Design of a Gain-Scheduled LQR Controller for Landing of a Reusable Launch Vehicle

This study develops a gain-scheduled Linear Quadratic Regulator (LQR) for the final landing burn of a reusable booster. Using thrust vector control (TVC) and thrust modulation as the primary braking and adjustment force, the vehicle booster is made to land with minimal velocity at the correct coordinates. The Falcon-9-inspired descent trajectory is used as a reference point for the landing. The nonlinear six-degree-of-freedom system is linearized at selected operating points along the reference trajectory, which includes different initial velocity, vehicle wet mass, and starting altitude. At each point, a controllable ten-state reduced model is used to compute a local LQR gain, and altitude interpolation is used to allow the controller to adjust the gain, reference state, and feedforward command. The controller is tested in eight nonlinear cases, including nominal descent, initial lateral and altitude offsets, a sustained thrust command disturbance, gimbal bias disturbance, and combined actuator–thrust and actuator–thrust–lateral disturbances. The vehicle makes soft landings for all the cases with vertical velocities between −0.713 m/s and −0.844 m/s, and a maximum final lateral error of 1.257 m, a maximum tilt of 5.22 deg, and gimbal demand within the imposed ±8 deg limit. In the lateral offset case, an initial 22.36 m horizontal error is reduced to about 0.005 m. A 2000-case Monte Carlo study of initial-state and mass dispersions gave a 100% pass rate, with touchdown velocities from −0.783 m/s to −0.654 m/s and a maximum final lateral error of 0.250 m. Within the assumptions of the present simulation model, the results show that LQR can be deployed as a practical baseline controller for reusable-booster landing burn studies.