Three-Stage Feedback Controller Design With Applications to a Three Time-Scale System

A new technique was presented that facilitates design of independent full-state feedback controllers at the subsystem levels. Different types of local controllers, for example, eigenvalue assignment, robust, optimal (in some sense L1, H2, H∞, ...) may be used to control different subsystems. This feature has not been available for any known linear feedback controller design. In the second part of the paper, we specialize the results obtained to the three time-scale linear systems (singularly perturbed control systems) that have natural decomposition into slow, fast, and very fast subsystems. The proposed technique eliminates numerical ill-condition of the original three-time scale problems.

Near Energy Optimal Control Allocation for Dual-Input Over-Actuated Systems

This paper proposes a method for near energy optimal allocation of control effort in dual-input over-actuated systems using a linear time-invariant (LTI) controller. The method assumes a quadratic energy cost functional, and the non-causal energy optimal control ratio within the redundant actuation space is defined. Near energy optimal control allocation is addressed by using a LTI controller to align the control inputs with a causal approximation of the energy optimal control ratio. The use of a LTI controller for control allocation leads to low computation burden compared to techniques in the literature which require optimization at each time step. Moreover, the proposed method achieves broadband, near optimal control allocation, as opposed to traditional allocation methods which make use of a static system model for control allocation. The proposed method is validated through simulations and experiments on an over-actuated hybrid feed drive system. Significant improvements in energy efficiency without sacrificing positioning performance are demonstrated.

Nonlinear Coupled Transverse and Axial Vibration of Variable Cross-Section Beam Flexures Interconnecting Rigid Body

The objective of this paper is to analytically study the nonlinear behavior of variable cross-section beam flexures interconnecting an eccentric rigid body. Hamilton’s principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. Using a single mode approximation, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. The method of multiple scales are employed to obtain parametric closed-form solutions. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. These analytical expressions provide design insights for modeling and optimization of more complex flexure mechanisms for improved dynamic performances.

Segregation of Heterogeneous Robotics Swarms via Convex Optimization

The division of labor amongst a heterogeneous swarm of robots increases the range and sophistication of the tasks the swarm can accomplish. To efficiently execute a task the swarm of robots must have some starting organization. Over the past decade segregation of robotic swarms has grown as a field of research drawing inspiration from natural phenomena such as cellular segregation. A variety of different approaches have been undertaken to devise control methods to organize a heterogeneous swarm of robots. In this work, we present a convex optimization approach to segregate a heterogeneous swarm into a set of homogeneous collectives. We present theoretical results that show our approach is guaranteed to achieve complete segregation and validate our strategy in simulation and experiments.

Auto-Tuning Tub-Level Control of Blender in Hydraulic Fracturing

Hydraulic fracturing is one of the key technologies for producing shale oil and gas. During hydraulic fracturing, a blender is used to mix sand with water and chemicals to obtain a fluidic mixture that will be pumped down a well to frack rocks. In order to achieve high-quality fracturing during a job, the blender needs to maintain its tub level as well as the density of the fluidic mixture. In this paper, an auto-tuning proportional-integral (PI) control is developed for the blender automation system to maintain the tub level of its fluidic mixture. The control system adopts a single-loop PI with gains that can be auto-tuned during a job. A relay feedback test is conducted for auto-tuning the PI gains online. The auto-tuning PI control has been successfully tested in a blender simulator. Experimental results have shown that the control performance was improved after auto-tuning and that the control system was adaptive to variation in system parameters.

Nonlinear Dynamics of Upright Human Balance While Using a Passive-Cane

Recent mathematical models of human posture have been explored to better understand the space of control parameters that result in stable upright balance. These models have demonstrated that there are two types of instabilities — a leaning instability and an instability leading to excessive oscillation. While these models provide insight into the stability of upright bipedal stance, they are not sufficient for individuals that require the aid of assistive technologies, such as a passive-cane or a walker. Without a valid model one is unable to understand the control parameters required for maintain upright posture or if similar instabilities even exist when assistive technologies are used. Therefore in this study, we developed a mathematical model of human posture while using a passive-cane to examine the nonlinear dynamics of stance. First, we developed a simple mathematical model of cane assisted human stance by adapting the inverted pendulum model of Chagdes et al., [1]. We modeled the human body, upper arm, forearm, cane, and ground as a two-degree-of-freedom, five-bar-linkage with pin joints representing the ankle, shoulder, elbow, and wrist joints. Second, we investigate upright stability in the parameter space of feedback gain and time-delay. We hypothesize that the analysis will show similar instabilities compared to that of a human standing without assistive technology. We also hypothesize that the space of control parameters which stabilize upright equilibrium posture will increase when a cane is incorporated. This study has two potential applications. First, the developed mathematical model could allow clinicians to better assess technology assisted balance and if needed help clinicians to customize a treatment plan for an individual that allows them to avoid unstable postural dynamics. Second, the mathematical model can be used to design customized assistive technology for people of difference physical properties and impairments.

Damage Detection of Bridge Network With Spatiotemporal Pattern Network

The alarmingly degrading state of transportation infrastructures combined with their key societal and economic importance calls for automatic condition assessment methods to facilitate smart management of maintenance and repairs. In particular, scalable data-driven approaches is of great interest, because it can deal with large volume of streaming data without requiring models that can be inaccurate and computationally expensive to run. Properly designed, a data-driven methodology could enable fast and automatic evaluation of infrastructures, discovery of causal dependencies among various sub-system dynamic responses, and inference and decision making with uncertainties and lack of labeled data. In this work, a spatiotemporal pattern network (STPN) strategy built on symbolic dynamic filtering (SDF) is applied to explore spatiotemporal behaviors in bridge network. Data from strain gauges installed on two bridges are simulated by finite element method, and the causality among strain data in spatial and temporal resolutions is analyzed. Case studies are conducted for truck identification and damage detection from simulation data. Results show significant capabilities of the proposed approach in: (i) capturing spatiotemporal features to discover causality between bridges (geographically close), (ii) robustness to noise in data for feature extraction, and (iii) detecting and localizing damage via the comparison of behaviors within the bridge network.

Dynamics of a Rotor-Pendulum With a Small, Stiff Propeller in Wind

As small rotorcraft grow in capability, the possibilities for their application increase dramatically. Many of these new applications require stable outdoor flight, necessitating a closer look at the aerodynamic response of the aircraft in windy environments. This paper develops the equations of motion for a single-propeller test stand by analyzing the blade-flapping response of a small-stiff propeller in wind. The system dynamics are simulated to show behavior under various wind conditions, and stable system equilibria are identified. Experiments with a rotor-pendulum validate the simulations, including system equilibria and gust response.

Preliminary Investigation of Provability of Li-Ion Macroscale Models Subject to Capacity Fade

Estimating the remaining useful life of lithium-ion batteries is crucial for their application as energy storage devices in stationary and automotive applications. It is therefore important to understand battery degradation based on chemistry, usage patterns, and operating environment. Different degradation mechanisms that affect performance and durability of lithium-ion batteries have been identified over the past decades. Amongst them, the solid-electrolyte interface (SEI) layer growth has been observed to be the most influential cause of capacity fading. In this paper, we introduce for the very first time, a framework that evaluates the predictive ability of physics-based macroscopic models in capturing battery dynamics as function of their state-of-health (SoH). Using data from accelerated aging experiments, we identify the applicability conditions of classical electrochemical models. This analysis is performed using a phase diagram approach that involves parameters controlling the micro-scale dynamics inside the lithium-ion cell.

A Reference Governor for Nonlinear Systems Based on Quadratic Programming

The reference governor modifies set-point commands to a closed-loop system in order to enforce state and control constraints. In this paper, we describe an approach to reference governor implementation for nonlinear systems, which is based on bounding (covering) the response of a nonlinear system by the response of a linear model with a set-bounded disturbance input. Such a design strategy is of interest as it reduces the online optimization problem to a convex quadratic programming (QP) problem with linear inequality constraints, thereby permitting standard QP solvers to be used. A numerical example is reported.