A general methodology has been developed for the design of a robust control law for a family of lightly damped second order problems. In this research effort, the passivity approach has been extended to systems having non-collocated input/output pairs by introducing an observer that incorporates the nominal dynamical model of the plant. The developed passive observer-based control law emulates numerous dynamic vibration absorbers which are tuned to a targeted frequency using classical methods and the tuning ratios are time-invariant. However, the uniqueness of this approach is that the damping parameters of the emulated absorbers are continuously varied by means of a fuzzy logic control algorithm to provide near minimum-time suppression of vibration. The developed approach is applied to both several benchmarks in the field of structural dynamics as well as experiments using piezo-ceramic sensors and actuators. Results show that this methodology provides stability and performance robustness on the one hand as well as requiring relatively low amount of actuation authority for desired nominal plant closeloop behavior.
The present study deals with an AFCA (Adaptive Fuzzy Control Algorithm) for an Euler-Bemoulli approximation of a two-dimensional version of a cantilever beam-like orthogonal tetrahedral space truss. Transient disturbances, modeled as a unit impulse, excite all the modes of the beam. The resulting transverse displacement at the free end of the beam and its corresponding rate are observed by sensors placed there, and active control of the beam is provided by a collocated force actuator.
A design methodology, based on fuzzy logic which assumes no a priori knowledge of plant dynamics, for the closed-loop control algorithm results in relatively quick settling times, low overshoots and dying out of vibration within a few seconds. The control algorithm is enhanced and made much faster by eliminating the need of repeatedly solving the set of differential equations of motion of an emulated dynamic vibration absorber. When the control force is turned off after a mere 15 seconds, almost all the vibrational energy is dissipated as the beam returns to its undisturbed state throughout its length. In addition, the performance of the AFCA is insensitive to varying initial conditions. To examine the robustness of the control system to changes in the temporal dynamics of the cantilever beam, the transient disturbance response to a considerably perturbed plant is simulated. The Young's modulus of the beam was raised as well as lowered by 60%, substantially perturbing the natural frequencies of vibration compared to the nominal plant. The AFCA provided similar settling times and rates of vibrational energy dissipation, satisfying the aim of plant model independence.
The control of exible structures employing the passivity approach has been extended to systems having noncollocated input/output pairs by introducing an observer that incorporates the nominal dynamical model of the plant. The passive observer-based control is applied to the American Control Conference benchmark problem, whereby, the control force emulates a dynamic vibration absorber attached to a virtual wall with passive control elements (spring, mass, and dashpot). The springs and mass elements of the controller are constant, whereas the damping coef cients are selected as time dependent in an attempt to choose continuously the most appropriate amount of damping in compliance with the design goals. A novel approach is introduced, whereby the passive observer-based control law is modi ed by varying the damping coef cient of the virtual dashpot by means of an adaptive fuzzy logic algorithm. This modi ed system exhibits quick settling times and desirable performance characteristics. Results from the statistical robustness analysis for the developed controller are compared to 10 other (linear) solutionsof the benchmarkproblem. The comparisonis based onrobust stability, robust performance (settling time), and control effort. The results obtained by the adaptive fuzzy logic algorithm are superior to those obtained by all other methods, and, consequently, further application of the fuzzy algorithm is advocated.
The present investigation deals with the application of an Adaptive Fuzzy Control Algorithm for active vibration control of an experimental flexible beam. The two-dimensional model of the experimental cantilever beam, given by an orthogonal tetrahedral space truss, represents a slender cantilever aluminum (7075-T6) beam of rectangular cross-section (1145 × 60 × 1.95 mm3). A variety of transient disturbances are introduced to excite the first four modes of the beam. The resulting transverse displacements are observed by a single sheet (50 × 50 mm2) of piezoceramic material placed at the clamped end of the beam. Active control of the beam is provided by one, two or three identical sheets of piezoceramic material collocated with the sensor. The control moments applied by the piezoceramic actuator are made to emulate the behavior of a discrete dynamic vibration absorber. The virtual absorber is tuned to the fundamental frequency using classical methods and the tuning ratios are time-invariant. However, the uniqueness of this approach is that the damping parameters of the emulated absorber are continuously varied by means of a fuzzy logic control algorithm to provide near minimum-time suppression of vibration. It is demonstrated that application of this methodology allows for its real-time implementation and provides relatively quick settling times in the closed-loop.
In this study a general approach is introduced for the design of a robust control law for suppression of structure borne vibration. This control law is based on a passive design in the form of dynamic vibration absorbers. Passive absorbers minimize vibration at a speci c frequency, but their performance is improved by introducing adaptive tuning of the absorber. An adaptive dynamic vibration absorber is tuned to the forcing frequency, using classical methods. The tuning ratio is time varying and adapts itself to variations in the forcing frequency. However, the uniqueness of the approach in this study is that the damping parameter of the absorber is continuously varied by means of a fuzzy-logic control algorithm to provide a lower sound pressure level. The inputs of the fuzzy control law are the displacement and velocity of the main structure. The effectiveness of the control algorithm for active vibration control is demonstrated using MATLAB® simulations of a single-degree-of-freedom plant. This methodology provides superior performance in the presence of signi cant mistuning compared to a more conventional approach.