This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the ...velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. As a comparison to the proposed controller, an acceleration constrained time-optimal control is analyzed which as expected demands a larger maneuver time. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.
This dissertation focuses on precision motion control of vibratory systems in the presence of model parameter uncertainties. The use of local sensitivity and global sensitivity measure in the design ...of robust control profiles for point-to-point motion are explored. Extensive experimental validation is used to validate the simulation results and generate statistical measures of the output of the tests. The dissertation starts with the exploration of minimum-time point-to-point motion control of a gantry crane system with velocity bounds. Optimal control theory is used to guide the synthesis of optimal bang-off-bang profiles control profiles whose parameters are solved by formulating a nonlinear programming problem. Sensitivity states are used to augment the system model for the synthesis of robust motion control profiles. Experimental validation is performed on a two-degree-of-freedom gantry crane system with a suspended payload which includes a mechanism to consistently vary the length of the pendulum to emulate uncertainties in the natural frequency of vibration of the pendulum. Box and whisker charts are used to illustrate and compare the performance of the time-optimal and robust time-optimal controllers. The second approach proposed for precision motion control profiles are FIR filters which target an uncertain low frequency mode of vibration and can deal with higher modes of excitation as unmodeled dynamics. Magnitude constraints in the frequency domain are imposed in a convex programming framework to ensure attenuation of dominant resonant modes and minimal excitation of high-frequency unmodeled modes. Different cost functions for filter optimization, filter lengths, transition widths, and robustness in the notch area are studied too. Experimental validation is conducted using a clamped beam with a tip mass, comparing time-delay filters with the proposed Finite Impulse Response filters. The third contribution related to precision motion control focuses on real-time estimation of modal parameters to permit an adaptive input-shaping design to regulate payloads of gantry cranes undergoing point-to-point maneuvers. The modal parameter estimation is enabled by the use of computer vision and ArUco markers and the experiments illustrate the feasibility of real-time estimation and control of uncertain vibratory systems. Another core contribution of this dissertation is the synthesis of a new global sensitivity measure based on Shapley effects. This is a variance-based metric which involves evaluation of numerous marginal contributions of uncertain variables to characterize the uncertainties in the output of interest. Benchmark problems are studied to gauge the performance of the Shapley-based measure and Shapley effects are shown to routinely outperform Sobol indices in correctly rank ordering the importance of uncertain variables. Since the Monte Carlo cost of evaluating Shapley effects is high, polynomial chaos based surrogate models are developed and Shapley effects are shown to be algebraic maps of the polynomial chaos coefficients. The Shapley effects are used to illustrate a robust design using a Euler-Bernoulli beam with two lumped masses, where the locations of the masses are uncertain. The aim is to minimize or maximize the impact uncertain second mass location on the second mode of the beam structure. Finally, a controller design approach is proposed based on Shapley effects where it is experimentally confirmed that Shapley-based controller designs outperform the traditional time-delay filter structure when uncertainty is applied to both lumped masses.
The center of percussion is an essential physics concept with a variety of practical applications. For any handheld object there is a point that, once a force is applied to it, results in no ...acceleration at the hands because the translational and angular accelerations from the force cancel each other out. This point is referred to as the center of percussion. Although the concept of the center of percussion is applicable to a variety of different areas, this paper focuses on America’s favorite pastime; the sport of baseball. The center of percussion of a baseball bat, also referred to as the “sweet spot”, is the optimal spot for making contact with a moving baseball. This paper demonstrates the development of a tabletop model for visually explaining this process of identifying the center of percussion to an audience. The setup is an instrumented experiment with an integrated data acquisition system to collect, visualize, and analyze the data for the demonstration of the process to identify a baseball bat’s center of percussion.
Dynamics is a core discipline in Mechanical and Aerospace Engineering programs and with the ubiquitous nature of control in modern-day applications, the field of mechatronics has gained popularity. ...Mechatronics refers to the field of engineering which integrates the engineering disciplines of mechanical, control, electronics, and computing. To create a testbed to illustrate a tabletop mechatronics system, the paper details the design, and fabrication of an active pendulum whose length can be changed in real-time using solenoids. This permits illustrating two concepts: (1) damping of pendulum oscillations which emulates the sway of a crane and (2) amplification of the oscillations which emulates the pumping of a playground swing. The paper describes the steps prior to experimental validation which includes: modeling, system identification, signal processing, and controller implementation. Numerical simulations are used to prototype the controller and eventually to compare the simulation results to the experimental ones. The results of all the experiments illustrate a close match between the simulated and experimental results. To permit reproduction of the experiment, the design details and code to implement the controllers are posted in a public repository.
This paper focuses on the development of a global sensitivity based design of robust input shapers. The Derivative-based Global Sensitivity Measure (DGSM) which consists of the expected value of the ...absolute value of the gradient of the terminal residual energy with respect to the uncertain parameters, is used to tradeoff performance to robustness. A multi-objective cost function which is a convex combination of the terminal residual energy for rest-to-rest maneuvers and the DGSM, is used to design robust input shapers. The proposed approach is illustrated on a single spring-mass-dashpot system and the benchmark floating oscillator. As compared to the traditional Zero Vibration Derivative Input Shaper, the proposed approach is demonstrated to reduce the average residual energy over the domain of uncertainty.
This paper focuses on the development of minimum time control profiles for point-to-point motion of a gantry crane system in the presence of uncertainties in modal parameters. Assuming that the ...velocity of the trolley of the crane can be commanded and is subject to limits, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system from a point of rest to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied. As the magnitude of the rigid body displacement is increased, the collapse and birthing of switches in the optimal control profile are observed and explained. Robustness to uncertainties in modal parameters is accounted for by forcing the state sensitivities at the terminal time to zero. The observation that the time-optimal control profile merges with the robust time-optimal control is noted for specific terminal displacements and the migration of zeros of the time-delay filter parameterizing the optimal control profile are used to explain this counter intuitive result. A two degree of freedom gantry crane system is used to experimentally validate the observations of the numerical studies and the tradeoff of increase in maneuver time to the reduction of residual vibrations is experimentally illustrated.
This paper presents an approach for estimating Shapley effects for use as global sensitivity metrics to quantify the relative importance of uncertain model parameters. Polynomial Chaos expansion, a ...well established approach for developing surrogate models is proposed to be used to estimate Shapley effects. Polynomial Chaos permits the transformation of a stochastic process to a deterministic model which can then be used to efficiently evaluate statistical moments of the quantity of interest. These moments include conditional variances which are algebraically mapped to Shapley effects. The polynomial chaos based estimates of Shapley effects are validated using Monte Carlo simulations and tested on the benchmark Ishigami function and on the dynamic SEIR epidemic model and the Bergman Type 1 diabetes model. The results illustrate the correct ranking of uncertain variables for the Ishigami function in contrast to the Sobol indices and illustrates the time-varying rank ordering of the model parameters for the dynamic models.
The focus of this work is on the development of a model for a gantry crane transporting a non point-mass payload such as pipes, where besides the payload swinging, includes the twisting motion also, ...which can be hazardous if not adequately controlled. Euler-Lagrange equations of motion are derived which permit accounting for payloads whose center of mass does not coincide with the hoisting cable attachment. Work-Energy principle is used to ensure that a collocated Proportional-Derivative (PD)-controller is stabilizing and an input shaper is used to shape the reference profile to permit minimal residual vibration of the payload.
Silicon nanostructures are synthesized with a DC atmospheric pressure microplasma jet using an Ar/SiH4/H2 gas mixture. The plasma is characterized by OES and imaged using an EMCCD camera. The effect ...of hydrogen admixture to the formed structures is studied by transmission electron microscopy. Under specific conditions, crystalline silicon nanoparticles grow in an amorphous matrix investigated by electron energy loss spectroscopy. As‐grown silicon nanoparticles are collected in ethanol for dynamic light scattering and photoluminescence measurements. The size distribution peaks at 4 nm. The silicon nanocrystals exhibit roomtemperature photoluminescence that peaks at ∼415 and ∼465 nm.
This article reports results regarding the use of a microplasma jet as a generation tool for silicon nanostructures. We demonstrate that the microplasma source can be used to form silicon nanocrystals at atmospheric pressure using a gas mixture of Ar/SiH4/H2. Further, the role of hydrogen admixture in the particle generation process is investigated. This work contributes to the understanding of silicon nanocrystal generation mechanism in non‐equilibrium atmospheric pressure microplasmas.
The focus of this paper is on the development of velocity constrained time-optimal control profiles for point-to-point motion of a gantry crane system. Assuming that the velocity of the trolley of ...the crane can be commanded, an optimal control problem is posed to determine the bang-off-bang control profile to transition the system to the terminal states with no residual vibrations. Both undamped and underdamped systems are considered and the variation of the structure of the optimal control profiles as a function of the final displacement is studied and the collapse and birthing of switches in the control profile are explained. To account for uncertainties in model parameters, a robust controller design is posed and the tradeoff of increase in maneuver time to the reduction of residual vibrations is illustrated.
