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Nonlinear Dynamics and PD Control of a Cantilevered Nanomanipulator
Nonlinear Dynamics and PD Control of a Cantilevered Nanomanipulator
Graduate Research, Rice University
Department of Mechanical Engineering and Material Science
Advisor: Dr. Fathi Ghorbel
Overview
This research focused on the modeling, analysis, and control of a piezoelectric cantilevered nanomanipulator, such as the probe of an Atomic Force Microscope (AFM), used for manipulating objects at the nanoscale. The manipulation process at this scale is governed by nonlinear interaction forces, such as van der Waals and adhesion forces, which significantly affect system dynamics and stability.
Objectives
Develop a nonlinear dynamic model of a cantilevered nanomanipulator.
Analyze system behavior under nonlinear forces and disturbances.
Design a control strategy to enable precise, stable manipulation of nanoscale targets.
Key Contributions
Modeled the nonlinear dynamics of a piezoelectric nanomanipulator, incorporating nonlinear interaction forces and flexible dynamics.
Conducted Lyapunov-based stability analysis to examine equilibrium states and ensure bounded system behavior.
Investigated the effects of parameter variations (stiffness, damping, actuation gain) and disturbance forces (e.g., stick-slip motion) on system performance.
Implemented and optimized a Proportional-Derivative (PD) control law to minimize displacement error and counteract the influence of nano-scale disturbance forces.
Demonstrated that active modulation of probe stiffness enabled improved control authority and system responsiveness during manipulation tasks.
Impact
This research provided a foundation for precision control of AFM probes and other nanomanipulators in applications such as nanoassembly, surface characterization, and biological manipulation. The modeling approach and control framework contribute to enabling stable and accurate manipulation at atomic and molecular scales.
Educational Tool To Visualize & Learn Numerical Methods for Solving Nonlinear Equations
Educational Tool To Visualize & Learn Numerical Methods for Solving Nonlinear Equations
Graduate Research, Rice University
Department of Mechanical Engineering and Material Science
Overview
Developed an interactive MATLAB-based graphical user interface (GUI) designed to enhance conceptual understanding of iterative methods for solving nonlinear equations, including:
Bisection Method
Newton-Raphson Method
Secant Method
Fixed Point Iteration
The tool allows users to visually explore convergence behavior, sensitivity to initial guesses, and rate of convergence, helping demystify numerical techniques often perceived as abstract.
Key Features
Real-time graphical updates to show function plots and iteration steps
User-controlled parameters for initial guesses, tolerances, and method selection
Embedded error tracking and convergence feedback
Impact
Optimized the GUI design based on user experience testing involving students from various departments at Rice University, including Mechanical Engineering, Chemical Engineering, and Applied Mathematics.
Adopted in teaching and tutoring contexts to promote interactive, visual-first learning of numerical methods.
Hopf Bifurcation and Nonlinear Dynamics in the Global Financial System
Hopf Bifurcation and Nonlinear Dynamics in the Global Financial System
Graduate Research, Rice University
Department of Mechanical Engineering and Material Science
Overview
Conducted a theoretical and computational study of the nonlinear dynamic behavior of the global financial system, focusing on how instabilities and transitions can emerge from complex interdependencies among macroeconomic variables.
Key Contributions
Developed a nonlinear dynamical system model representing key interactions within the global financial system.
Performed an analytical derivation of Hopf bifurcation conditions, identifying the onset of periodic or oscillatory behavior due to changes in system parameters.
Applied the finite difference method to simulate the modulation equations, verifying the occurrence and characteristics of the bifurcation.
Simulated the effects of parametric perturbations (e.g., interest rates, investment rates, global capital flows) and analyzed their influence on system stability and dynamic response.
Impact
Provided insights into the emergence of cycles and instability in financial systems under seemingly stable operating conditions.
Demonstrated how nonlinear effects and bifurcations can be used to understand systemic risk and global financial fragility.
The framework may inform policy modeling and risk mitigation strategies in macroeconomic planning.
Exhaust-Driven Adsorption Air-Conditioning System for Automotive Applications
Exhaust-Driven Adsorption Air-Conditioning System for Automotive Applications
Undergraduate Research, Veermata Jijabai Technological Institute (VJTI)
Department of Mechanical Engineering
Overview
This project focused on designing an energy-efficient automotive air-conditioning system that operates without a compressor by utilizing waste heat from engine exhaust to drive an adsorption-based refrigeration cycle. The goal was to reduce the engine's parasitic load and improve fuel efficiency without compromising cooling performance.
Key Contributions
Developed a thermodynamic performance model of the adsorption-based air-conditioning system for a typical 6-seater Sports Utility Vehicle (SUV).
Designed and synthesized a novel adsorbent–refrigerant pair, optimized to maximize the coefficient of performance (COP) of the system.
Constructed and tested a functioning prototype, validating its performance under a range of ambient humidity and temperature conditions.
Generated performance curves and operating envelopes, demonstrating the viability of exhaust heat–powered cooling across diverse climates.
Impact
Provided a sustainable alternative to engine-driven vapor compression systems in automobiles.
Demonstrated that adsorption-based cooling systems can operate effectively using low-grade waste heat, potentially improving overall vehicle energy efficiency.
Contributed to green automotive design by eliminating refrigerant compressors and reducing greenhouse gas emissions associated with conventional AC systems.
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