In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n × n matrices of H? frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses

Nonlinear dynamics analysis of the spur gear system for railway locomotive

Investigation on coupling effects between surface wear and dynamics in a spur gear system

Modeling and analysis of a spur gear pair considering multi-state mesh with time-varying parameters and backlash

The evaluation of a nonlinear energy sink absorber based on the transmissibility

The global homoclinic bifurcation and transition to chaotic behavior of a nonlinear gear system are studied by means of Melnikov analytical analysis. It is also an effective approach to analyze homoclinic bifurcation and detect chaotic behavior. A generalized nonlinear time varying (NLTV) dynamic model of a spur gear pair is formulated, where the backlash, time varying stiffness, external excitation, and static transmission error are included. From Melnikov method, the threshold values of the control parameter for the occurrence of homoclinic bifurcation and onset of chaos are predicted. Additionally, the numerical bifurcation analysis and numerical simulation of the system including bifurcation diagrams, phase plane portraits, time histories, power spectras, and Poincare sections are used to confirm the analytical predictions and show the transition to chaos.

/pdf/global-bifurcation-and-chaos-analysis-in-nonlinear-vibration-34wrze0apx.pdf

Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

Isolating the sensitive equipment from vibrating base or the foundation from machinery vibration is of practical importance in a number of engineering fields. With the development of the vibration control techniques and increasing requirements for the higher-performance vibration isolation in industry and everyday life, active vibration isolation exhibits the best performances. In this paper, active vibration isolation reducing vibration transmitted from vibrating base to sensitive equipment and from machinery to foundation was investigated. Controller as static output feedback was considered to design components of active isolation system. An active control is provided by using H∞ control criteria to design this controller. This criterion is presented as a cost function and then optimized by Particle Swarm Optimization (PSO) algorithm. The approach is validated using numerical simulation. Results show that this static output feedback H∞ controller using PSO algorithm can get good performance to reduce the effect of unwanted vibration and disturbances.

/pdf/active-vibration-isolation-of-machinery-and-sensitive-funj03uhuh.pdf

Active vibration isolation of machinery and sensitive equipment using H ∞ control criterion and particle swarm optimization method

https://profdoc.um.ac.ir/articles/a/1045047.pdf

Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

The homoclinic bifurcation and transition to chaos in gear systems are studied both analytically and numerically. Applying Melnikov analytical method, the threshold values for the occurrence of chaotic motion are obtained. The influence of system parameters on the character of vibration is studied. The numerical simulation of the system including bifurcation diagram, phase plane portraits, Fourier spectra, and time histories is considered to confirm the analytical predictions for the occurrence of homoclinic bifurcation and chaos in nonlinear gear systems.

https://downloads.hindawi.com/journals/sv/2014/809739.pdf

Bifurcation and Chaos Prediction in Nonlinear Gear Systems

هلاقم تاعلاطا هدیکچ لماک یشهوژپ هلاقم تفایرد : 09 رذآ 1392 شریذپ : 16 نمهب 1392 تیاس رد هئارا : 22 ریت 1393 خرچ هدند اه متسیس رد زیون داجیا و تاشاعترا مهم عبانم زا یکی یم بوسحم یتعنص راود ياه دنوش . هب لاقتنا متسیس کی هئارا و یحارط روظنم خرچ تردق هدند خرچ تاشاعترا لاعف لرتنک متسیس کی شهوژپ نیا رد ،هنیهب و مارآ يا هدند و داهنشیپ ناقاتای یم رارق یبایزرا دروم دریگ . لدم خرچ متسیس تاشاعترا یکیمانید هدند ،هنادند مرف تارییغت ،تخاس ياهاطخ لیبق زا یحارط رد هتساوخان ياهرتماراپ زا یخرب نتفرگ رظنرد اب يا یم هئارا ،یلامعا رواتشگ تاشاشتغا زا یشان تاکیرحت نینچمه و بصن ياهاطخ دوش . لقادح هب و شهاک يارب نیا بولطمان تارثا ندناسر هعومجم تاشاعترا رب اهرتماراپ ، یم داهنشیپ یلاعف لرتنک متسیس دوش . هب ،هدش حرطم یلرتنک هدیا رد کیرحت يورین کی لامعا و يریگراک ناقاتای یم متسیس ياه دشاب . رظن دروم لرتنک متسیس لرتنک رایعم ساسارب و کبدیف لرتنک زا هدافتسا اب H∞ هدایپ يزاس یم دوش . هب رایعم نیا هئارا هنیزه عبات کی تروص و هنیهب متیروگلا هب ای تارذ هورگ يزاس راصتخا PSO شور زا هک هنیهب ياه شور نیب رد دوجوم يزاس شوه ياه ،تسا یعونصم یم رارق هدافتسا دروم متسیس خساپ ندومن هنیهب يارب دریگ . هب نشیپ یلرتنک متسیس درکلمع یسررب روظنم ش ،هدش داه هیب يزاس یم رارق یبایزرا دروم لصاح جیاتن و ماجنا متسیس دریگ . ناگژاو دیلک : خرچ هدند تاشاعترا لرتنک لرتنک کبدیف

Amin Saghafi

Papers

Global bifurcation and chaos analysis in nonlinear vibration of spur gear systems

Active vibration isolation of machinery and sensitive equipment using H ∞ control criterion and particle swarm optimization method

Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

Bifurcation and Chaos Prediction in Nonlinear Gear Systems

Vibrations control of gear-bearing dynamic system