Mars Sky Crane Controls

Problem

Control the height and pitch of a simplified Mars sky crane while tracking the assigned height profile and rejecting disturbances.

Constraint

The height controller had to reach a 10 m step with no steady-state error, a rise time under 15 seconds, and no overshoot. The pitch loop also had low-frequency tracking-error, high-frequency noise-attenuation, and closed-loop stability targets.

What I did

• Converted the supplied nonlinear equations into a 12-state model, linearized it about hover, and assembled the state-space matrices and transfer functions in MATLAB.
• Used root loci to study how the PID gains moved the closed-loop poles, then tuned the height controller to KP = 1000, KI = 1, and KD = 12000.
• Designed a loop-shaped pitch controller and checked its gain, phase, and frequency response with a Bode plot.
• Completed the supplied linear Simulink model, adapted it to the supplied nonlinear dynamics function, and scripted 300-second simulations with tracking and control-input plots.
• Removed the uncontrollable yaw states for the bonus analysis, placed ten closed-loop poles from -10 to -1, rebuilt the gain matrix for the full state vector, and applied disturbances.

Result

• The reported height step response reached 10 m in under 15 seconds with zero steady-state error and virtually no overshoot.
• With the pole-placement regulator and added disturbances, the modeled position states stayed bounded near zero during the 300-second run.