Aerospace Blockset

Modeling a Classical Three-Loop Autopilot

The missile autopilot controls the acceleration normal to the missile body. In this case study, the autopilot structure is a three-loop design using measurements from an accelerometer placed ahead of the center of gravity and a rate gyro to provide additional damping. The figure below shows the classical configuration of an autopilot. The controller gains are scheduled on incidence and Mach number and they are tuned for robust performance at an altitude of 3050 meters (10000 feet).

Designing an autopilot entails the following:

• Trimming and Linearizing an Airframe Model

• Models of the airframe pitch dynamics are derived for a number of trimmed flight conditions.

• Autopilot Design

• Provides overview of the autopilot design process.

Trimming and Linearizing an Airframe Model

To design the autopilot using classical design techniques requires that linear models of the airframe pitch dynamics be derived for a number of trimmed flight conditions. MATLAB can determine the trim conditions and derive linear state-space models directly from the nonlinear Simulink model. This saves time and helps to validate the model. The functions provided by the Control System Toolbox allow the designer to visualize the behavior of the airframe open loop frequency (or time) responses.

The Airframe trim demo shows how to trim and linearize an airframe model. To run this demo, enter the following in the MATLAB Command Window:

• aeroblk_lin_aero
  
  

The output from this demo is a Bode diagram in the Control System Toolbox viewer.

Autopilot Design

Autopilot design can begin after the missile airframe has been linearized at a number of flight conditions. Typically, autopilot designs are carried out on a number of linear airframe models derived at varying flight conditions across the expected flight envelope. To implement the autopilot in the nonlinear model involves storing the autopilot gains in two-dimensional lookup tables, and incorporating an anti-windup gain to prevent integrator windup when the fin demands exceed the maximum limits. Testing the autopilot in the nonlinear Simulink model is the best way to demonstrate satisfactory performance in the presence of nonlinearities, such as actuator fin and rate limits and dynamically changing gains.

The Autopilot subsystem is an implementation of the classical three-loop autopilot design within Simulink.

Modeling Airframe Dynamics

Modeling the Homing Guidance Loop