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1. Stochastic flutter analysis of a torsional-vibration-based energy harvester affected by random aeroelastic loads and wind turbulence

   https://doi.org/10.1088/1742-6596/2647/11/112009  

   Piciucco, Davide; Caracoglia, Luca (June 2024, Journal of Physics: Conference Series)

   This paper investigates the energy production of a “meso-scale”, wind-based energy harvester that exploits the torsional aeroelastic instability of a rigid blade-airfoil, elastically supported at equidistant supports. Torsional flutter is a single mode aeroelastic instability phenomenon, in which a diverging dynamic angular rotation of a body occurs. The apparatus relies on a simple mechanism that uses flow-induced pitch motion to extract and convert airflow kinetic energy to electrical energy. The system is composed by a rigid blade-airfoil, connected to a support structure through a non-linear restoring force (torsional spring-like) mechanism that enables the rotation about a reference pivot axis. The proposed technology is designed to be efficient in the range of low and medium wind speeds (10-13 m/s), in which horizontal-axis wind turbines and other harvesters are not efficient. Deterministic pre-flutter, incipient flutter and post-critical vibrations of the apparatus have been already explored in a previous study. This work aims to further investigate the aeroelastic behavior of the “flapping foil” by examining the effect of turbulence, random experimental error and modeling simplifications of the aeroelastic forces. The analysis is conducted at incipient flutter in the frequency domain using classical unsteady force models. Monte Carlo methods are employed to solve for the probability of incipient flutter speed. Several configurations are considered to improve the efficiency of the energy harvester. 

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2. A New Vibrational Control System in Nature: Flapping Flight

   Taha, H; Kiani, M (January 2019, AIAA SciTech)

   Vibrational control is an open loop stabilization technique via the application of highamplitude, high-frequency oscillatory inputs. The averaging theory has been the standard technique for designing vibrational control systems. However, it stipulates too high oscillation frequency that may not be practically feasible. Therefore, although vibrational control is very robust and elegant (stabilization without feedback), it is rarely used in practical applications. The only well-known example is the Kapitza pendulum; an inverted pendulum shose pivot is subject to vertical oscillation. the unstable equilibrium of the inverted pendulum gains asymptotic stability due to the high-frequency oscillation of the pivot. In this paper, we provide a new vibrational control system from Nature; flapping flight dynamics. Flapping flight is a rich dynamical system as a representative model will typically be nonlinear, time-varying, multi-body, multi-time-scale dynamical system. Over the last two decades, using direct averaging, there has been consensus in the flapping flight dynamics community that insects are unstable at the hovering equilibrium due to the lack of pitch stiffness. In this work, we perform higher-order averaging of the time-periodic dynamics of flapping flight to show a vibrational control mechanism due to the oscillation of the driving aerodynamic forces. We also experimentally demonstrate such a phenomenon on a flapping apparatus that has two degrees of freedom: forward translation and pitching motion. It is found that the time-periodic dynamics of the flapping micro-air-vehicle is naturally (without feedback) stabilized beyond a certain threshold. Moreover, if the averaged aerodynamic thrust force is produced by a propeller revolving at a constant speed while maintaining the wings stationary at their mean positions, no stabilization is observed. Hence, it is concluded that the observed stabilization in the flapping system at high frequencies is due to the oscillation of the driving aerodynamic force and, as such, flapping flight indeed enjoys vibrational stabilization. 

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3. Locomotion of a Multi-link Nonholonomic Snake Robot

   Dear, T; Kelly, S; Travers, M; Choset, H. (July 2017, Proceedings of the ASME Dynamic Systems and Control Conference)

   Robot system models often have difficulty allowing for direct command over all input degrees of freedom if the system has a large number of imposed constraints. A snake robot with more than three links and a nonholonomic wheel on each link cannot achieve arbitrary configurations in all of its joints simultaneously. For such a system, we assume partial command over a subset of the joints, and allow the rest to evolve according to kinematic chained and dynamic models. Different combinations of commanded and passive joints, as well as the presence of dynamic elements such as torsional springs, can drastically change the coupling interactions and stable oscillations of the joints. We use the oscillation modes that emerge to inform feedback controllers that achieve desired overall locomotion of the robot. 

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4. Optimal phase-selective entrainment of electrochemical oscillators with different phase response curves

   https://doi.org/10.1063/5.0205480  

   Luis_Ocampo-Espindola, Jorge; Singhal, Bharat; Li, Jr-Shin; Kiss, István Z (July 2024, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance. 

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5. Hierarchical MPC with Coordinating Terminal Costs

   https://doi.org/10.23919/ACC45564.2020.9147685  

   Raghuraman, Vignesh; Renganathan, Venkatraman; Summers, Tyler H.; Koeln, Justin P. (July 2020, American Control Conference)

   null (Ed.)

   The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism. 

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