  A fail-safe algorithm in case of motor failure was developed, simulated, and
tested. For practical fail-safe flight, the quadcopter may fly with only three
or two opposing propellers. Altitude for two-propeller architecture was
maintained by a PID controller that is independent from the inner and outer
controllers. A PID controller on propeller force deviations from equilibrium
was augmented to the inner controller of the three-propeller architecture. Both
architectures used LQR for the inner attitude controller and a damped second
order outer controller that zeroes the error along the horizontal coordinates.
The restrictiveness, stability, robustness, and symmetry of these architectures
were investigated with respect to their output limits, initial conditions, and
controller frequencies. Although the three-propeller architecture allows for
distribution of propeller forces, the two-propeller architecture is more
efficient, robust, and stable. The two-propeller architecture is also robust to
model uncertainties. It was shown that higher yaw rate leads to greater
stability when operating in fail-safe mode.
