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The solution of a case study problem of suspended payload sway damping by moving a pivot base in vertical direction is presented. Unlike for the classical problem of anti-sway control for moving the base in the horizontal direction, implemented e.g. in cranes, a direct solution by using control feedback theory for linear systems is not possible. Once the model is linearized, it becomes uncontrollable. Thus, a derivation of a nonlinear controller is needed to solve the task. In this context, two solutions are proposed. The first solution is based on imposing harmonic motion of the base with double frequency of the payload natural frequency. Synchronization of the base and the payload deflection angle is done either by proportional time-delay controller or by proportional-derivative delay free controller. Secondly, the Lyapunov's second method is directly applied to derive a nonlinear controller. For both cases, balancing the dissipated energy, rules for determining equivalent damping are explicitly derived. After discussing and solving the corresponding implementation aspects, both simulation and experimental validations are performed. The experimental validation is performed on a simplified problem, where only horizontal motion is possible. The simulation based validation is performed on a nonlinear two dimensional model of a quadcopter carrying a suspended payload.

A control design and numerical study is presented for the problem of maneuvering a quadcopter with suspended load. An inverse shaper with a distributed time delay is applied to the feedback path in order to pre-compensate the oscillatory mode of the two-body system. As the first step, the mode to be targeted by the inverse shaper is determined, which is neither the oscillatory mode of the overall system dynamics, nor the oscillatory mode of the suspended load. Next, the established cascade control scheme for UAVs with slave PD pitch angle controller and master PID velocity controller is adopted and supplemented by the inverse shaper tuned to the isolated flexible mode. The numerical and simulation based analysis reveals the key design aspects and dynamics features — due to including the inverse shaper with time delays, the closed loop system becomes infinite dimensional. As the main result, the positive effects of including the inverse shaper in the loop feedback are demonstrated. First of all, the oscillatory mode is well compensated when excited by both the set-point and disturbance changes. Besides, it is shown that the mode compensation is preserved even when reaching the saturation limits at the control actions.

A generally applicable spectral design to realize non-collocated vibration suppression performed primarily by a delayed resonator is presented. The vibration suppression is achieved by direct assignment of imaginary axis zeros of the receptance, i.e. the transfer function between the periodic disturbance force and the target's displacement. In order to increase the stability margin and to widen the range of frequencies which can be suppressed, the non-collocated vibration absorption by a delayed resonator is supplemented by a stabilizing controller tuned by spectral optimization. A unifying aspect of the resonator and the controller is that both use time-delayed output feedback where both the gains and delays are used as controller parameters. Another important aspect of the proposed method is that it can be applied to a system of general structure, where possibly paths exist between the entry point of the disturbance force and the non-collocated absorber that by-pass the suppression target, thereby precluding the existence of a resonating substructure. The proposed method has been experimentally validated on a multi-degree of freedom experimental setup actuated by voicecoils.