Browsing by Author "Nayfeh, Nader Ali"
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- Adaptation of Delayed Position Feedback to the Reduction of Sway of Container CranesNayfeh, Nader Ali (Virginia Tech, 2002-12-04)Cranes are increasingly used in transportation and construction. increasing demand and faster requirements necessitate better and more efficient controllers to guarantee fast turn-around time and to meet safety requirements. Container cranes are used extensively in ship-to-port and port-to-ship transfer operations. In this work, we will extend the recently developed delayed position feedback controller to container cranes. In contrast with traditional work, which models a crane as a simple pendulum consisting of a hoisting cable and a lumped mass at its end, we have modeled the crane as a four-bar mechanism. The actual configuration of the hoisting mechanism is significantly different from a simple pendulum. It consists typically of a set of four hoisting cables attached to four different points on the trolley and to four points on a spreader bar. The spreader bar is used to lift the containers. Therefore, the dynamics of hoisting assemblies of large container cranes are different from that of a simple pendulum. We found that a controller which treats the system as a four-bar mechanism has an improved response. We developed a controller to meet the following requirements: traverse an 80-ton payload 50 m in 21.5 s, including raising the payload 15 m at the beginning and lowering the payload 15 m at the end of motion, while reducing the sway to 50 mm within 5.0 s at the end of the transfer maneuver. The performance of the controller has been demonstrated theoretically using numerical simulation. Moreover, the performance of the controller has been demonstrated experimentally using a 1/10th scale model. For the 1/10th scale model, the requirements translate into: traverse an 80 kg payload 5 m in 6.8 s, including raising 1.5 m at the beginning and lowering 1.5 m at the end of motion, while reducing the sway to 5 mm in under 1.6 s. The experiments validated the controller.
- Local and Global Stability and Dynamics of a Class of Nonlinear Time-Delayed One-Degree-of-Freedom SystemsNayfeh, Nader Ali (Virginia Tech, 2006-07-17)We investigate the dynamics and stability of nonlinear time-delayed one-degree-of-freedom systems possessing quadratic and cubic nonlinearities and subjected to external and parametric disturbances. Due to the time-delay terms, the trivial solution of the unforced system undergoes Hopf bifurcations. We use the method of multiple scales to determine the normal forms of the Hopf bifurcations and hence determine whether they are locally supercritical or subcritical. Then, we use a combination of a path following scheme, the normal forms, and the method of harmonic balance to calculate and trace small- and large-amplitude limit cycles and use Floquet theory to ascertain their stability and hence generate global bifurcation diagrams. We validate these diagrams using numerical simulations. We apply the results to two important physical problems: machine-tool chatter in lathes and control of the sway of container cranes using time-delayed position feedback. We find that the Hopf bifurcations in machine tools are globally subcritical even when they are locally supercritical. We find multiple large-amplitude solutions coexisting with the linearly stable trivial solution. Consequently, there are three operating regions for machine tools: an unconditionally stable region, an unconditionally unstable region, and a conditionally stable region. In the latter region, the multiple responses lead to hysteresis. Then, we investigate the use of bifurcation control to transform the subcritical bifurcations into supercritical ones. We find that cubic-velocity feedback with appropriate gains can shrink or even eliminate the conditionally stable region. Then, we find that time-delayed acceleration feedback with an appropriate gain can completely eliminate the linear instability region. In contrast, we find that the Hopf bifurcations in controlled cranes are locally and globally supercritical. Finally, we investigate the effectiveness of time-delayed position feedback in rejecting external and parametric disturbances in ship-mounted cranes.