Control of quantum phenomena: Past, present, and future

Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. The current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. The two most critical theoretical insights were (1) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (2) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control, which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in adaptive feedback control experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. Adaptive feedback control of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control designs in experimental realizations, and real-time quantum feedback control. The paper concludes with a prospective of open research directions that are likely to attract significant attention in the future.Comment: Review article, final version (significantly updated), 76 pages, accepted for publication in New J. Phys. (Focus issue: Quantum control

Nonlinear Energy Harvesting Under White Noise

While purposeful introduction of stiffness nonlinearities into the dynamics of energy harvesters is aimed at enhancing performance under non-stationary and random excitations, most of the conclusions reported in the current literature are based on the steady-state response which assumes a harmonic fixed-frequency excitation. As a result, we still do not have a clear understanding of how the nature of the excitation influences the output power, or what role stiffness nonlinearities play in the transduction of energy harvesters under random excitations. To fill this gap in the current knowledge, this thesis investigates the response of nonlinear mono- and bi-stable energy harvesters to environmental excitations that can be approximated via a white noise process. For the mono-stable case, statistical linearization is utilized to analytically approximate the statistical averages of the response. The influence of the nonlinearity and the symmetry of the restoring force on the mean power is investigated under optimal electric loading conditions. It is shown that the nonlinearity has no influence on the output power unless the ratio between the time constant of the harvesting circuit and the period of the mechanical oscillator is small. In such case, a mono-stable harvester with a symmetric nonlinear restoring force can never produce higher mean power levels than an equivalent linear harvester regardless of the magnitude or nature of the nonlinearity. On the other hand, asymmetries in the restoring force are shown to provide performance improvements over an equivalent linear harvester. For energy harvesters with a bi-stable potential function, statistical linearization, direct numerical integration of the stochastic differential equations, and finite element solution of the Fokker-Plank-Kolmogorov equation governing the response probability density function are utilized to understand how the shape and symmetry of the potential energy function influence the mean output power of the harvester. It is observed that, both of the finite element solution and the direct numerical integration provide close predictions for the mean power regardless of the shape of the potential energy function. Statistical linearization, on the other hand, yields non-unique and erroneous predictions unless the potential energy function has shallow potential wells. It is shown that the mean power exhibits a maximum value at an optimal potential shape. This optimal shape is not directly related to the shape that maximizes the mean square displacement even when the time constant ratio, i.e., ratio between the time constants of the mechanical and electrical systems is small. Maximizing the mean square displacement yields a potential shape with a global maximum (unstable potential) for any value of the time constant ratio and any noise intensity, whereas maximizing the average power yields a bi-stable potential which possesses deeper potential wells for larger noise intensities and vise versa. Away from the optimal shape, the mean power drops significantly highlighting the importance of characterizing the noise intensity of the vibration source prior to designing a bi-stable harvester for the purpose of harnessing energy from white noise excitations. Furthermore, it is demonstrated that, the optimal time constant ratio is not necessarily small which challenges previous conceptions that a bi-stable harvester provides better output power when the time constant ratio is small. While maximum variation of the mean power with the nonlinearity occurs for smaller values of the time constant ratio, these values do not necessarily correspond to the optimal performance of the harvester. Finally, it is shown that asymmetries in the potential shape of bi-stable harvesters do not improve the mean power unless the symmetric potential function is designed away from its optimal parameters

Vibrational and stochastic resonances in driven nonlinear systems:part two

Nonlinearity is ubiquitous in both natural and engineering systems. The resultant dynamics has emerged as a multidisciplinary field that has been very extensively investigated, due partly to the potential occurrence of nonlinear phenomena in all branches of sciences, engineering and medicine. Driving nonlinear systems with external excitations can yield a plethora of intriguing and important phenomena – one of the most prominent being that of resonance. In the presence of additional harmonic or stochastic excitation, two exotic forms of resonance can arise: vibrational resonance or stochastic resonance, respectively. Several promising state-of-the-art technologies that were not covered in Part One of this Theme Issue are discussed here. They include inter alia the improvement of image quality, the design of machines and devices that exert vibrations on materials, the harvesting of energy from various forms of ambient vibration, and control of aerodynamic instabilities. They form an important part of the Theme Issue as a whole, which is dedicated to an overview of vibrational and stochastic resonances in driven nonlinear systems. resonances in driven nonlinear systems

Active suspension control of electric vehicle with in-wheel motors

In-wheel motor (IWM) technology has attracted increasing research interests in recent years due to the numerous advantages it offers. However, the direct attachment of IWMs to the wheels can result in an increase in the vehicle unsprung mass and a significant drop in the suspension ride comfort performance and road holding stability. Other issues such as motor bearing wear motor vibration, air-gap eccentricity and residual unbalanced radial force can adversely influence the motor vibration, passenger comfort and vehicle rollover stability. Active suspension and optimized passive suspension are possible methods deployed to improve the ride comfort and safety of electric vehicles equipped with inwheel motor. The trade-off between ride comfort and handling stability is a major challenge in active suspension design. This thesis investigates the development of novel active suspension systems for successful implementation of IWM technology in electric cars. Towards such aim, several active suspension methods based on robust H∞ control methods are developed to achieve enhanced suspension performance by overcoming the conflicting requirement between ride comfort, suspension deflection and road holding. A novel fault-tolerant H∞ controller based on friction compensation is in the presence of system parameter uncertainties, actuator faults, as well as actuator time delay and system friction is proposed. A friction observer-based Takagi-Sugeno (T-S) fuzzy H∞ controller is developed for active suspension with sprung mass variation and system friction. This method is validated experimentally on a quarter car test rig. The experimental results demonstrate the effectiveness of proposed control methods in improving vehicle ride performance and road holding capability under different road profiles. Quarter car suspension model with suspended shaft-less direct-drive motors has the potential to improve the road holding capability and ride performance. Based on the quarter car suspension with dynamic vibration absorber (DVA) model, a multi-objective parameter optimization for active suspension of IWM mounted electric vehicle based on genetic algorithm (GA) is proposed to suppress the sprung mass vibration, motor vibration, motor bearing wear as well as improving ride comfort, suspension deflection and road holding stability. Then a fault-tolerant fuzzy H∞ control design approach for active suspension of IWM driven electric vehicles in the presence of sprung mass variation, actuator faults and control input constraints is proposed. The T-S fuzzy suspension model is used to cope with the possible sprung mass variation. The output feedback control problem for active suspension system of IWM driven electric vehicles with actuator faults and time delay is further investigated. The suspended motor parameters and vehicle suspension parameters are optimized based on the particle swarm optimization. A robust output feedback H∞ controller is designed to guarantee the system’s asymptotic stability and simultaneously satisfying the performance constraints. The proposed output feedback controller reveals much better performance than previous work when different actuator thrust losses and time delay occurs. The road surface roughness is coupled with in-wheel switched reluctance motor air-gap eccentricity and the unbalanced residual vertical force. Coupling effects between road excitation and in wheel switched reluctance motor (SRM) on electric vehicle ride comfort are also analysed in this thesis. A hybrid control method including output feedback controller and SRM controller are designed to suppress SRM vibration and to prolong the SRM lifespan, while at the same time improving vehicle ride comfort. Then a state feedback H∞ controller combined with SRM controller is designed for in-wheel SRM driven electric vehicle with DVA structure to enhance vehicle and SRM performance. Simulation results demonstrate the effectiveness of DVA structure based active suspension system with proposed control method its ability to significantly improve the road holding capability and ride performance, as well as motor performance

Vibrational and stochastic resonances in driven nonlinear systems

Nonlinear systems are abundant in nature. Their dynamics have been extensively investigated due to their multidisciplinary applicability, ranging from all branches of physical and mathematical sciences to engineering as well as to life sciences and medicine. When driven by external forces, nonlinear systems can exhibit plethora of interesting and important properties - one of the most prominent being resonance. In the presence of a second, higher frequency, driving force, whether stochastic or deterministic/periodic, a resonance phenomenon arises that can generally be termed stochastic resonance or vibrational resonance. Operating a system in or out of resonance promises applications in several advanced technologies, such as the creation of novel materials at the nano, micro and macroscales including, but not limited to, materials having photonic band gaps, quantum control of atoms and molecules as well as miniature condensed matter systems. Motivated in part by these potential applications, this Theme Issue provides a concrete up-to-date overview of vibrational and stochastic resonances in driven nonlinear systems. It assembles state-of-the-art, original contributions on such induced resonances - addressing their analysis, occurrence, and applications from either the theoretical, numerical and experimental perspectives, or through combinations of these

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

This paper investigates the dynamical response of a nonlinear piezoelectric energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in sub- and super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case

Electromagnetic Biostimulation of Living Cultures for Biotechnology, Biofuel and Bioenergy Applications

The surge of interest in bioenergy has been marked with increasing efforts in research and development to identify new sources of biomass and to incorporate cutting-edge biotechnology to improve efficiency and increase yields. It is evident that various microorganisms will play an integral role in the development of this newly emerging industry, such as yeast for ethanol and Escherichia coli for fine chemical fermentation. However, it appears that microalgae have become the most promising prospect for biomass production due to their ability to grow fast, produce large quantities of lipids, carbohydrates and proteins, thrive in poor quality waters, sequester and recycle carbon dioxide from industrial flue gases and remove pollutants from industrial, agricultural and municipal wastewaters. In an attempt to better understand and manipulate microorganisms for optimum production capacity, many researchers have investigated alternative methods for stimulating their growth and metabolic behavior. One such novel approach is the use of electromagnetic fields for the stimulation of growth and metabolic cascades and controlling biochemical pathways. An effort has been made in this review to consolidate the information on the current status of biostimulation research to enhance microbial growth and metabolism using electromagnetic fields. It summarizes information on the biostimulatory effects on growth and other biological processes to obtain insight regarding factors and dosages that lead to the stimulation and also what kind of processes have been reportedly affected. Diverse mechanistic theories and explanations for biological effects of electromagnetic fields on intra and extracellular environment have been discussed. The foundations of biophysical interactions such as bioelectromagnetic and biophotonic communication and organization within living systems are expounded with special consideration for spatiotemporal aspects of electromagnetic topology, leading to the potential of multipolar electromagnetic systems. The future direction for the use of biostimulation using bioelectromagnetic, biophotonic and electrochemical methods have been proposed for biotechnology industries in general with emphasis on an holistic biofuel system encompassing production of algal biomass, its processing and conversion to biofuel

Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay

In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis