next up previous
Next: DISK RETRIEVAL MECHANISM Up: The MIT / Draper Previous: GUIDANCE

FLIGHT CONTROL

The design criterion for the flight control system was robustness to modeling errors, sensor noise, and environmental disturbances. Performance is not necessary because the design assumes that the vehicle will always remain near hover. Limited computational ability of the flight computer and a delay inherent in the position gyro measurements are the principle design constraints.

The first phase of flight control development was to model the system. To this end, a simple model of helicopter dynamics was developed, and the physical parameters of our vehicle were empirically measured. This model was numerically linearized about hover using MATLAB. We concluded that the limited computational capability of the flight computer was insufficient to implement a multivariable controller. Therefore, we assumed that the effect of dynamic coupling was negligible at hover, and adopted an un-coupled compensator architecture, consisting of four independent channels (i.e., pitch, roll, heading, and altitude). There is an open-loop feed-forward term in the tail rotor controller which is proportional to changes in the collective command.

The pitch, roll, and yaw channels each take the form of an LQG compensator. In the pitch axis, the plant is modeled as tex2html_wrap_inline331 where tex2html_wrap_inline333 is the longitudinal cyclic input and tex2html_wrap_inline335 is a white noise torque disturbance. The position and rate gyro sensors are modeled as:
displaymath337

displaymath339
where tex2html_wrap_inline341 and tex2html_wrap_inline343 are white sensor noises and w is a drift in the angular rate sensor, which is modeled as tex2html_wrap_inline347 where tex2html_wrap_inline349 is white noise. The position gyros are internally drift corrected.

In state space form, the LQG compensator is:
displaymath351

displaymath353

displaymath355

displaymath357
where tex2html_wrap_inline359, tex2html_wrap_inline361 is the state estimate, and tex2html_wrap_inline363 is the error. tex2html_wrap_inline365 was chosen according to the steady state sensor and process noise covariances. The bandwidth of the Kalman filter, approximately tex2html_wrap_inline367 Hz., was chosen to avoid the effect of a 0.4 sec. delay in the position gyro measurements. The gains were chosen as an tex2html_wrap_inline371 optimal controller, minimizing a weighted sum of angular error, angular rate, and control changes. The weights were tuned through test flights.

The compensator may be implemented, in state space form, as:
displaymath373

displaymath375
The z-transform of this continuous-time compensator runs on the flight computer at tex2html_wrap_inline271 Hz., requiring 26 multiplications and 17 additions in each channel, per iteration.

The altitude control loop uses a PID compensator to set the main rotor collective blade pitch. Altitude and vertical speed are estimated using an on-board ultrasonic sonar, and the reference altitude is commanded by the guidance subsystem. The throttle is controlled open-loop as a function of the collective command, providing approximately constant rotor RPM.


next up previous
Next: DISK RETRIEVAL MECHANISM Up: The MIT / Draper Previous: GUIDANCE

Bill Hall
Fri Jan 31 14:15:17 EST 1997