Subsystem Models

For a missile or aircraft to fly effectively, many components must work together harmoniously. Just to name the most important ones: airframe, propulsion, controls, autopilot, sensors, guidance, navigation, and, in the case of a manned aircraft, the pilot. As we build a simulation, these subsystems must be modeled mathematically or included as hardware. In a flight simulator the pilot has the privilege to represent himself.

The shape of the airframe determines the aerodynamic forces and moments, and its structure determines the mass properties and deflections under loads. For our simplified pseudo-five-DoF approach we assume that the airframe is rigid. As mentioned earlier, the moments are balanced, and the drag as a result of steady – state control deflections is included in the aerodynamic forces. We model the aerodynamics using the so-called trimmed force approach.

Propulsion can be delivered by a simple rocket, a turbojet, a ramjet, or some other exotic device. It provides the force that overcomes drag and gravity and accelerates the vehicle. We simplify its features by employing tables for thrust and specific fuel consumption and introduce first-order lags for delays in the system.

In pseudo-five-DoF simulations, because of the treatment of the aerodynamics, controls are not modeled explicitly. What a simplification! Actuators need not be included, and you can forget about hinge moments. However, we give up the opportunity to study the dynamics of the controls and the effect of saturation of the control rates and deflections.

The stability and controllability of the vehicle are governed by the autopilot. The outer-loop feedback variable categorizes the type of autopilot. We distinguish between rate, acceleration, altitude, bank, flight path, heading, and incidence angle hold autopilots. Make sure, however, that for any type of autopilot, the incidence angle and its rate are computed and provided for the kinematic calculations (see Sec. 9.1). The autopilots are simplified models of the control-loop dynamics, and their responses simulate the vehicle’s attitude dynamics.

Sensors measure the states of the vehicle wrt other frames, like inertial, Earth, body, or target frames. They may be part of the air data system, inertial navigation system, autopilot, propulsion, landing, or targeting systems. Those with high band­width, like gyros and accelerometers, are modeled by gains without dynamics, and their output is corrupted by noise. Gimbaled homing seekers, on the other hand, exhibit transients near the autopilot bandwidth and should, therefore, be modeled dynamically, although for simple applications we also use kinematic seekers.

The smarts of a missile reside in its guidance laws. Given the state of the missile relative to the target, it sends the steering commands to the autopilot for intercept. We distinguish between pursuit, proportional, line, parabolic, and arc guidance. Guidance occupies the outermost control loop of the vehicle. In pseudo – five-DoF simulations, with the autopilot providing the vehicle response, this loop may be modeled with sufficient detail to be representative of six-DoF performance. Experience has shown that you could design the guidance loop initially in five-DoF and later include it in your full six-DoF simulation without modifications.

Finally, the navigation subsystem furnishes the vehicle with its position and velocity relative to the inertial or geographic frames. The core is the IMU with its accelerometers and gyros. Once their measurements are converted into navigation information, it becomes the INS. Errors in the measurements and computations corrupt the navigation solution. Therefore, navigation aids are employed to update the INS. Loran, Tacan, GPS or just overflight of a landmark can provide the external stimuli. Uncertainties are modeled by the INS error equations and by the noisy updates and filter dynamics.