arXiv subjects

Tarunraj Singh

Publications and source records attributed to Tarunraj Singh.

13 recordsLinked to original sources

arXiv2026

Time-Optimal Operation of a Load-Hoisting Gantry Crane

This paper addresses the problem of designing time-optimal control profiles for point-to-point control of a gantry crane moving in a two dimensional plane. It is assumed that the hoisting motor completes the hoisting maneuver at a constant rate and completes its transition in the same time that it takes for the cart to reach its terminal position. This results in a linear time-varying model and a closed form solution to the time-optimal control problem is shown to be parameterized with Bessel functions. A comprehensive analysis of the structure of the time-optimal control profile is studied by examining the switching function which illustrates the mechanism of introduction and decimation of switches in the bang-off-bang control profile. The variation of the number of switches in the optimal control profile is presented and a non-intuitive control profile structure is noted, one which initiates with a stationary cart, while the hoisting cable length is changed prior to the initiation of motion of the cart. To address the issue of uncertainties in the initial cable length, a model with the sensitivity of the system states with respect to the initial cable length is used to augment the system model and is used for the design of robust time-optimal controllers. Experimental results validate the time-optimal and robust time-optimal control profiles.

eess.SY↗

arXiv2024

Analytical Gradient and Hessian Evaluation for System Identification using State-Parameter Transition Tensors

In this work, the Einstein notation is utilized to synthesize state and parameter transition matrices, by solving a set of ordinary differential equations. Additionally, for the system identification problem, it has been demonstrated that the gradient and Hessian of a cost function can be analytically constructed using the same matrix and tensor metrics. A general gradientbased optimization problem is then posed to identify unknown system parameters and unknown initial conditions. Here, the analytical gradient and Hessian of the cost function are derived using these state and parameter transition matrices. The more robust performance of the proposed method for identifying unknown system parameters and unknown initial conditions over an existing conventional quasi-Newton method-based system identification toolbox (available in MATLAB) is demonstrated by using two widely used benchmark datasets from real dynamic systems. In the existing toolbox, gradient and Hessian information, which are derived using a finite difference method, are more susceptible to numerical errors compared to the analytical approach presented. Keywords: Gradient-based Optimization, Transition matrix and tensors, Gradient and Hessian, System identification.

eess.SY↗

arXiv2023

Dynamic Instability of Follower Forced Euler Bernoulli Cantilever Beam With Tip Mass

This work focuses on the stability analysis of an Euler Bernoulli cantilever beam with a tip mass at the free end, subject to a follower force. This can serve as a viable model for analysis of elastic instability occurring due to fluid-structure interaction of structural components submerged in fluids and gases. A linear model with appropriate boundary conditions is developed using the energy formulation. The characteristic equation of the linear model establishes the relationship between the pulsation of the beam and the magnitude of applied follower force. The evolution of temporal eigenvalues with respect to the magnitude of the follower force helps in evaluation of the critical follower forces responsible for different modes of instability. The presented model demonstrates the existence of only dynamic instability in the system. Furthermore, the model predicts that both types of the dynamic instability i.e., flutter and divergence, are possible in the system.

physics.class-ph↗

arXiv2023

From Playground Swings to Sway Control of Cranes: An Active Pendulum Experiment

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 include: 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.

physics.ed-ph↗

arXiv2023

Minimum Time Control of a Gantry Crane System with Rate Constraints

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.

eess.SY↗

arXiv2023

Shapley Effect Estimation using Polynomial Chaos

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.

stat.AP↗

arXiv2022

Energy-Time Optimal Control of Wheeled Mobile Robots

This paper focuses on the energy-time optimal control of wheeled mobile robots undergoing point-to-point transitions in an obstacles free space. Two interchangeable models are used to arrive at the necessary conditions for optimality. The first formulation exploits the Hamiltonian, while the second formulation considers the first variation of the augmented cost to derive the necessary conditions for optimality. Jacobi elliptic functions are shown to parameterize the closed form solutions for the states, control and costates. Analysis of the optimal control reveal that they are constrained to lie on a cylinder whose circular cross-section is a function of the weight penalizing the relative costs of time and energy. The evolving optimal costates for the second formulation are shown to lie on the intersection of two cylinders. The optimal control for the wheeled mobile robot undergoing point-to-point motion is also developed where the linear velocity is constrained to be time-invariant. It is shown that the costates are constrained to lie on the intersection of a cylinder and an extruded parabola. Numerical results for various point-to-point maneuvers are presented to illustrate the change in the structure of the optimal trajectories as a function of the relative location of the terminal and initial states.

cs.RO↗

arXiv2020

Identifying Weakly Connected Subsystems in Building Energy Model for Effective Load Estimation in Presence of Parametric Uncertainty

It is necessary to estimate the expected energy usage of a building to determine how to reduce energy usage. The expected energy usage of a building can be reliably simulated using a Building Energy Model (BEM). Many of the numerous input parameters in a BEM are uncertain. To ensure that the building simulation is sufficiently accurate, and to better understand the impact of imprecisions in the input parameters and calculation methods, it is desirable to quantify uncertainty in the BEM throughout the modeling process. Uncertainty quantification (UQ) typically requires a large number of simulations to produce meaningful data, which, due to the vast number of input parameters and the dynamic nature of building simulation, is computationally expensive. Uncertainty Quantification (UQ) in BEM domain is thus intractable due to the size of the problem and parameters involved and hence it needs an advanced methodology for analysis. The current paper outlines a novel Weakly-Connected-Systems (WCSs) identification-based UQ framework developed to propagate the quantifiable uncertainty in the BEM. The overall approach is demonstrated on the physics-based thermal model of an actual building in Central New York.

cs.CE↗

arXiv2020

Reduced-order modeling using Dynamic Mode Decomposition and Least Angle Regression

Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Regression (LARS). We modify LARS to be complex-valued and utilize LARS to select DMD modes. We refer to the resulting algorithm as Least Angle Regression for Dynamic Mode Decomposition (LARS4DMD). Sparsity-Promoting Dynamic Mode Decomposition (DMDSP), a popular mode-selection algorithm, serves as a benchmark for comparison. Numerical results from a Poiseuille flow test problem show that LARS4DMD yields reduced-order models that have comparable performance to DMDSP. LARS4DMD has the added benefit that the regularization weighting parameter required for DMDSP is not needed.

stat.ML↗

arXiv2011

Comparison of SCIPUFF Plume Prediction with Particle Filter Assimilated Prediction for Dipole Pride 26 Data

This paper presents the application of a particle filter for data assimilation in the context of puff-based dispersion models. Particle filters provide estimates of the higher moments, and are well suited for strongly nonlinear and/or non-Gaussian models. The Gaussian puff model SCIPUFF, is used in predicting the chemical concentration field after a chemical incident. This model is highly nonlinear and evolves with variable state dimension and, after sufficient time, high dimensionality. While the particle filter formalism naturally supports variable state dimensionality high dimensionality represents a challenge in selecting an adequate number of particles, especially for the Bootstrap version. We present an implementation of the Bootstrap particle filter and compare its performance with the SCIPUFF predictions. Both the model and the Particle Filter are evaluated on the Dipole Pride 26 experimental data. Since there is no available ground truth, the data has been divided in two sets: training and testing. We show that even with a modest number of particles, the Bootstrap particle filter provides better estimates of the concentration field compared with the process model, without excessive increase in computational complexity.

stat.AP↗

arXiv2011

Decision Based Uncertainty Propagation Using Adaptive Gaussian Mixtures

Given a decision process based on the approximate probability density function returned by a data assimilation algorithm, an interaction level between the decision making level and the data assimilation level is designed to incorporate the information held by the decision maker into the data assimilation process. Here the information held by the decision maker is a loss function at a decision time which maps the state space onto real numbers which represent the threat associated with different possible outcomes or states. The new probability density function obtained will address the region of interest, the area in the state space with the highest threat, and will provide overall a better approximation to the true conditional probability density function within it. The approximation used for the probability density function is a Gaussian mixture and a numerical example is presented to illustrate the concept.

stat.CO↗

arXiv2011

Approximate Interval Method for Epistemic Uncertainty Propagation using Polynomial Chaos and Evidence Theory

The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probability distributions, the intuition is to quantify the uncertainty in the response using Polynomial Chaos expansion and discard all the information provided about the randomness of the output and extract only the bounds of its compact support. To solve for the bounding range of polynomials, we transform the Polynomial Chaos expansion in the Bernstein form, and use the range enclosure property of Bernstein polynomials to find the minimum and maximum value of the response. This procedure is used to propagate Dempster-Shafer structures on closed intervals through nonlinear functions and it is applied on an algebraic challenge problem.

stat.CO↗

arXiv2011

Approximate Propagation of both Epistemic and Aleatory Uncertainty through Dynamic Systems

When ignorance due to the lack of knowledge, modeled as epistemic uncertainty using Dempster-Shafer structures on closed intervals, is present in the model parameters, a new uncertainty propagation method is necessary to propagate both aleatory and epistemic uncertainty. The new framework proposed here, combines both epistemic and aleatory uncertainty into a second-order uncertainty representation which is propagated through a dynamic system driven by white noise. First, a finite parametrization is chosen to model the aleatory uncertainty by choosing a representative approximation to the probability density function conditioned on epistemic variables. The epistemic uncertainty is then propagated through the moment evolution equations of the conditional probability density function. This way we are able to model the ignorance when the knowledge about the system is incomplete. The output of the system is a Dempster-Shafer structure on sets of cumulative distributions which can be combined using different rules of combination and eventually transformed into a singleton cumulative distribution function using Smets' pignistic transformation when decision making is needed.

stat.ME↗