Majed A. Majeed

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.

Low-Velocity Impact Response of Structures With Local Plastic Deformation: Characterization and Scaling

This paper presents a methodology for the characterization and scaling of the response of structures having different shapes, sizes, and boundary conditions that are under impact by spherical objects. The objectives are to demonstrate the accuracy of a new bilinear contact law that accounts for permanent indentation in the contact zone, and to show the efficacy of a characterization diagram in the analysis and design of structures subject to impact. The characterization diagram shows the normalized functional relationship between the maximum impact force and three nondimensional parameters that cover the complete dynamic spectrum for low-velocity impact. The validity of using the bilinear elastoplastic contact law is demonstrated by both finite element (FE) and Rayleigh-Ritz discretization procedures for simply-supported plates. The efficacy of the characterization diagram, which was developed using simple structural models, is demonstrated by the FE simulations of more complicated and realistic structures and boundary conditions (clamped, stiffened plates, and cylindrical panels). All of the necessary parameters needed for the characterization are ‘measured’ using the FE models simulating real-world experiments. Impact parameters are varied to cover the complete dynamic spectrum with excellent results.

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 Hybrid Command-Shaping Control System for Highly Accelerated Double-Pendulum Gantry Cranes

A gantry cranes 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 transforms 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-degrees-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-shaping controller is designed to generate acceleration commands to suppress travel and residual oscillations of a highly accelerated double-pendulum gantry 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 a gantry 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.© 2009 ASME

Modeling and Analysis of Elastoplastic Impacts on Supported Composites

This paper presents an elastoplastic impact model for a spherical object impacting a supported composite layer or a half-space. The model utilizes a contact law that has been developed based on elastic-plastic and fully plastic indentation theories. For an impact event, the model parameters can easily be obtained analytically, computationally using Finite Elements (FE), and from experiments, by assuming transversely isotropic material behavior. Simulations are compared to those from a nonlinear FE model developed in ABAQUS, and to limited experimental data, with excellent results.

Graded Finite Element Modeling of Constrained Layer Damping Treatments with Functionally Graded Viscoelastic Material

Passive constrained layer damping (PCLD) is a simple, powerful, and successful technique to solve structural vibration problems. The design of PCLD treatments is mainly subject to the physical and geometrical properties of the viscoelastic material. The use of functionally graded viscoelastic (FGV) material as a core layer in beams with PCLD treatments has been introduced by the authors in an earlier work. The main objective of the present work is to develop and formulate a finite element model for beams treated with FGV constrained layer damping. Natural frequencies and modal loss factors obtained by the finite element model are compared to those obtained by the assumed modes method from a previous work and results from both approaches are compared.

Free Vibrations Stability Analysis and Control of a Cantilever beam with Multiple Time Delay State Feedback

gures showing the stability regions as a function of the controller gains and delay are presented. The characteristic damping of the controller as predicted by the linear model is compared to that calculated using direct longtime 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 three-mode full nonlinear model. Results of the simulations demonstrate an excellent controller performance in mitigating the rst-mode vibration.

Multi-Mode Vibration Control of Plates Using a Single Actuator and a Single Sensor

Multi-mode vibration control using single actuator and single sensor is considered as a difficult control scheme. Most researchers use multi actuators and multi controllers to control multimode structural vibrations. In the present work, a multi-mode control model consists of a single actuator and single sensor, both attached at the top of simply supported thin plate, is developed. A piezoelectric actuator is used and it is assumed to be perfectly bonded to the plate, which means the bonding thickness is neglected. The sensed accelerometer signal is integrated and then filtered to include only the first and the second vibration modes. The linear equations of motion of the plate are derived and discretized using Galerkin’s Method. The resulting coupled equations are combined with velocity delay feedback controller to reduce the structure vibration. Genetic Algorithm is then used to optimize controller parameters using the root mean square of the input signal as an objective function. The results showed that the use of single-input single-output (SISO) delay feedback multimode controller can efficiently be used on any structure to control multimode systems.Copyright

Characterization and Scaling of Low Velocity Impact Response of Structures With Local Plastic Deformation: Implications for Design

This paper presents a methodology for the characterization and scaling of response of structures having different shapes, sizes, and boundary conditions that are under impact by blunt objects through a characterization diagram. The diagram is constructed from an analytical functional relationship of the normalized maximum impact force and three non-dimensional parameters, namely the ‘Relative Stiffness’, ‘Relative Mobility,’ and ‘Effective Mass Ratio’. The efficacy of this diagram, which is developed using simple structural models, is demonstrated by FE simulations of more complicated and realistic structures and boundary conditions (clamped, stiffened plates and cylindrical panels). All the necessary parameters needed for characterization are determined using FE models simulating real-world experiments. The characterization method is validated for a wide range of impact parameters that cover the entire dynamic spectrum. It is expected that by determining the model parameters for various engineering structural elements and support conditions, the impact response and subsequent damage may be predicted in an early stage using the characterization diagram. The diagram can also be used to assess the accuracy of simple lumped parameter models and to provide clear guidelines for the choice of an adequate model for a given impact situation. As a result, the characterization diagram and simple models can be used for both the evaluation of finite element and other solutions, and as guides in the design of experiments and in scaling experimental results. The characterization diagram can be used as a powerful analytical prediction tool in various stages of design of complex structures subject to impact such as, initial design, testing and commissioning.Copyright