System Modeling Coursework
P.R. VENKATESWARAN
Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal
Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152
Fax: 0820 2571071
Email: [email protected], [email protected]
Web address: http://www.esnips.com/web/SystemModelingClassNotes
WARNING!
• I claim no originality in all these notes. These are the
compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation.
• For best results, it is always suggested you read the
Definition for a missile
• A missile can be defined as an aerospace vehicle
with varying guidance capabilities that is self propelled through space for the purpose of inflicting damage on a designated target.
• Fabricated for air-to-air, surface to air and surface to
Components of a missile
• Propulsion system
• Warhead section
• Guidance system
• Control surfaces
Choice is between a guided and a non guided missile!
Components of a guided missile
• Airframe
• Guidance
• Motor (or propulsion)
Airframe
• The type and size depends on
– Guidance characteristics
– Motor size
Guidance
• Guidance is the means by which a missile steers or is
steered to a target.
• The type of guidance is also dependent on the
motor, warhead and threat.
• More specifically, the type of guidance chosen is
dependent on the overall weapon system in which the missile will be used, on the type of threat the missile will be used against, the characteristics of the threat target, and other factors.
Motor
• The motor characteristics depends on
– Guidance requirements
– The threat
Warhead
• Dependent on the threat and type of guidance
• The common procedure is to size the guidance
requirements (e.g. accuracy, response time, range capability) from the threat, select an airframe that can deliver the required aerodynamic performance, size the motor based on threat and airframe considerations and size the warhead from guidance and airframe considerations.
Basic factors affecting the missile design
• Threat
• Operating environment
• Cost
• State of the art
– Since the last three is normally known, the missile design centers on meeting the threat in the environment with the state of the art, at minimum cost.
Factors affecting motor type selection
• Aerodynamic heating due to the incremental missile
velocity
• Aerodynamic drag, which decreases missile velocity
• Maximum altitude at which the missile must
perform
Types of missile motors: All Boost
• It typically will make the missile accelerate rapidly,
causing high peak velocities. However, this
causes high missile drag, high aerodynamic heating, and short time of flight, for a given range
Types of Missile Motors: All Sustain
• It has low acceleration, resultingin lower aerodynamic drag and longer time of flight, for a given range.
• It can be used in a look up engagement, and to provide
sufficient velocity for maneuvering at high altitude.
• The motor is suitable for head on engagements, or in look-up
Types of missile motors: Boost Sustain
• The boost sustain motor represents an attempt to combine the best features of the boost and all-sustain designs.
Missile speed
• Guided tactical missiles are sometimes referred to according to their airspeed relative to the speed of sound and their type of propulsion system
• The highest rate of airspeed that can be reached safely and still ensure correct operation is considered as that missile’s classification. The common classification are
– Subsonic (airspeeds less than mach 1)
Skid to turn (STT) missile
• It is the commonly used in analysis and design of
surface to air and air to air weapon systems
• The reason is the inertial cross coupling between
roll, pitch and yaw is negligible.
• Both aerodynamics and rigid body dynamics are
Response of the system
• The pitch/yaw plane rotational responses behave
like a spring mass damper system. It is given as:
• The equation can also be written as:
Modeling drag and lift
• For the purposes of control design, drag can be
modeled by parabolic drag form
• If Lift is considered as control, it is subjected to the
constraint where W is the weight and
gm(v) represents the load factor limit, which may
arise due to a structural limit, control surface actuator, or autopilot stability considerations. In general, lift is a function of missile speed.
Load factor expression
• The dynamics for the angle of attack (AOA), α, as well as dα/dt, load factor nz and pitch rate are commonly modeled after the short period approximations of longitudinal motion.
Dynamics of load factor in pitch plane
• The load factor and angle of attack transfer
functions are identical in form.
• Specifically, the dynamics for the load factor in the
pitch plane, nz, can be modeled by the following
Dynamics of load factor in pitch plane
• The parameters ζ,ω and Tα can be found by linear
analysis of the entire closed loop system.
• This transfer function is valid provided that the
laod factor being modeled is located at the centre
of pressure, that is , the point ahead of the centre of gravity where the effect of pitch acceleration and horizontal tail force cancel.
The Missile Guidance system model
• Guidance is the means by which a missile steers, or
is steered, to a target.
• A guided missile is guided according to a certain
guidance law.
• The inputs are target location and missile to target
separation.
General Problems of Guidance System Design
1. Help to maximize the single shot kill probability (SSKP) by minimizing the miss distance
2. Sources of miss distance
• Initial heading error
• Acceleration bias
• Gyro drifts (if gyros are used in seeker stabilisation)
• Glint (scintillation noise)
General Problems of Guidance System Design
2. Preserve stability of the parasitic attitude loop
3. Filtering
• Limit power consumption and saturation of the actuators
• Prevent noise from excessive hitting of dynamic range limits, such as auto pilot g limits
Functions of the missile seeker subsystem
1. Provide the measurements of target motion required to mechanise the guidance law.
2. Track the target with the antenna or other energy receiving device (eg. Radar, infrared, laser or optical)
3. Track the target continuously after acquisition
4. Measure the LOS (Line of sight) angular rate dλ/dt.
5. Stabilise the seeker against a missile pitching rate dθm/dt (also, yawing rate) that may be much larger than the LOS rate dλ/dt to be measured.
References
• Missile Guidance and Control Systems, George M.
