Optimal Collocated and Multivariable Hybrid Active-Passive Vibration Control Design

Abstract

Hybrid control measures are optimized for collocated and multivariable attenuation of vibratory energy in a typical aircraft panel. Design techniques first optimize collocated hybrid controllers combining active and passive technology on the same footprint. These techniques are then extended to multivariable hybrid controllers containing at least two pairs of actuators and sensors in addition to passive damping. An optimization routine based on an energy-balancing cost metric selects active and passive control elements to minimize both the broadband vibratory energy of the structure and the weight, volume, and energy use of the control system. Further, optimization of inherent energy exchanges within the hybrid controller allows more aggressive, targeted, active control with minimal passive damping treatment. Optimization reveals idealized placements, sizes, and orientations of active and passive control elements. Active piezoceramic patches partner with passive constrained-layer damping treatment to extend and demonstrate the potential of optimal hybrid vibration control.

Optimization of active–passive damping treatments using piezoelectric and viscoelastic materials

“…The time derivatives of the dissipative coordinates qdr i are not included in the state vector since these variables are massless. This leads to ẋ = Ax + Bu + p y = Cx (10) where the perturbation vector p is the state distribution of the mechanical loads F m , B is the control distribution vector, corresponding to the piezoelectric loads per unit control voltage F * e induced by the piezoelectric actuators, the control input vector u is composed by the control voltages applied to each piezoelectric actuator, and the output vector y is composed of the measured quantities, written in terms of the state vector x through the output matrix C. The system dynamics is determined by the square matrix A. The state space system matrices and vectors are…”

“…By neglecting the contributions of viscoelastic relaxation modes and some elastic modes, related to eigenfrequencies out of the frequency range considered, a complex-based modal reduction is applied to the state space system (10). This is done through a modal decomposition, such that the right and left eigenvectors of A are evaluated by AT r = T r and A T T l = T l with T T l T r = I.…”

“…Ro and Baz [9] used a modal strain energy approach to search for the optimal location, size, thickness and viscoelastic material shear modulus of several ACL treatments bonded on a host plate. More recently, Kemp and Clark [10] have proposed an optimization routine based on the independent selection of active and passive elements to minimize vibratory energy, weight and control energy, and Hau et al [11] presented the damping maximization combined with weight and control voltage minimization for a rotating flexible arm with an ACL treatment.…”

Switched Stiffness Vibration Controllers for Fluidic Flexible Matrix Composites

“…Winthrop et al [9] describe the shortcomings of passive vibration control systems, including the inability to achieve isolation at very low frequencies, a trade-off between resonant and high-frequency attenuation, and an inability to adapt to variations in parameters and excitation frequencies. Hybrid vibration control utilizes both active and passive methods to reduce the energy consumption while improving performance [5,10].…”

“…The accuracy of trajectory tracking and set-point regulation is often limited by structural vibration. Vibration control is categorized as: active [1], passive [2], semi-active [3,4] or hybrid [5], based on the power consumption of the control system.Active vibration control systems normally can achieve …”