Abstract
A case study problem of damping oscillations of a pendulum by moving a pivot in vertical direction is presented. The motivation for solving this task comes from a broader research on designing advanced control algorithms for Unmanned Aerial Vehicles (UAVs) carrying a suspended payload. First, a nonlinear model for vertical motion of a quadcopter carrying a payload is derived and simplified to a nonlinear pendulum-like model. The main result is in deriving a nonlinear time-delay control law allowing to predefine a damping factor of the oscillations. Note that the problem at hand cannot be solved by a linear controller, as the oscillatory mode is not controllable once the model is linearised. The control law is then extended from pendulum to the quadcopter model considering an outer loop to control the horizontal motion. The theoretical results are then validated by simulations.
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