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This thesis addresses the problem of active vibration control in the presence of parametric resonance. Parametric resonance arises in a broad class of systems typically characterized by time-varying structures, such as stacker cranes with variable load changes. This thesis is divided mainly into two parts. In the first part, a mathematical and a multi-body model are developed and experimentally validated on a lab-scale prototype. In addition, modal analysis is carried out analytically and experimentally. The second part highlights the challenges that parametric resonance poses for control. For this purpose, three approaches are presented. One of the common features of these approaches is the use of nonlinear model predictive control (NMPC) for the predictive countermeasure to parametric resonance, mainly for optimal trajectory planning instead of conventional methods such as input shaping. Furthermore, all three approaches share insights from the modal analysis where the time propagation of the parametric resonance is predictable. In two approaches, trajectory planning can avoid critical frequencies such as resonance frequencies by involving them as soft boundary conditions. The third approach develops a promising and completely different concept of active vibration damping based on the idea of shaping the frequency spectrum of the state and the input. Unlike the usual time domain MPC formulation, this spetral shaping is formulated as an optimization problem defined in the frequency domain. In addition to computer simulations, a real-time implementation of the nonlinear model predictive vibration control is also performed on the test bench.
Real-time model predictive controller (MPC) implementation in active vibration control (AVC) is often rendered difficult by fast sampling speeds and extensive actuator-deformation asymmetry. If the control of lightly damped mechanical structures is assumed, the region of attraction containing the set of allowable initial conditions requires a large prediction horizon, making the already computationally demanding on-line process even more complex. Model Predictive Vibration Control provides insight into the predictive control of lightly damped vibrating structures by exploring computationally efficient algorithms which are capable of low frequency vibration control with guaranteed stability and constraint feasibility. In addition to a theoretical primer on active vibration damping and model predictive control, Model Predictive Vibration Control provides a guide through the necessary steps in understanding the founding ideas of predictive control applied in AVC such as: · the implementation of computationally efficient algorithms · control strategies in simulation and experiment and · typical hardware requirements for piezoceramics actuated smart structures. The use of a simple laboratory model and inclusion of over 170 illustrations provides readers with clear and methodical explanations, making Model Predictive Vibration Control the ideal support material for graduates, researchers and industrial practitioners with an interest in efficient predictive control to be utilized in active vibration attenuation.
Real-time model predictive controller (MPC) implementation in active vibration control (AVC) is often rendered difficult by fast sampling speeds and extensive actuator-deformation asymmetry. If the control of lightly damped mechanical structures is assumed, the region of attraction containing the set of allowable initial conditions requires a large prediction horizon, making the already computationally demanding on-line process even more complex. Model Predictive Vibration Control provides insight into the predictive control of lightly damped vibrating structures by exploring computationally efficient algorithms which are capable of low frequency vibration control with guaranteed stability and constraint feasibility. In addition to a theoretical primer on active vibration damping and model predictive control, Model Predictive Vibration Control provides a guide through the necessary steps in understanding the founding ideas of predictive control applied in AVC such as: · the implementation of computationally efficient algorithms · control strategies in simulation and experiment and · typical hardware requirements for piezoceramics actuated smart structures. The use of a simple laboratory model and inclusion of over 170 illustrations provides readers with clear and methodical explanations, making Model Predictive Vibration Control the ideal support material for graduates, researchers and industrial practitioners with an interest in efficient predictive control to be utilized in active vibration attenuation.
Addresses the causes of and possible solutions to autoparametric resonance in mechanical systems.
This eBook is the fourth in a series of books on the critical earthquake response of elastic or elastic-plastic structures under near-fault or long-duration ground motions, and includes six original research papers which were published in the specialty section Earthquake Engineering in ‘Frontiers in Built Environment’. Several extensions of the first eBook, the second eBook and the third eBook are included here. The first article is on the comparison of earthquake resilience of various building structures including innovative base-isolation systems and control systems. Pulse-type ground motions and resonant harmonic ground motions are used for investigating the earthquake resilience of those innovative building structures. The second article is concerned with the performance of an innovative seismic response controlled system with shear walls and concentrated dampers in lower stories. The resonant one-cycle sine waves and resonant harmonic waves are used as the input ground motions. The third article is related to the robustness evaluation of a base-isolation building-connection hybrid controlled building structure under the critical long-period and long-duration ground motion. The multi impulse is used as a substitute for a long-period and long-duration ground motion and the model reduction to a single-degree-of-freedom (SDOF) system is conducted to propose a simple response evaluation method. The fourth article is an extension of the previously proposed energy balance approach to a damped bilinear hysteretic SDOF system under a double impulse as a substitute for a near-fault ground motion. The energy absorption through viscous damping is incorporated appropriately in the energy balance and the application of the proposed method to actual recorded ground motions is presented. The fifth article is on the robustness evaluation of base-isolation building-connection hybrid controlled building structures considering uncertainties in deep ground. The earthquake ground motion amplitude at the earthquake bedrock is evaluated by the Boore’s stochastic method in 1983 including the fault rupture and the wave propagation into the earthquake bedrock. Then the phase angle property at the earthquake bedrock is investigated by introducing the concept of phase difference which is defined for each earthquake type. A wave at the ground surface nearly resonant to the base-isolation building-connection hybrid controlled building structure is produced by considering uncertainties in deep ground. The sixth article is concerned with the critical response of nonlinear base-isolated buildings considering soil-structure interaction under a double impulse as a substitute for a near-fault ground motion. The complicated model of a nonlinear base-isolated building on ground is modeled into an SDOF system after a few model reduction processes. The approach presented in this eBook, together with the previous eBooks, is an epoch-making accomplishment to open the door for simpler and deeper understanding of structural reliability and resilience of built environments in the elastic-plastic and nonlinear range.
My objective in writing this book was to cross the bridge between the structural dynamics and control communities, while providing an overview of the potential of SMART materials for sensing and actuating purposes in active vibration c- trol. I wanted to keep it relatively simple and focused on systems which worked. This resulted in the following: (i) I restricted the text to fundamental concepts and left aside most advanced ones (i.e. robust control) whose usefulness had not yet clearly been established for the application at hand. (ii) I promoted the use of collocated actuator/sensor pairs whose potential, I thought, was strongly underestimated by the control community. (iii) I emphasized control laws with guaranteed stability for active damping (the wide-ranging applications of the IFF are particularly impressive). (iv) I tried to explain why an accurate pred- tion of the transmission zeros (usually called anti-resonances by the structural dynamicists) is so important in evaluating the performance of a control system. (v) I emphasized the fact that the open-loop zeros are more difficult to predict than the poles, and that they could be strongly influenced by the model trun- tion (high frequency dynamics) or by local effects (such as membrane strains in piezoelectric shells), especially for nearly collocated distributed actuator/sensor pairs; this effect alone explains many disappointments in active control systems.
This monograph presents an introduction to Harmonic Balance for nonlinear vibration problems, covering the theoretical basis, its application to mechanical systems, and its computational implementation. Harmonic Balance is an approximation method for the computation of periodic solutions of nonlinear ordinary and differential-algebraic equations. It outperforms numerical forward integration in terms of computational efficiency often by several orders of magnitude. The method is widely used in the analysis of nonlinear systems, including structures, fluids and electric circuits. The book includes solved exercises which illustrate the advantages of Harmonic Balance over alternative methods as well as its limitations. The target audience primarily comprises graduate and post-graduate students, but the book may also be beneficial for research experts and practitioners in industry.