Active vibration control of a curved sandwich beam using a nonlinear PPF algorithm

Nonlinear behaviour resulting from large-amplitude vibrations is often categorized as softening or hardening, according to the direction of the shift in the natural frequency. While nonlinear hardening systems have been controlled in the past, often using positive position feedback (PPF) and both linear and nonlinear algorithms, softening systems have often been overlooked. In this experimental study, a curved sandwich beam with clamped boundary conditions when subject to large external forcing was subjected to various active vibration controllers based on linear and nonlinear PPF algorithms. The curved beam is a softening system presenting both quadratic and cubic stiffness terms. Piezoelectric patches were used as controller transducers. Both linear and nonlinear controller types were tested, with nonlinear controllers including both quadratic and cubic gain terms. Furthermore, single-input single-output (SISO) and multi-input multi-output (MIMO) architectures were both tested, with SISO controllers including only a single actuator and sensor pair and MIMO controllers involving two actuators and two sensors. While increasing the amplitude of the nonlinear terms in the not-optimized controller was found to significantly improve vibration attenuation, the optimized controller showed a smaller improvement following the introduction of nonlinear terms in its algorithm.