This document provides information about a 4-day professional development course on missile autopilots taught by Paul Jackson. The course covers topics such as missile equations of motion, linear systems theory, autopilot hardware, pitch autopilot design, and advanced concepts. It includes examples from real-world missile systems. Attendees will learn fundamentals of autopilot design and analysis with an emphasis on linear systems and feedback control applied to missile dynamics and aerodynamic modeling.

1. Professional Development Short Course On:
Missile Autopilots
Instructor:
Paul Jackson
ATI Course Schedule: http://www.ATIcourses.com/schedule.htm
ATI's Missile Autopilots: http://www.aticourses.com/introduction_missile_autopilots.htm
349 Berkshire Drive • Riva, Maryland 21140
888-501-2100 • 410-956-8805
Website: www.ATIcourses.com • Email: ATI@ATIcourses.com

2. Missile Autopilots
Summary
This applications-oriented course provides a
comprehensive overview of missile autopilots. The
course begins with an overview of the missile
equations of motion and aerodynamic models,
followed by a review of linear system theory
including frequency response and Bode plots, root
locus, stability criteria, and compensator design.
This introductory material is followed by detailed
discussion of modern missile autopilot design topics
including hardware and hardware modeling, November 17-20, 2008
autopilot design requirements, and autopilot design
examples. The remainder of the course focuses on Columbia, Maryland
'real world' issues such as nonlinearities, gain
scheduling, discretization, pitch-yaw-roll autopilot $1795 (8:30am - 4:00pm)
design, and other advanced concepts. Examples "Register 3 or More & Receive $10000 each
are included throughout the course. Off The Course Tuition."
Instructors
Paul Jackson is the supervisor of the
Engineering and Development “We went from theory to
Section of the Guidance and Control
Group at the Applied Physics advanced design & analysis
Laboratory (APL) and is the APL Lead techniques ... all with real world
for Standard Missile-2 Guidance and
Control. Since joining the staff of APL issues.”
in 1988, he has worked as an analyst
on missile guidance and control
systems, particularly for the US Navy Tomahawk
and Standard missiles. His early contributions came Course Outline
as a member of the APL team that was among the
first to demonstrate the application of modern robust 1. Overview of Missile Autopilots. Definitions,
control techniques such as H-Infinity Control and Types of Autopilots, Example Applications
Mu-Synthesis to the missile autopilot design 2. Equations of Motion. Coordinate Systems,
problem. Subsequent experience includes the Transformations, Euler Angles, Force Equations,
design, analysis, and simulation of missile autopilot Moment Equations, Aerodynamic Variables,
and guidance algorithms and hardware. Mr. Linearization, Aerodynamics
Jackson has presented papers at AIAA and the IEEE 3. Linear Systems. State Variables, Block
conferences and is a former member of the AIAA Diagrams, Laplace Transforms, Transfer Functions,
Guidance, Navigation and Control Technical Impulse Response, Step Response, Stability, Second
Committee. Order Systems, Frequency Response, Root Locus,
Nyquist Stability Theory
4. Feedback Control. Need for Feedback, Design
What You Will Learn Criteria, Types of Feedback, Compensator Design via
Root Locus, Compensator Design via Frequency
• The underlying physics governing missile dynamics.
Response
• Theory and applications for autopilot design and
optimization. 5. Autopilot Hardware. Actuators, Principles of the
Gyro, Gyro Modeling, Principles of Accelerometers,
• Autopilot requirements and design tradeoffs between Accelerometer Modeling
performance and robustness.
6. Pitch Autopilot Design. Time Domain
• Choosing autopilot implementation approaches. Requirements, Frequency Domain Requirements,
• Applications to real-world missile systems. Acceleration Feedback, Acceleration and Rate
• Fundamentals for autopilot design and analysis with Feedback, Pitch Over Autopilot, Three-Loop Autopilot
emphasis on linear systems. 7. Implementation Issues. Body Modes, Actuator
• Missile dynamics including aerodynamic modeling. Saturation, Integrator Windup, Gain Scheduling,
• Feedback, feedback design criteria, types of Discretization
feedback, compensator design. 8. Pitch-Yaw-Roll Autopilot Design. Classical
• Autopilot hardware modeling including actuators, Approach, Skid-to-Turn, Bank-to-Turn, Design
gyros, and accelerometers. Examples
• Pitch Autopilot Design. 9. Advanced Concepts. Multivariable Stability
• Pitch-Yaw-Roll Autopilot Design. Analysis, LQR Optimal Control, Modern Robust Control
• Advanced Design and Analysis Techniques. Design Techniques
Register online at www.ATIcourses.com or call ATI at 888.501.2100 or 410.956.8805 Vol. 94 – 31

3. www.ATIcourses.com
Boost Your Skills 349 Berkshire Drive
Riva, Maryland 21140
with On-Site Courses Telephone 1-888-501-2100 / (410) 965-8805
Tailored to Your Needs
Fax (410) 956-5785
Email: ATI@ATIcourses.com
The Applied Technology Institute specializes in training programs for technical professionals. Our courses keep you
current in the state-of-the-art technology that is essential to keep your company on the cutting edge in today’s highly
competitive marketplace. Since 1984, ATI has earned the trust of training departments nationwide, and has presented
on-site training at the major Navy, Air Force and NASA centers, and for a large number of contractors. Our training
increases effectiveness and productivity. Learn from the proven best.
For a Free On-Site Quote Visit Us At: http://www.ATIcourses.com/free_onsite_quote.asp
For Our Current Public Course Schedule Go To: http://www.ATIcourses.com/schedule.htm

4. 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.
© 1998 Paul Jackson
1/3

5. Autopilot Components
Autopilot
Mathematical System of Equations
Implemented Digital or Analog
External Command and Measurements are Inputs
Control Command is Output
Actuator
Mechanical Device that Effects a Variable Force and Moment on
Airframe
Fin, Nozzle, ...
Airframe
Missile Body Including Fixed Aerodynamic Surfaces
Experiences Aerodynamic Lift and Moment
Sensor
Mechanical Device to Sense Missile Motion
Accelerometer, Gyroscope, ...
© 1998 Paul Jackson
1/4

6. Example Applications
Acceleration Autopilot
Control Missile Acceleration Perpendicular to Airframe
Interceptors
Altitude Autopilot
Control Missile Altitude
Cruise Missiles
Terrain Following
Control Missile Clearance Relative to Terrain
Cruise Missiles
Pitchover Autopilot
Control Missile Attitude
Missile Boost Phase
Others
© 1998 Paul Jackson
1/5

7. Day 1
Equations of Motion
Linear Systems
Frequency Response
Aerodynamics
Feedback Control
© 1998 Paul Jackson
1/6

8. Day 2
Nyquist Stability Criterion
Root Locus
Compensator Design
Hardware
Autopilot Design Requirements
Acceleration Autopilot
Three Loop Autopilot
Roll Control
© 1998 Paul Jackson
1/7

9. Day 3
Altitude Control
Pitch Over Autopilot
Flexible Modes
Gain Scheduling
Discretization
Hardware Nonlinearities
Skid-to-Turn Autopilot
Bank-to-Turn Autopilot
© 1998 Paul Jackson
1/8

10. Day 4
Airframe Design Trade Study
Linear Quadratic Regulator
Multivariable Stability
H-Infinity Control
© 1998 Paul Jackson
1/9

11. 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
© 1998 Paul Jackson
1/10

12. 3D Aerodynamic Poles
3D Model has Five States
Angle-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
© 1998 Paul Jackson
1/11

13. Acceleration Feedback Summary
Lead Compensation Ineffective Because Compensation
Zero is Too Close or Right of Dominant Closed Loop Poles
Cancellation 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
© 1998 Paul Jackson
1/12

14. Response to Disturbance
Pitch Rate Response to Angular Acceleration Impulse
Disturbance (e.g. Pitch Moment due to Change in Sideslip,
Wind Gust)
60
40
Body Rate Feedback
q deg/sec
20
Quickly Damps Out
0
Disturbance Inputs
-20
-40
0 0.2 0.4 0.6 0.8 1
© 1998 Paul Jackson
1/13

15. Flexible Mode Modeling
Flexible Mode Dynamics Modeled in Parallel to Rigid Body
Dynamics for All Harmonics of Interest
Flex
Body
δ Rigid Acc.
Body Gyro
Flex
Body
© 1998 Paul Jackson
1/14

16. Acceleration Command Following
35
30
25
Acceleration (g)
20
15
10
5
0
-5
0 2 4 6 8 10
Time (sec)
Gain Scheduled Autopilot Tracks the
Command
© 1998 Paul Jackson
1/15

17. Delp/Dely Compensated Response
in addition to pitch/yaw, alpha/beta compensation
1.5 0.1
1 0
Nz (g)
Ny (g)
0.5 -0.1
0 -0.2
-0.5 -0.3
0 0.5 1
1
compensated
p (deg/sec) 0.5
Control Cross Coupling
Compensation Effectively
Eliminates Roll Transient 0
-0.5
0 0.5 1
© 1998 Paul Jackson
1/16

18. Acceleration Response
15 40
x- aft cp, o - forward cp
10 30
Nz (g)
5 Unmarked - Desired Model
20
0 10
-5 0
0 0.5 1 1 1.5 2
30 16
25 14
20 12
15 10
10 8
2 2.5 3 3 3.5 4
Acceleration Response Nearly Matches Desired Model
Stable Airframe Slightly Slower
© 1998 Paul Jackson
1/17

19. Dynamics Model
T = 5800 lb
δ L = 7 ft
cg
θ
J=2800 ft-lb-sec^2
TL
θ= δ Inertial Reference
J
Assumes Small Angle for TVC Deflection
No Aerodynamic Induced Moment
Subsonic, Slender Body
Assume Fixed CG
Typically Shifts as Rocket Motor Burns
Might Have to Gain Schedule
© 1998 Paul Jackson
1/18

20. Boost Your Skills
with On-Site Courses
Tailored to Your Needs
The Applied Technology Institute specializes in training programs for technical
professionals. Our courses keep you current in the state-of-the-art technology that is
essential to keep your company on the cutting edge in today’s highly competitive
marketplace. 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 a
large number of contractors. Our training increases effectiveness and productivity. Learn
from the proven best.
ATI’s on-site courses offer these cost-effective advantages:
• You design, control, and schedule the course.
• Since the program involves only your personnel, confidentiality is maintained. You can
freely discuss company issues and programs. Classified programs can also be arranged.
• Your employees may attend all or only the most relevant part of the course.
• Our instructors are the best in the business, averaging 25 to 35 years of practical, real-
world experience. Carefully selected for both technical expertise and teaching ability, they
provide information that is practical and ready to use immediately.
• Our on-site programs can save your facility 30% to 50%, plus additional savings by
eliminating employee travel time and expenses.
• The ATI Satisfaction Guarantee: You must be completely satisfied with our program.
We suggest you look at ATI course descriptions in this catalog and on the ATI website.
Visit and bookmark ATI’s website at http://www.ATIcourses.com for descriptions of all
of our courses in these areas:
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I suggest that you read through these course descriptions and then call me personally, Jim
Jenkins, at (410) 531-6034, and I’ll explain what we can do for you, what it will cost, and what
you can expect in results and future capabilities.
Our training helps you and your organization
remain competitive in this changing world.
Register online at www.aticourses.com or call ATI at 888.501.2100 or 410.531.6034