Dynamics of Mechatronics Systems

The following sections are included:

• Preface
• Acknowledgments
• Contents

The following sections are included:

• Mechatronics
• Systems
• Units of Measurement

Before a human had appeared on the Earth, the universe, stellar and planetary systems have already existed. Water and tectonic systems were developed, and flora and fauna were functioning on the Earth. A human developed his creative skills to eventually turn them into the ability to produce material goods. Preparation of material goods associated with abstract thinking were engaging mind and model, which was a virtual prototype of materialization. The diversity of the resulting solutions was a reason to their research and improvement for the utilitarian purposes. Therefore, the modeling of real-world objects appearing in the nature or created by other people was born. At the same time as learning about the environment was in progress, some possibility of its use for practical purposes (current and prospective) was observed. A man has created models of common cognitive systems existing in nature to satisfy human curiosity…

The following sections are included:

• Electric Charge and its Quantization
• Capacitance, Resistance and Electric Laws
  • Electric Flux
  • Capacitance and Capacitors
  • Resistance
  • Electric Laws
  • Poisson's and Laplace's Equation
• Induced Electric Fields
  • Electromotive Force
  • Rectangular Loop with a Conductor Moving in a Magnetic Field
  • Alternating Current
• Magnetic and Electromagnetic Phenomena
  • Magnets and Magnetic Fields
  • Magnetic Charge and a Dipole
  • Magnetic Effect of Current
  • The Law of Ampére and its Generalization
  • Magnetic Dipole Moment of a Closed Planar Current-Carrying Loop
  • Electromagnetic Induction
  • Electric and Magnetic Susceptibility and Permeability
  • Permeability and Susceptibility as Tensors and Dyadics
  • Diamagnetic Materials
  • Paramagnetic Materials
  • Ferromagnetic Materials
• An Introduction to Electromagnetic Fields

The following sections are included:

• Piezoelectric Materials, Materials Laws and Constitutive Equations
• One-dimensional Rod Polarized Along its Axis — an Example of an Actuator

In Tables 5.1 and 5.2, the most common cross sections of hydraulic and pneumatic flow elements, formulas for flow rates, and critical Reynolds number Re defining applicability range of these elements are presented…

Electrohydraulic servomechanisms are a perfect example of mechatronic devices which, by their design and processing of signals, create a link between various fields of science and engineering such as solid mechanics, fluid mechanics, electronics, electrical engineering and computer science (numerical programming, CAD). The issues related to control and optimization of dynamic processes and optimization of shapes are not less important. To ensure smooth operation of these devices, a good understanding of the relationships between theoretical and experimental aspects that merge these fields of science is highly required…

The following sections are included:

• Newtonian Model
• Wave Model
• Magnetic Field vs. Free Atom
• Electron Orbital Perturbation by a Proton Moving in a Magnetic Field
• Planar Dynamics of a Particle in a Magnetic Field
• 3D Dynamics of a Charge

Complete analysis of the electromagnetic phenomena, including static and induced electric fields as well as magnetic effects, and others, can be carried out using a compact set of equations called Maxwell's equations. Maxwell's equations contribute to other important sets of equations regarding Newton's laws of classical mechanics and three laws of thermodynamics (see [Edminister and Hahvi (2011); Fleisch (2008); Schwartz (1972)])…

The following sections are included:

• Introduction
• Methods of Optimization
  • Experimental Methods
  • Mathematical Methods
• Examples
  • Linear and Nonlinear Programming
  • Dynamic Programming
  • Geometric Programming Methods
  • Stiffness Optimization of a Spindle System
  • Minimization of Total Power Loss in a Hydrostatic Bearing

Fuzzy logic control algorithms are regarded as a relatively new concept in modern control theory. This chapter delivers a comparative analysis of two qualitatively different approaches used for angular velocity control of a DC (direct current) motor subject to chaotic disturbances coming from a gear with a transmission belt carrying a vibrating load. The purpose is to achieve an accurate control of the speed of the DC motor (a plant), especially when the motor parameters and some external loading conditions are partially unknown. Firstly, the classical approach based on the PID control is considered and then, a fuzzy logic based alternative is proposed. Two different controllers are presented for the purpose of completion of the classical PID controller and a Takagi-Sugeno type fuzzy logic PI controller. Both control algorithms were implemented on an 8-bit AVR ATmega644PA microcontroller. On the basis of step responses of the plant, an analysis as well as an interesting comparison of controllers performance has been presented…

Stick-slip vibrations appear during relative motion between contacting surfaces of miscellaneous frictional pairs. They depend on the viscous force, Coulomb force or other velocity-dependent forces. These effects appear in almost all mechanical systems, for instance, in positioning systems like servomechanisms, impulse encoders and stepper motors which operate at or about zero velocity of relative motion between shafts and sliding bearings. This chapter extends our study on numerical modeling of a DC (direct current) motor treated as a dynamical system with stickslip effects which appear in transient motion even while the direction of rotation of its rotor crosses zero velocity speed. These investigations are aimed at some future applications of the control technique serving for explanation of bifurcation phenomena existing in such kind of discontinuous systems. Putting emphasis on nonlinear effects, we apply the well-known but slightly extended sliding surface method allowing for compensation of frictional effects. A limit cycle on a phase plane, as well as time histories of control inputs and system outputs, were obtained using numerical simulations performed in LabVIEW…

In this chapter, a lumped mass mechanical model of a thorax subjected to a blast pressure wave is taken into consideration. A thorax spring-dashpot model developed by Lobdell is implemented in numerical modeling of the dynamics of the multibody system. The five-degree-of-freedom mechanical model of a chest adjacent to an elastic backrest is subjected to an impulse loading generated by the blast pressure wave released by an explosion. The so-called coupling of the pressure wave to the thorax is reconsidered. With respect to the evident existence of inherent time delays of displacements, the system of coupled bodies is described by a time delay differential equations that are derived from the large-scale systems approach. Numerical solutions present interesting dynamical behavior of the bio-inspired system, resulting from inherent time delays and a time of arrival of the blast pressure wave. It is pointed out that the inherent state time delays change the dynamical response of the multibody system. Proper time of deployment of the foam-based armor plate reduces relative compression of the thorax, which is to be protected by a bullet-proof waistcoat…

Active control can be adopted in optimization of fast impulsive response systems occurring in body interacting biomechanics. Such kinds of control of mechanical or biological structures are not new, but can be still explored and successively used. This chapter focuses on application of one controlling force to minimize a relative compression of a human chest which has been caused by some impacting action of an elastic external force. A virtual actuator controlling deformation in the analyzed rheological dynamical system of three-degree-of-freedom acts between the back side of the human thorax and the back rest. Reduction of internal displacements in the thorax has been estimated solving the linear quadratic regulator (LQR) optimization problem. Time histories of the controlled and uncontrolled system responses, evaluation of response's shape after changing coefficients of the control method as well as dependency of the objective function estimation on the proportional gain vector are presented and discussed.

The following sections are included:

• Bibliography
• Index