Aerospace Blockset

Modeling Airframe Dynamics

The model of the missile airframe in this demo uses advanced control methods applied to missile autopilot design [1], [2], [3]. The model represents a tail-controlled missile traveling between Mach 2 and Mach 4, at altitudes ranging between 3050 meters (10000 feet) and 18290 meters (60000 feet), and with typical angles of attack in the range of ±20 degrees.

Missile Airframe Model

The core element of the model is a nonlinear representation of the rigid body dynamics of the airframe. The aerodynamic forces and moments acting on the missile body are generated from coefficients that are nonlinear functions of both incidence and Mach number. You can model these dynamics easily in the Simulink environment using the Aerospace Blockset.

The model of the missile airframe consists of two main components:

• ISA Atmosphere Model Block calculates the change in atmospheric conditions with changing altitude.
• Aerodynamics & Equations of Motion Subsystem calculates the magnitude of the forces and moments acting on the missile body and integrates the equations of motion.

To view the missile airframe model, enter the following in the MATLAB Command Window:

• aeroblk_guidance_airframe
  
  
  

ISA Atmosphere Model Block

The ISA Atmosphere Model block is an approximation of the International Standard Atmosphere (ISA). This block consists of two sets of equations. One set of equations models is used for the troposphere region, and the other set of equations models is used for the lower stratosphere region. The troposphere region lies between sea level and 11000 meters (36089 feet). The ISA model assumes a linear temperature drop with increasing altitude in the troposphere region. The lower stratosphere region ranges between 11000 meters (36089 feet) and 20000 meters (65617 feet). The ISA models the stratosphere by assuming that the temperature remains constant in the lower stratosphere region. The figure below displays how the speed of sound and the air density vary with altitude.

The following equations define the troposphere:

The following equations define the lower stratosphere:

The symbols are defined as follows.

T0	Absolute temperature at mean sea level in degrees Kelvin
	Air density at mean sea level in kg/m3
	Static pressure at mean sea level in N/m2
	Altitude in m
	Absolute temperature at altitude h in degrees Kelvin
	Air density at altitude h in kg/m3
	Static pressure at altitude h in N/m2
	Speed of sound at altitude h in m/s2
	Lapse rate in degrees Kelvin/m
	Characteristic gas constant J/kg-degrees Kelvin
	Specific heat ratio
	Acceleration due to gravity in m/s2

You can look under the mask of the ISA Atmosphere Model block to see how these equations are implemented in the model.

Aerodynamics & Equations of Motion Subsystem

The Aerodynamics & Equations of Motion subsystem generates the forces and moments applied to the missile in the body axes and integrates the equations of motion that define the linear and angular motion of the airframe. The aerodynamic coefficients are stored in data sets, and, during the simulation, the value at the current operating condition is determined by interpolation using the Interpolation (n-D) using PreLook-Up block.

These are the three-degrees-of-freedom body axis equations of motion, which are defined in the Equations of Motion (Body Axes) block:

These are the aerodynamic forces and moments equations, which are defined in the Aerodynamics subsystem:

These are the stability axes variables, which are calculated in the Incidence & Airspeed block:

The symbols are defined as follows.

	Attitude in radians
	Body rotation rate in rad/s
	Missile mass in kg
	Acceleration due to gravity in m/s2
	Moment of inertia about the y axis in kg-m2
	Acceleration in the Z body axis in m/s2
	Change in body rotation rate in rad/s2
	Thrust in the X body axis in N
	Air density in kg/m3
	Reference area in m2
	Coefficient of aerodynamic force in the X axis
	Coefficient of aerodynamic force in the Z axis
	Coefficient of aerodynamic moment about the Y axis
	Reference length in meters
	Fin angle in radians
	Aerodynamic force in the X body axis in N
	Aerodynamic force in the Z body axis in N
	Aerodynamic moment along the Y body axis
	Dynamic pressure in Pa
	Airspeed in m/s
	Incidence in radians
	Velocity in the X body axis in m/s
	Velocity in the Z body axis in m/s

Missile Guidance System Model

Modeling a Classical Three-Loop Autopilot