Scaling Effects on Controllers for Multirotors

Multirotors are complex non-linear systems with controllers containing multiple control loops. The control gains can be difficult to tune, and these gains in turn can be substantially different for multirotors of different sizes. This research develops a method to adapt the control gains tuned for a multirotor of one size to another multirotor of a different size, using the Bucking-ham Pi Theorem. The theory was first validated by considering a multirotor and its theoretically scaled counterpart such that the two multirotors are precisely similar-i.e. the second quadrotor is an exact scaled version of the first. The results showed that the relationship between a multirotor's physical parameters and its control gains was accurately captured by the Buckingham Pi Theorem. Two more realistic multirotors were then studied to determine an appropriate method to estimate the control gains for these dissimilar systems of different sizes. The results show that the proposed approach provides a simple yet rigorous approach to map the control gains between two multirotors of different sizes.