Mohsen Dadfarnia

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.

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

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.

Lyapunov-Based Vibration Control of Translational Euler-Bernoulli Beams Using the Stabilizing Effect of Beam Damping Mechanisms

A translational cantilevered Euler-Bernoulli beam with tip mass dynamics at its free end is used to study the effect of several damping mechanisms on the stabilization of the beam displacement. Specifically, a Lyapunov-based controller utilizing a partial differential equation model of the translational beam is developed to exponentially stabilize the beam displacement while the beam support is regulated to a desired set-point position. Depending on the composition of the tip mass dynamics assumption (i.e. body-mass, point-mass, or massless). it is shown that proper combination of different damping mechanisms (i.e. strain-rate, structural, or viscous damping) guarantees exponential stability of the beam displacement. This novel Lyapunov-based approach. which is based on the energy dissipation mechanism in the beam, brings new dimensions to the stabilization problem of translational beams with tip mass dynamics. The stability analysis utilizes relatively simple mathematical tools to illustrate the exponential and asymptotic stability results. The numerical results are presented to show the effectiveness of the controller.

A piezoelectric driven ratchet actuator mechanism with application to automotive engine valves

Abstract Increasing demands on the performance of internal combustion engines, specifically automobile engines, require the production of more mechanical energy for a given amount of chemical fuel with reduced tailpipe emissions. Of particular interest in the development of high performance/low emission engines is the control and timing of individual engine valves. This paper investigates the design of an innovative piezoelectric ceramic (PZT) based actuator mechanism with a novel stepping motion amplifier to deliver force and displacement at higher magnitudes and operating frequencies. The target application is an engine valve train which traditionally uses cam-based lifter driven rocker arms to regulate the cylinders’ intake and exhaust valve motion. The proposed PZT-based actuator mechanism introduces a high frequency, lightweight, precise position solution for cylinder-by-cylinder variable valve timing. Numerical results are provided to demonstrate the feasibility of a PZT-based/camless valve train. The new valve train demonstrates similar cam-based performance characteristics while enabling computer controlled individual valve timing opportunities.

Adaptive non model-based piezoelectric control of flexible beams with translational base

An adaptive, nonmodel-based controller is proposed for the tracking control of a flexible cantilever beam with a translational base support. A piezoelectric (PZT) patch actuator is bonded on the top surface of the beam to apply a controlled moment for vibration suppression requirement. By selecting a Lyapunov function candidate based on a very simple energy relationship, an adaptive nonlinear feedback gain for the PZT input voltage and a simple PD controller for the moving base input force are designed to make the closed-loop system energy dissipative and hence stable. Due to the non model-based nature of the controller, some favorable features appear such as elimination of control spillovers, suppression of residual oscillations of the beam and simplicity of the control implementation. The feasibility of the controller is demonstrated using numerical simulations. Although the controller derivation is based on the original distributed partial differential model, a two-node finite element model is used for the numerical solution of the coupled PDE of the system.

Lyapunov-based piezoelectric control of flexible cartesian robot manipulators

A Lyapunov-based control strategy is proposed for regulating problem of a Cartesian robot manipulator, which is modeled as a flexible cantilever beam arm with a translational base support. The 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. 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 base 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. The feasibility of the controller is validated through numerical simulations.

A new software tool for synthesis of linear PID controllers

A new versatile software utility for synthesis of linear PID controllers is described, and the software listing is presented. The software is in the MATLAB environment. Closed-form PID controller gain design equations are developed. The design approach is systematic, and it is based on frequency matching technique with a model matching criteria. The objective is to design a closed-loop feedback system with a PID controller whose dynamic and static behavior would mimic a user-defined reference linear model. The design procedure is automated via a new MATLAB command. The software also has applications in synthesis of nonlinear PID controllers. Because the design equations are of a closed form, the speed of calculations is high; therefore, design software may be used in designing self-tuning adaptive PID controllers.

Distributed-Parameters Base Modeling and Vibration Analysis of Micro-Cantilevers Used in Atomic Force Microscopy

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 such as electronics, semi-conductors, materials, manufacturing, polymers, biological analysis, and biomaterials. The noncontact AFM offers unique advantages over other contemporary scanning probe techniques such as contact AFM and scanning tunneling microscopy. 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 ad-hoc 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 Hamilton’s Extended Principle. By properly selecting a set of general coordinates, the resulting non-homogenous boundary value problem is then converted to a homogenous one, and hence, analytically solvable. The AFM controller can then be designed based on the original infinite dimensional distributed-parameters system which, in turn, removes some of the disadvantages associated with the truncated-model base controllers such as control spillovers, residual oscillations and increased order of the control. Numerical simulations are provided to support these claims.Copyright

An Investigation of Damping Mechanisms in Translational Euler-Bernoulli Beams Using a Lyapunov-Based Stability Approach

A translational cantilevered Euler-Bernoulli beam with tip mass dynamics at its free end is used to study the effect of several damping mechanisms on the stabilization of the beam displacement. Specifically, a Lyapunov-based controller utilizing a partial differential equation model of the translational beam is developed to exponentially stabilize the beam displacement while the beam support is regulated to a desired set-point position. Depending on the composition of the tip mass dynamics assumption (i.e. body-mass, point-mass, or massless), it is shown that proper combination of different damping mechanisms (i.e., strain-rate, structural, or viscous damping) guarantees exponential stability of the beam displacement. This novel Lyapunov-based approach, which is based on the energy dissipation mechanism in the beam, brings new dimensions to the stabilization problem of translational beams with tip mass dynamics. The stability analysis utilizes relatively simple mathematical tools to illustrate the exponential and asymptotic stability results. The numerical results are presented to show the effectiveness of the controller.Copyright

A Reduced-Order Observer Based Piezoelectric Control of Flexible Cartesian (SCARA) Robot Manipulator

An observer based control strategy is proposed for a flexible Cartesian (SCARA) Robot which is modeled as a flexible cantilever beam with a translational base support. A piezoelectric (PZT) patch actuator is bonded on the top surface of the flexible arm to apply a controlled moment for vibration suppression requirement. Utilizing three measurable quantities (i.e., the base displacement, arm tip deflection and the strain at the root end of the arm), a reduced-order observer is designed to estimate the velocity related variables, which are not measurable. A simple PD controller is selected for the moving base regulation control, while a Lyapunov function candidate based on a very simple energy relationship is utilized for the PZT input voltage to make the closed-loop system energy dissipative and hence stable. In this paper, the PZT input voltage control uses the velocity related signals estimated by the reduced-order observer, which makes the control structure simpler. The feasibility of the controller is validated by the numerical simulations and experimental results.Copyright