Case 02 / Flight dynamics
Aircraft trim and linearization
Find a steady-flight operating point, derive a local linear model and compare its response with the nonlinear aircraft simulation.
MATLAB trim solution · matched linear / nonlinear responsesWhat does a steady flight condition look like, and how accurately does a linear model describe nearby motion?
I solved for steady, level flight in a nonlinear aircraft model, calculated numerical state and input Jacobians, and compared linear and nonlinear responses to identical elevator and aileron pulses. Small and larger inputs show how the approximation changes as the aircraft moves away from the trim condition.
Method and workflow
- 01
Choose a flight condition
Set 120 m/s and 3,000 m altitude, with body velocities and attitude consistent with level flight.
- 02
Solve the equilibrium
Search elevator, throttle and pitch until the longitudinal acceleration and pitch-acceleration residuals approach zero.
- 03
Build A and B
Use central finite differences about the same equilibrium. Separate longitudinal and lateral modes.
- 04
Check the approximation
Apply matched control pulses and compare nonlinear and linear motion, including where the local approximation starts to diverge.
Trim first. Then perturb.
Calculated about this trim point. The pole locations describe the local model.
Calculated about this trim point. The pole locations describe the local model.
Dynamics residual norm: 1.09e-11 for the trim equations. This is a numerical equilibrium check, not a measure of real-aircraft model accuracy.
Same run. Every view.
Related flight-control analysis
Model assumptions and scope
- The analysis uses a representative aircraft parameter set. The displayed geometry illustrates the recorded motion.
- The angle-of-attack-rate contribution is held at zero in both models.
- The comparison uses open-loop control pulses around a single trimmed operating point.
Potential extensions
Repeat the comparison over a speed/altitude grid, then build and verify gain-scheduled control loops.
Let’s work through it.
Robotics, simulation and control consultation across Canada, with remote support available internationally. Share your system and the result you need.