Motion Planning of a Nonholonomic Multibody System Using Genetic Algorithm

The motion planning problem of a nonholonomic multibody system is investigated. Nonholonomicity arises in many mechanical systems subject to nonintegrable velocity constraints or nonintegrable conservation laws. When the total angular momentum is zero, the control problem of system can be converted to the motion planning problem for a driftless control system. In this paper, we propose an optimal control approach for nonholonomic motion planning. The genetic algorithm is used to optimize the performance of motion planning to connect the initial and final configurations and to generate a feasible trajectory for a nonholonomic system. The feasible trajectory and its control inputs are searched through a genetic algorithm. The effectiveness of the genetic algorithm is demonstrated by numerical simulation.

A Review of Recent Developments in Atomic Force Microscopy Systems With Application to Manufacturing and Biological Processes

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of microstructural parameters and intermolecular forces at nanoscale level with atomic-resolution characterization. Typically, these microcantilever systems are operated in three open-loop modes; non-contact mode, contact mode, and tapping mode. In order to probe electric, magnetic, and/or atomic forces of a selected sample, the non-contact mode is utilized by moving the cantilever slightly away from the sample surface and oscillating the cantilever at or near its natural resonance frequency. Alternatively, the contact mode acquires sample attributes by monitoring interaction forces while the cantilever tip remains in contact with the target sample. The tapping mode of operation combines qualities of both the contact and non-contact modes by gleaning sample data and oscillating the cantilever tip at or near its natural resonance frequency while allowing the cantilever tip to impact the target sample for a minimal amount of time. Recent research on AFM systems has focused on many fabrication and manufacturing processes at molecular levels due to its tremendous surface microscopic capabilities. This paper provides a review of such recent developments in AFM imaging systems with emphasis on operational modes, microcantilever dynamic modeling and control. Due to the important contributions of AFM systems to manufacturing, this paper also provides a comprehensive review of recent applications of different AFM systems in these important areas.

Magnetic Field-Induced Nonlinear Vibration of an Unbalanced Rotor

The free and forced flexural vibrations are investigated for rotors of electric motors operating in unsymmetrical magnetic fields. The magnetic potential energy reserved in the air-gap is analytically derived and the unbalanced magnetic pull is obtained through the law of energy conservation. With this excitation, the equations of motion of the unbalanced rotor are developed for nonlinear displacements response. For small dynamic eccentricities, the equations of motion are simplified and the rotor is compared to a free Duffing oscillatory system. The analytic solution for forced vibrations subject to residual mass-unbalance excitations is also obtained. Jump phenomenon in the solution is pointed out, and the effects of initial eccentricity and flux density on the natural frequency are also investigated.

Automotive Hydraulic Valve Fluid Field Estimator Based on Non-Dimensional Artificial Neural Network (NDANN)

A conventional automatic transmission (AT) hydraulic control system includes many spool-type valves that have highly asymmetric flow geometry. An accurate analysis of their flow fields typically requires a time-consuming computational fluid dynamics (CFD) technique. A simplified flow field model that is based on a lumped geometry is computationally efficient. However, it often fails to account for asymmetric flow characteristics, leading to an inaccurate analysis. In this work, a new hydraulic valve fluid field model is developed based on a non-dimensional neural network (NDANN) to provide an accurate and numerically efficient tool in AT control system design applications. A “grow-and-trim” procedure is proposed to identify critical non-dimensional inputs and optimize the network architecture. A hydraulic valve testing bench is designed and built to provide data for neural network model development. NDANN-based fluid force and flow rate estimator are established based on the experimental data. The NDANN models provide more accurate predictions of flow force and flow rates under broad operating conditions compared with conventional lumped flow field models. The NDANN fluid field estimator also exhibits input-output scalability. This capability allows the NDANN model to estimate the fluid force and flow rate even when the design geometry parameters are outside the range of the training data.

Simultaneous Manipulator/Controller Design Optimization Using Multi-Objective Evolutionary Algorithms

A multi-objective design methodology that uses an evolutionary algorithm optimization process is presented and is applied to the simultaneous optimal design of a robotic manipulator/controller for performing point-to-point motion tasks. Dynamic performance measures, for the closed-loop system, are optimized by considering a nonlinear PD controller and quintic polynomial trajectories for point-to-point motions. Results of the simultaneous optimal design of a planar manipulator, a nonlinear controller, and some sample trajectories are presented to illustrate the efficacy of this methodology.

An Enterprise Decision Model for Optimal Vehicle Design and Technology Valuation

Design optimization traditionally has dealt with engineering design decisions. Yet it is well understood that optimal product decisions must be based on engineering as well as marketing and production considerations. An enterprise decision model attempts to link these aspects of the product development enterprise so that the value of the designed product to the enterprise can be assessed. The model also values new product technology in accordance with the enterprise’s current operations to increase the likelihood of commercialization success before committing to a new strategy. The valuation technique uses comprehensive engineering simulation to provide a preliminary understanding of the technology’s market and design potential. The model represents the enterprise in a mathematical formulation that simultaneously optimizes initial product design, product pricing, operating costs associated with capacity allocation and design decisions, and the value created by new products. The article demonstrates such a model for optimal vehicle design in a medium truck market experiencing hybrid penetration.

Fractal Basin Boundaries and Chaotic Motions in Spring-Pendulum System

This study investigates chaotic response in the spring-pendulum system. In this system beside of strange attractors, multiple regular attractors may coexist for some values of system parameters, where it is important to study the global behavior of the system using the basin boundaries of the attractors. Multiple scales method is used to distinguish the regions of stable and unstable attractors. In unstable regions, bifurcation diagram and poincare´ maps are used to study the existence of quasi-periodic and chaotic attractors. Results show that the jumping phenomena may occur when multiple regular attractors exist and for this case fractal basins of attraction are developed using numerical simulations.

Hydraulic Driven Rotating Flexible Beam: Theoretical Modal Analysis and Proportional Servo Drive Parameter Influence

Understanding the behavior of system with flexible elements is increasingly important in modern day technology. Reducing the mass of machine elements leads to a remarkable improvement in dynamic performance. However, a loss of precision also occurs with such an increase in flexibility. In order to arrive at a better understanding of systems with flexible elements, we are investigating the particular behavior of a hydraulic servo driven rotating flexible beam with the aim of obtaining a methodology that could be applied to a real application. To investigate this behavior, a set of models has been developed. In this paper, a theoretical model, using classical modal analysis methodology, is presented. The flexible beam is modeled in a standard way and the hydraulic servo drive is modeled as a boundary condition. Only normal modes will be investigated. This approach allows considering the servo proportional constant and the cylinder mass. It will be show that the servo proportional constant has low influence in the system eigen frequencies. The theoretical model predictions are validated experimentally.

Bifurcation Control of Ro¨ssler System

In this paper, a new method is proposed for controlling bifurcations of nonlinear dynamical systems. This approach employs the idea used in deriving the transition variety sets of bifurcations with constraints to find the stability region of equilibrium points in parameter space. With this method, one can design, via a feedback control, appropriate parameter values to delay either static, or dynamic or both bifurcations as one wishes. The approach is applied to consider controlling bifurcations of the Ro¨ssler system. The uncontrolled Ro¨ssler has two equilibrium solutions, one of which exhibits static bifurcation while the other has Hopf bifurcation. When a feedback control based on the new method is applied, one can delay the bifurcations and even change the type of bifurcations. An optimal control law is obtained to stabilize the Ro¨ssler system using all feasible system parameter values. Numerical simulations are used to verify the analytical results.

Analysis on Critical Phenomena of a Hysteretic System

In this paper, a nonlinear mechanical system with external forcing is investigated to study the critical phenomena of the system. The system involves a von der Pol type damping and a hysteretic damper representing a restoring force. Numerical simulations are used to show that under an external exciting force, the hysteretic restoring force may not follow the routes described by a conventional form of piecewise function, but exhibit some irregular behavior. We call this unusual situation the critical phenomenon of the system. Simulations results suggest that a device with hysteretic property (e.g., the damper considered in this paper) may change its typical characteristics under external forcing. This new finding may enhance the study of nonlinear dynamical systems with hysteretic property under external excitement.