| Aerospace Blockset | |
Modeling Airframe Dynamics
The model of the missile airframe used in this demonstration has been presented in a number of published papers (References [1], [2], and [3]) on the use of advanced control methods applied to missile autopilot design. 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 ranging between ±20 degrees.
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. The model can easily be created in the Simulink environment using the Aerospace Blockset.
The model of the missile airframe consists of two main components:
To view the missile airframe model, enter the following in the MATLAB Command Window:
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 the troposphere region and the other set of equations models the lower stratosphere region. The troposphere region lies between sea level and 11000 meters (36089 feet). It is assumed that there is 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). It is assumed 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.
is the absolute temperature at mean sea level in degrees Kelvin.
is the air density at mean sea level in kg/m3.
is the static pressure at mean sea level in N/m2.
is the absolute temperature at altitude, h, in degrees Kelvin.
is the air density at altitude h in kg/m3.
is the static pressure at altitude h in N/m2.
is the speed of sound at altitude h in m/s2.
is the lapse rate in degrees Kelvin/m.
is the characteristic gas constant J/kg-degrees Kelvin.
is the 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.
The following are the three-degrees-of-freedom body axis equations of motion, which are defined in the Equations of Motion (Body Axes) block:
The following are the aerodynamic forces and moments equations, which are defined in the Aerodynamics subsystem:
The following are the stability axes variables, which are calculated in the Incidence & Airspeed block:
is the body rotation rate in rad/s.
is the acceleration due to gravity in m/s2.
is the moment of inertia about the y axis in Kg-m2.
is the acceleration in the Z body axis in m/s2.
is the change in body rotation rate in rad/s2.
is the thrust in the X body axis in N.
is the coefficient of aerodynamic force in the X axis.
is the coefficient of aerodynamic force in the Z axis.
is the coefficient of aerodynamic moment about the Y axis.
is the reference length in meters.
is the aerodynamic force in the X body axis in N.
is the aerodynamic force in the Z body axis in N.
is the aerodynamic moment along the Y body axis.
is the dynamic pressure in Pa.
is the velocity in the X body axis in m/s.
is the velocity in the Z body axis in m/s
| | Missile Guidance System Model | Modeling a Classical Three-Loop Autopilot | |
is the altitude in m.
is the specific heat ratio. 
is the attitude in radians.
is the missile mass in Kg.
is the air density in Kg/m3.
is the reference area in m2.
is the fin angle in radians.
is the airspeed in m/s.
is the incidence in radians.