim Condition
Conclusion: If the M vs. α Curve has a Negative (Positive) Slope at the Trim Condition, the Missile is Aerodynamically Stable (Unstable)
Aerodynamic Stability also called Static Stability
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© 1998 Paul Jackson
3D Aerodynamic Poles
3D Model has Five StatesAngle-of-Attack, Sideslip, Pitch, Yaw, Roll Rate
Two (Complex) Poles Associated with Pitch Dynamics are Called "Short Period (Weathercock)"Two (Complex) Poles Associated with Yaw Dynamics are Called "Dutch Roll"One Pole Associated with Roll Dynamics is Called "Roll Subsidence"Aerodynamic Coupling can Sometimes Obscure Relationship Between Poles and States
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© 1998 Paul Jackson
Acceleration Feedback Summary
Lead Compensation Ineffective Because Compensation Zero is Too Close or Right of Dominant Closed Loop PolesCancellation Ineffective Because of Poor Disturbance Rejection Properties
Using Complex Zeros to Pull Airframe Poles to Left (Combination of Above Strategies) Could Still Suffer from Same Problems
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© 1998 Paul Jackson
Response to Disturbance
Pitch Rate Response to Angular Acceleration Impulse Disturbance (e.g. Pitch Moment due to Change in Sideslip, Wind Gust)
q de
g/se
c Body Rate Feedback Quickly Damps Out Disturbance Inputs
0 0.2 0.4 0.6 0.8 1-40
-20
0
20
40
60
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© 1998 Paul Jackson
Flexible Mode Modeling
Flexible Mode Dynamics Modeled in Parallel to Rigid Body Dynamics for All Harmonics of Interest
RigidBody
Acc.Gyro
FlexBody
FlexBody
δ
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© 1998 Paul Jackson
Acceleration Command Following
0 2 4 6 8 10-5
0
5
10
15
20
25
30
35
Time (sec)
Acce
lera
tion
(g)
Gain Scheduled Autopilot Tracks the Command
1/15
© 1998 Paul Jackson
Delp/Dely Compensated Response
0 0.5 1-0.5
0
0.5
1
1.5
-0.3
-0.2
-0.1
0
0.1
0 0.5 1-0.5
0
0.5
1
Control Cross Coupling Compensation Effectively Eliminates Roll Transient
compensated
Nz
(g)
Ny
(g)
p (d
eg/s
ec)
in addition to pitch/yaw, alpha/beta compensation
1/16
© 1998 Paul Jackson
Acceleration Response
0 0.5 1-5
0
5
10
15
1 1.5 20
10
20
30
40
2 2.5 310
15
20
25
30
3 3.5 48
10
12
14
16
x- aft cp, o - forward cp
Nz
(g)
Acceleration Response Nearly Matches Desired ModelStable Airframe Slightly Slower
Unmarked - Desired Model
1/17
© 1998 Paul Jackson
Dynamics Model
δ
θ
Inertial Reference
cg
L = 7 ft
T = 5800 lb
J=2800 ft-lb-sec^2
θ δ=TLJ
Assumes Small Angle for TVC DeflectionNo Aerodynamic Induced Moment
Subsonic, Slender BodyAssume Fixed CG
Typically Shifts as Rocket Motor BurnsMight Have to Gain Schedule
1/18
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professionals. Our courses keep you current in the state-of-the-art technology that isessential to keep your company on the cutting edge in today’s highly competitivemarketplace. For 20 years, we have earned the trust of training departments nationwide,and have presented on-site training at the major Navy, Air Force and NASA centers, and for alarge number of contractors. Our training increases effectiveness and productivity. Learnfrom the proven best.
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