Khaled A. Alhazza

A hybrid command-shaper for double-pendulum overhead cranes

A crane is generally modeled as a simple pendulum with a point mass attached to the end of a massless rigid link. Numerous control systems have been developed to reduce payload oscillations in order to improve safety and positioning accuracy of crane operations. However, large-size payloads may transform the crane model from a simple-pendulum system to a double-pendulum system. Control systems that consider only one mode of oscillations of a double pendulum may excite large oscillations in the other mode. In multi-degree-of-freedom systems, command-shaping controllers designed for the first mode may eliminate oscillations of higher modes provided that their frequencies are odd integer multiples of the first mode frequency. In this work, a hybrid command-shaper is designed to generate acceleration commands to suppress travel and residual oscillations of a double-pendulum overhead crane. The shaper consists of a primary double-step command-shaper complemented by a virtual feedback system. The primary command-shaper is designed to eliminate oscillations in a slightly modified version of the crane model with frequencies satisfying the odd integer multiple criterion. The virtual feedback loop is then used to modify the commands of the primary shaper to accommodate the difference between the modified and the original models of the crane. It is shown that the suggested hybrid command-shaper is capable of minimizing oscillations of both modes of a scaled experimental double-pendulum model of an overhead crane. Results show that the hybrid command-shaper produces a reduction of 95% in residual oscillations in both modes of the double pendulum over the time-optimal rigid-body commands.

A review of the vibrations of plates and shells

In this paper, we present an updated review of papers, conference papers, dissertations, and books dealing with the vibrations of plates and shells. The paper includes 236 citations, and it also includes a section on reduced-order models in cables, beams, plates, and shells. The references are categorized by shell type and assumptions. This review will provide a very useful list of references for research.

Free vibrations control of a cantilever beam using combined time delay feedback

A new multi-input single-output delay feedback controller is presented to reduce free vibrations of a cantilever beam. A linear model using the first mode is derived and used to analyze and characterize the damping produced by different delay-feedback controllers as a function of the controllers gains and delay. The stability regions and amount of damping produced by three different single delay feedback and the new combined delayed feedback are investigated. A three-dimensional figure for the new controller showing the stability regions as a function of the controller gains and delay is presented. The characteristic damping of the controller as predicted by the linear model is compared with that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controllers gains and delay are obtained, simulated, and compared. To validate the single mode approximation, numerical simulations are performed using three-mode full nonlinear model. The results obtained using multi-input delay-feedback controllers demonstrate an excellent improvement in mitigating the first-mode vibration.

A Novel Wave-Form Command-Shaping Control With Application on Overhead Cranes

In this work, a novel continuous command-shaping control strategy for a simple harmonic oscillator is proposed and implemented on an overhead crane model. A Wave-Form (WF) acceleration command profile is derived analytically, and its performance is validated numerically. To enhance the performance of the proposed command-shaping control strategy, a Modulated Wave-Form (MWF) acceleration command profile is derived. It was determined that the proposed Wave-Form and Modulated Wave-Form command profiles are capable of eliminating the travel and residual oscillations. Furthermore, unlike traditional impulse and step command-shaping, the proposed command profiles have smoother intermediate acceleration, velocity, and displacement profiles.Copyright

Adjustable maneuvering time wave-form command shaping control with variable hoisting speeds

Classical input shaping is based on convolving a general input signal with a sequence of timed impulses. These impulses are chosen to match certain modal parameters of the system under control to eliminate residual vibrations in rest-to-rest maneuvers. This type of input shaping is strongly dependent on the system period. In this work, an adjustable maneuvering time wave form command shaper is presented. The equation of motion of a simple pendulum model of a crane is derived and solved in order to eliminate residual vibrations at the end of motion. Several cases are simulated numerically and validated experimentally on an experimental model of an overhead crane. Results show that the proposed command shaper is capable of eliminating residual vibrations effectively with a single continuous wave form command. The work is extended to include the effect of hoisting on the shaper performance. Several functions are used to simulate hoisting. To overcome the added complexity of hoisting on the system, an approximation technique is used to determine initial shaped command parameters, which are later used in a genetic algorithm optimization scheme. Numerical and experimental results prove that the proposed command shaper can effectively eliminate residual vibrations in rest-to-rest maneuvers.

An Iterative Learning Control Technique for Point-to-Point Maneuvers Applied on an Overhead Crane

An iterative learning control (ILC) strategy is proposed, and implemented on simple pendulum and double pendulum models of an overhead crane undergoing simultaneous traveling and hoisting maneuvers. The approach is based on generating shaped commands using the full nonlinear equations of motion combined with the iterative learning control, to use as acceleration commands to the jib of the crane. These acceleration commands are tuned to eliminate residual oscillations in rest-to-rest maneuvers. The performance of the proposed strategy is tested using an experimental scaled model of an overhead crane with hoisting. The shaped command is derived analytically and validated experimentally. Results obtained showed that the proposed ILC control strategy is capable of eliminating travel and residual oscillations in simple and double pendulum models with hoisting. It is also shown, in all cases, that the proposed approach has a low sensitivity to the initial cable lengths.

Nonlinear free vibration control of beams using acceleration delayed-feedback control

A single-mode delayed-feedback control strategy is developed to reduce the free vibrations of a flexible beam using a piezoelectric actuator. A nonlinear variational model of the beam based on the von Karman nonlinear type deformations is considered. Using Galerkins method, the resulting governing partial differential equations of motion are reduced to a system of nonlinear ordinary differential equations. A linear model using the first mode is derived and is used to characterize the damping produced by the controller as a function of the controllers gain and delay. Three-dimensional figures showing the damping magnitude as a function of the controller gain and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct long-time integration of a three-mode nonlinear model. Optimal values of the controller gain and delay using both methods are obtained, simulated and compared. To validate the single-mode approximation, numerical simulations are performed using a three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the first-mode vibration.

Command-Shaping Control System for Double-Pendulum Gantry Cranes

Traditionally, multi-mode command-shaping controllers are tuned to the system frequencies. This work suggests an opposite approach. A frequency-modulation (FM) strategy is developed to tune the system frequencies to match the frequencies eliminated by a single-mode command-shaper. The shaper developed in this work is based on a double-step command-shaping strategy. Using the FM Shaper, a simulated feedback system is used to modulate the closed-loop frequencies of a simulated double-pendulum model to the point where the closed-loop second mode frequency becomes an odd multiple of the closed-loop first mode frequency, which is the necessary condition for a satisfactory performance of a single-mode command-shaper. The double-step command-shaper is based on the closed-loop first mode frequency. The input commands to the plant of the simulated closed-loop system are then used to drive the actual double-pendulum. Performance is validated experimentally on a scaled model of a double-pendulum gantry crane.© 2011 ASME

A Smooth Wave-Form Command Shaping Control

To avoid excitation of higher modes of flexible and multi-mode systems, it is important to eliminate sudden and jerky inputs. To achieve this goal, researchers tend to use different smoothing techniques to reduce the effect of the command roughness. In this work, a new smooth command-shaping technique for oscillation reduction of simple harmonic oscillators is proposed. A continuous smooth wave-form acceleration command-shaper is proposed. The shaper parameters are tuned to eliminate residual vibrations in rest-to-rest maneuvers. The performance of the proposed shaper is determined analytically, simulated numerically, and validated experimentally on a scaled model of an overhead crane. Results obtained show that the proposed smooth wave-form shaper is capable of eliminating travel and residual oscillations. Furthermore, unlike traditional step command shapers, the proposed command profiles have completely smooth acceleration, velocity, and displacement profiles. Experimental results demonstrate the ability of our proposed smooth wave-form commands to eliminate residual vibrations at the end of rest-to-rest maneuvers.Copyright

A Frequency-Modulation Command-Shaping Strategy for Multi-Mode Systems

Single-mode shaped commands can be implemented for oscillations control of multi-mode systems provided that all frequencies of the system are odd-multiples of the shaped command frequency. This criterion is utilized in this work to develop a command shaping strategy for multi-mode systems. A frequency-modulation command shaper is derived based on the use of a single-mode command-shaping technique. The proposed strategy is based on deriving a closed-loop model of a multi-mode system with its modal frequencies modulated so that higher mode frequencies are odd-multiples of the first mode frequency. A single-mode double-step primary command-shaper with a design frequency equal to the first mode frequency of the closed-loop system is then used. The input command to the plant of the closed-loop system is used as shaped commands for the multi-mode system. Numerical simulations are used to demonstrate the performance of the proposed strategy along with experiments on scaled models of a triple, quadruple, and quintuple-pendulums.Copyright