Nader Jalili

Robust Multiple Frequency Trajectory Tracking Control of Piezoelectrically Driven Micro/Nanopositioning Systems

A novel modeling and control methodology is proposed in this paper for real-time compensation of nonlinearities along with precision trajectory control of piezoelectric actuators in various range of frequency operation. By integrating a modified Prandtl-Ishlinskii hysteresis operator with a second-order linear dynamics, a nonlinear dynamic model and an inverse feedforward controller are developed and experimentally validated for a piezoelectrically driven nanopositioning stage. This modeling and control framework, however, lacks the accuracy due to the hysteresis model limitation, parametric uncertainties, and ever present unmodeled dynamics. Utilizing the sliding mode control strategy coupled with a perturbation estimation technique, a robust controller is then proposed for trajectory tracking of the actuator displacement. The controller gains are adjusted based on an intelligent comparison of the dynamic model and the control law. Eventually, the performance of the proposed controller is verified for the nanopositioning stage which is equipped with a high resolution capacitive position sensor. Experimental results demonstrate that the controller is capable of precisely tracking triangular and multiple frequency sinusoidal trajectories, which are common practices in many scanning probe microscopy systems.

Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages

Precision control of multiple-axis piezo-flexural stages used in a variety of scanning probe microscopy systems suffers not only from hysteresis nonlinearity, but also from parametric uncertainties and the cross-coupled motions of their axes. Motivated by these shortfalls, a Lyapunov-based control strategy is proposed in this article for simultaneous multiple-axis tracking control of piezo-flexural stages. A double-axis stage is considered for system analysis and controller validation. Hysteresis and coupling nonlinearities are studied through a number of experiments, and it is demonstrated that the widely used proportional-integral (PI) controller lacks accuracy in high-frequency tracking. Adopting the variable structure control method, a robust adaptive controller is then derived with its stability guaranteed through the Lyapunov criterion. It is shown that a parallelogram-type zone of attraction can be explicitly formed for the closed-loop system to which the error phase trajectory converges. Practical implementation of the controller demonstrates effective double-axis tracking control of the stage in the presence of hysteresis and coupling nonlinearities and despite parametric uncertainties for low-and high-frequency trajectories. Moreover, good agreements are achieved between the experiments and theoretical developments.

A Comparative Study and Analysis of Semi-Active Vibration-Control Systems

Semi-active (SA) vibration-control systems are those which otherwise passively generated damping or spring forces are modulated according to a parameter tuning policy with only a small amount of control effort. SA units, as their name implies, fill the gap between purely passive and fully active vibration-control systems and offer the reliability of passive systems, yet maintain the versatility and adaptability of fully active devices. During recent years there has been considerable interest towards practical implementation of these systems for their low energy requirement and cost. This paper briefly reviews the basic theoretical concepts for SA vibration-control design and implementation, and surveys recent developments and control techniques for these systems. Some related practical applications in vehicle suspensions are also presented.

A Lyapunov-based piezoelectric controller for flexible Cartesian robot manipulators

A Lyapunov-based control strategy is proposed for the regulation of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam with a translational base support. The beam (arm) cross-sectional area is assumed to be uniform and Euler-Bernoulli beam theory assumptions are considered. Moreover, two types of damping mechanisms; namely viscous and structural dampings, are considered for the arm material properties. The arm base motion is controlled utilizing a linear actuator, while a piezoelectric (PZT) patch actuator is bonded on the surface of the flexible beam for suppressing residual beam vibrations. The equations of motion for the system are obtained using Hamiltons principle, which are based on the original infinite dimensional distributed system. Utilizing the Lyapunov method, the control force acting on the linear actuator and control voltage for the PZT actuator are designed such that the base is regulated to a desired set-point and the exponential stability of the system is attained. Depending on the composition of the controller, some favorable features appear such as elimination of control spillovers, controller convergence at finite time, suppression of residual oscillations and simplicity of the control implementation. The feasibility of the controller is validated through both numerical simulations and experimental testing.

Piezoelectric-Based Vibration Control

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Modeling, Nonlinear Dynamics, and Identification of a Piezoelectrically Actuated Microcantilever Sensor

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Reinforcement of Piezoelectric Polymers with Carbon Nanotubes: Pathway to Next-generation Sensors

Nanomechanical cantilever sensors (NMCSs) have recently emerged as an effective means for label-free chemical and biological species detection. They operate through the adsorption of species on the functionalized surface of mechanical cantilevers. Through this functionalization, molecular recognition is directly transduced into a micromechanical response. In order to effectively utilize these sensors in practice and correctly relate the micromechanical response to the associated adsorbed species, the chief technical issues related to modeling must be resolved. Along these lines, this paper presents a general nonlinear-comprehensive modeling framework for piezoelectrically actuated microcantilevers and validates it experimentally. The proposed model considers both longitudinal and flexural vibrations and their coupling in addition to the ever-present geometric and material nonlinearities. Utilizing Euler-Bernoulli beam theory and employing the inextensibility conditions, the coupled longitudinal-flexural equations of motion are reduced to one nonlinear partial differential equation describing the flexural vibrations of the sensor. Using a Galerkian expansion, the resulting equation is discretized into a set of nonlinear ordinary differential equations. The method of multiple scales is then implemented to analytically construct the nonlinear response of the sensor near the first modal frequency (primary resonance of the first vibration mode). These solutions are compared to experimental results demonstrating that the sensor exhibits a softening-type nonlinear response. Such behavior can be attributed to the presence of quadratic material nonlinearities in the piezoelectric layer. This observation is critical, as it suggests that unlike macrocantilevers where the geometric hardening nonlinearities dominate the response behavior, material nonlinearities dominate the response of microcantilevers yielding a softening-type response. This behavior should be accounted for when designing and employing such sensors for practical applications.

A Fresh Insight Into the Microcantilever-Sample Interaction Problem in Non-Contact Atomic Force Microscopy

Piezoelectric polymers such as poly(vinylidene fluoride) (PVDF) are being currently utilized as low-cost sensors in many structural vibration control applications and measurements. Their low electromechanical coupling coefficient, however, has always been a concern when utilized in different applications. In order to remedy this, carbon nanotubes, known for their extraordinary properties, can be mixed with such piezoelectric polymers as they have the potential to improve the electromechanical response of these polymers. Along this line of reasoning, different types of nanotubes; namely, single-walled and multiwalled are blended with a copolymer of PVDF. Through extensive experimental vibration testing and theoretical verification, it is found that the nanotube-based polymers yield better response characteristics than those of the plain piezoelectric polymers. More specifically, it is demonstrated that the dominant mechanism responsible for improved sensing performance is the increased Young’s modulus of elasticity of the nanotube-based polymer for the samples considered here. The significant change in properties of these piezoelectric polymers with different fabrication conditions and nanotube addition, though provokes doubts about standardization, creates a pathway for the development of next-generation sensors with enhanced or entirely new properties.

Functional Nanotube-based Textiles: Pathway to Next Generation Fabrics with Enhanced Sensing Capabilities:

The atomic force microscope (AFM) system has evolved into a useful tool for direct measurements of intermolecular forces with atomic-resolution characterization that can be employed in a broad spectrum of applications. The non-contact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy, especially when utilized for reliable measurements of soft samples (e.g., biological species). Current AFM imaging techniques are often based on a lumped-parameters model and ordinary differential equation (ODE) representation of the micro-cantilevers coupled with an adhoc method for atomic interaction force estimation (especially in non-contact mode). Since the magnitude of the interaction force lies within the range of nano-Newtons to pica-Newtons, precise estimation of the atomic force is crucial for accurate topographical imaging. In contrast to the previously utilized lumped modeling methods, this paper aims at improving current AFM measurement technique through developing a general distributed-parameters base modeling approach that reveals greater insight into the fundamental characteristics of the microcantilever-sample interaction. For this, the governing equations of motion are derived in the global coordinates via the Hamiltons Extended Principle. An interaction force identification scheme is then designed based on the original infinite dimensional distributed-parameters system which, in turn, reveals the unmeasurable distance between AFM tip and sample surface. Numerical simulations are provided to support these claims.

Modeling and experimental vibration analysis of nanomechanical cantilever active probes

With a surge in technological advancements and the needs of diverse communities such as consumers, military and navy, the textile industry is shifting its focus to fabrication of next-generation textiles that not only meet the basic conventional requirements, but also serve a host of other functions. In this pursuit of fabricating next-generation textiles, called here e-textiles (electronic textiles), a novel technique is presented to produce nanocomposite fabrics made from carbon nanotubes (CNTs) with enhanced sensing capabilities. Catering to the ever increasing demand of improved sensors, this work discusses the electrospinning fabrication scheme that has been employed to develop novel CNT-based piezoelectric strain sensors. The resulting sensors have been characterized by performing structural vibration experiments to evaluate their strain-sensing performance. When these new CNT-based piezopolymer composites are electrospun into smart fabrics, the strain-sensing ability (as measured by voltage across the sensor) is increased by a dramatic 35 times, from 2.4 to 84.5 mV for 0.05 wt% of the nanotubes. The dominant mechanism responsible for such improvement is found to be the alignment of dipoles in the piezoelectric material. Such alignment is mainly attributed due to ability of the electrospinning process to generate very thin fibers from polymer-nanotube solution. The direct and reverse conversion of electrical energy into mechanical energy in the proposed sensors can create a platform for developing next-generation smart fabric with applications in membrane structures, distributed shape modulation and energy harvesting.