ATI Professional Development Technical Training Short Course on Missile Autopilots

transcript

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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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.

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, ...

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

Equations of MotionLinear SystemsFrequency ResponseAerodynamicsFeedback Control

Nyquist Stability CriterionRoot LocusCompensator DesignHardwareAutopilot Design RequirementsAcceleration AutopilotThree Loop AutopilotRoll Control

Altitude ControlPitch Over AutopilotFlexible ModesGain SchedulingDiscretizationHardware NonlinearitiesSkid-to-Turn AutopilotBank-to-Turn Autopilot

Airframe Design Trade StudyLinear Quadratic RegulatorMultivariable StabilityH-Infinity Control

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

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

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

Response to Disturbance

Pitch Rate Response to Angular Acceleration Impulse Disturbance (e.g. Pitch Moment due to Change in Sideslip, Wind Gust)

c Body Rate Feedback Quickly Damps Out Disturbance Inputs

0 0.2 0.4 0.6 0.8 1-40

Flexible Mode Modeling

Flexible Mode Dynamics Modeled in Parallel to Rigid Body Dynamics for All Harmonics of Interest

RigidBody

Acc.Gyro

FlexBody

Acceleration Command Following

0 2 4 6 8 10-5

Time (sec)

Gain Scheduled Autopilot Tracks the Command

Delp/Dely Compensated Response

0 0.5 1-0.5

Control Cross Coupling Compensation Effectively Eliminates Roll Transient

compensated

in addition to pitch/yaw, alpha/beta compensation

Acceleration Response

0 0.5 1-5

1 1.5 20

2 2.5 310

3 3.5 48

x- aft cp, o - forward cp

Acceleration Response Nearly Matches Desired ModelStable Airframe Slightly Slower

Unmarked - Desired Model

Dynamics Model

Inertial Reference

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

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