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ABSTRACT This paper introduces a novel robust design approach aimed at reducing the sensitivity of a target metric to parameter uncertainties. Using Shapley effects from game theory as a global sensitivity proxy, we analyze a clamped‐free Euler‐Bernoulli beam with two uncertain mass positions. The first case study reduces sensitivity of the second mode frequency to mass location uncertainty and is validated experimentally on a gantry‐suspended beam. In the second case, a robust controller minimizes the Shapley effect of residual energy on mass location uncertainty. Our approach significantly reduces average residual energy compared to traditional Zero Vibration Derivative Input Shapers, as confirmed by experiments. 

Abstract This paper explores design of finite impulse response (FIR) filters for controlling underdamped systems while dealing with uncertainties in model parameters. By setting magnitude constraints in the frequency domain within a convex programing framework, it ensures that dominant resonant modes are attenuated at the end of the maneuver, high-frequency unmodeled modes are not excited, and there is no inordinate accentuation of frequencies in the passband of the filter. A mobile platform with an attached flexible beam serves as a testbed to validate the designs for rest to rest maneuvers, demonstrating how different cost functions of error between the desired and optimized magnitude response affect the filter performance. The study also examines robustness in the notch area by shifting the natural frequencies of the system by shifting a tip mass at the free end of the beam. The total energy at the final maneuver time of the first three system modes is calculated as a vibration suppression metric and is used to compare established input shapers with the proposed finite impulse response filters. 

This work presents a real-time time-delay filtering approach for reference shaping of high precision motion control of vibratory systems. The motion of the system is initiated with a judicious (arbitrary) step command and the acquired motion data is used to estimate the modal parameters in realtime.The modal data is subsequently used to synthesize the subsequent step commands to mitigate the residual vibrations. The proposed control algorithm is tested on a gantry crane structure with a suspended payload. Our method estimates the system parameters based on computer vision while tracking an ArUco fiducial marker which is integral with the payload. Computational efficiency is ensured by using C++ to deploy the algorithm. The goal is to minimize the residual energy at the terminal displacement for rest-to-rest maneuvers of a suspended payload with unknown dynamics. An inertial measurement unit is used to track the pendular angular velocity at the end of the maneuver and is not used in the model identification process. 

This paper introduces an algorithm for solving robust optimal controllers for nonlinear systems using the homotopy shooting method. Robustness is ensured by penalizing the sensitivity states of the models during the transition and at the final time. In two examples, the cost is represented by the tracking error and terminal residual energy for a rest-to-rest maneuver. The proposed approach is illustrated on a double mass-spring-damper system and on a Type 1 Diabetes model where the cost function includes the integral of the tracking error. Our method can be readily extended for de-sensitization of multiple states over the whole time interval. 

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. 

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. 

Global sensitivity analysis aims at quantifying and ranking the relative contribution of all the uncertain inputs of a mathematical model that impact the uncertainty in the output of that model, for any input-output mapping. Motivated by the limitations of the well-established Sobol' indices which are variance-based, there has been an interest in the development of non-moment-based global sensitivity metrics. This paper presents two complementary classes of metrics (one of which is a generalization of an already existing metric in the literature) which are based on the statistical distances between probability distributions rather than statistical moments. To alleviate the large computational cost associated with Monte Carlo sampling of the input-output model to estimate probability distributions, polynomial chaos surrogate models are proposed to be used. The surrogate models in conjunction with sparse quadrature-based rules, such as conjugate unscented transforms, permit efficient calculation of the proposed global sensitivity measures. Three benchmark sensitivity analysis examples are used to illustrate the proposed approach.