Energetically-Optimal Discrete and Continuous Stabilization of the Rimless Wheel With Torso

2019 ◽  
Author(s):  
Wankun Sirichotiyakul ◽  
Aykut C. Satici ◽  
Eric S. Sanchez ◽  
Pranav A. Bhounsule
Keyword(s):  
Closed Loop ◽  
Estimation Method ◽  
Linear Quadratic Regulator ◽  
Region Of Attraction ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Walking Gait ◽  
Rimless Wheel ◽  
The Impact ◽  
Discrete Controller

Abstract In this work, we discuss the modeling, control, and implementation of a rimless wheel with torso. We derive and compare two control methodologies: a discrete-time controller (DT) that updates the controls once-per-step and a continuous-time controller (CT) that updates gains continuously. For the discrete controller, we use least-squares estimation method to approximate the Poincaré map on a certain section and use discrete-linear-quadratic-regulator (DQLR) to stabilize a (closed-form) linearization of this map. For the continuous controller, we introduce moving Poincaré sections and stabilize the transverse dynamics along these moving sections. For both controllers, we estimate the region of attraction of the closed-loop system using sum-of-squares methods. Analysis of the impact map yields a refinement of the controller that stabilizes a steady-state walking gait with minimal energy loss. We present both simulation and experimental results that support the validity of the proposed approaches. We find that the CT controller has a larger region of attraction and smoother stabilization as compared with the DT controller.

Application of LQR Techniques to the Anti-Sway Controller of Overhead Crane

2010 ◽  
Vol 139-141 ◽  
pp. 1933-1936 ◽  
Author(s):  
Bin Yang ◽  
Bin Xiong
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Lagrange Equation ◽  
Linear Quadratic Regulator ◽  
Analytical Mechanics ◽  
Overhead Crane ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Weighting Matrix ◽  
Motion System

This paper explains and demonstrates how to design an anti-sway controller of overhead crane for eliminating pendulum of hook-headed. In this paper, we use Lagrange Equation in analytical mechanics to obtain a mathematical model of crane crab motion system. Then the paper comes up with a piece of new idea, i.e. applies linear quadratic regulator techniques to the anti-sway controller’ design of overhead crane. In order to make the designed linear optimal system meet the practical production requirements better, we use a parametric formula’s method of solutions to LQ inverse problems to obtain the weighting matrix Q. In fact, the method is simple and practical, and ensures the performance of closed-loop system is optimized. The paper will introduce the design steps of anti-sway controller of overhead crane and realization of anti-sway controller, which are new and original in this paper.

scholarly journals Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet

2018 ◽  
Vol 852 ◽  
pp. 146-177 ◽  
Author(s):  
Bartosz Protas ◽  
Takashi Sakajo
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Linear Quadratic Regulator ◽  
Vortex Sheet ◽  
Shear Layers ◽  
Feedback Stabilization ◽  
Loop System ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Mass Fluxes

In this investigation, we use a simple model of the dynamics of an inviscid vortex sheet given by the Birkhoff–Rott equation to obtain fundamental insights about the potential for stabilization of shear layers using feedback control. As actuation, we consider two arrays of point sinks/sources located a certain distance above and below the vortex sheet and subject to the constraint that their mass fluxes separately add up to zero. First, we demonstrate using analytical computations that the Birkhoff–Rott equation linearized around the flat-sheet configuration is in fact controllable when the number of actuator pairs is sufficiently large relative to the number of discrete degrees of freedom present in the system, a result valid for generic actuator locations. Next, we design a state-based linear-quadratic regulator stabilization strategy, where the key difficulty is the numerical solution of the Riccati equation in the presence of severe ill-conditioning resulting from the properties of the Birkhoff–Rott equation and the chosen form of actuation, an issue that is overcome by performing computations with a suitably increased arithmetic precision. Analysis of the linear closed-loop system reveals exponential decay of the perturbation energy and the corresponding actuation energy in all cases. Computations performed for the nonlinear closed-loop system demonstrate that initial perturbations of non-negligible amplitude can be effectively stabilized when a sufficient number of actuators is used. We also thoroughly analyse the sensitivity of the closed-loop stabilization strategies to the variation of a number of key parameters. Subject to the known limitations of inviscid vortex models, our findings indicate that, in principle, it may be possible to stabilize shear layers for relatively large initial perturbations, provided that the actuation has sufficiently many degrees of freedom.

Optimal attitude trajectory planning method for CMG actuated spacecraft

2017 ◽  
Vol 232 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Lijun Zhang ◽  
Chunmei Yu ◽  
Shifeng Zhang ◽  
Hong Cai
Keyword(s):  
Trajectory Planning ◽  
Closed Loop ◽  
Pseudospectral Method ◽  
Linear Quadratic Regulator ◽  
Fixed Time ◽  
Open Loop ◽  
Planning Method ◽  
Global Perspective ◽  
Linear Quadratic ◽  
Loop Control

This paper presents an optimal attitude trajectory planning method for the spacecraft equipped with control moment gyros as the actuators. Both the fixed-time energy-optimal and synthesis performance optimal cases are taken into account. The corresponding nonsingular attitude maneuvering trajectories (i.e. open-loop control trajectories) with the consideration of a series of constraints are generated via Radau pseudospectral method. Compared with the traditional steering laws, the optimal steering law designed by this method can explicitly avoid the singularity from the global perspective. A linear quadratic regulator closed-loop controller is designed to guarantee the trajectory tracking performance in the presence of initial errors, inertia uncertainties and external disturbances. Simulation results verify the validity and feasibility of the proposed open-loop and closed-loop control methods.

scholarly journals Ultrasensitive molecular controllers for quasi-integral feedback

2018 ◽  
Author(s):  
Christian Cuba Samaniego ◽  
Elisa Franco
Keyword(s):  
Computational Models ◽  
Closed Loop ◽  
Reaction Network ◽  
Robust Tracking ◽  
Closed Loop System ◽  
System Equilibrium ◽  
Molecular Reaction ◽  
Unknown Disturbances ◽  
Integral Controller ◽  
The Impact

AbstractFeedback control has enabled the success of automated technologies by mitigating the effects of variability, unknown disturbances, and noise. Similarly, feedback loops in biology reduce the impact of noise and help shape kinetic responses, but it is still unclear how to rationally design molecular controllers that approach the performance of controllers in traditional engineering applications, in particular the performance of integral controllers. Here, we describe a strategy to build molecular quasi-integral controllers by following two design principles: (1) a highly ultrasensitive response, which guarantees a small steady-state error, and (2) a tunable ultrasensitivity threshold, which determines the system equilibrium point (reference). We describe a molecular reaction network, which we name Brink motif, that satisfies these requirements by combining sequestration and an activation/deactivation cycle. We show that if ultrasensitivity conditions are satisfied, this motif operates as a quasi-integral controller and promotes homeostatic behavior of the closed-loop system (robust tracking of the input reference while rejecting disturbances). We propose potential biological implementations of Brink controllers and we illustrate different example applications with computational models.

Use of Rotor State Feedback to Improve Closed-Loop Stability and Handling Qualities

2012 ◽  
Vol 57 (2) ◽  
pp. 1-10 ◽  
Author(s):  
Joseph F. Horn ◽  
Wei Guo ◽  
Gurbuz Taha Ozdemir
Keyword(s):  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Quadratic Regulator ◽  
Linear Analysis ◽  
Dynamic Inversion ◽  
Control Law ◽  
Linear Quadratic ◽  
Handling Qualities ◽  
Model Following

A rotorcraft control law that uses rotor state feedback (RSF) is presented and demonstrated in simulation. The baseline control law uses a model following/dynamic inversion approach to control the roll, pitch, and yaw axes. The RSF control law was designed to integrate seamlessly with the baseline control law and can be readily engaged or disengaged. The RSF control gains were designed using linear quadratic regulator synthesis. Linear analyses showed that RSF could allow for the feedback gains on rates and attitude to be increased to values that would result in closed-loop instability without the use of RSF. The increased gains can be used to increase bandwidth and improve disturbance rejection. The controller was tested on a nonlinear model in both non–real-time and piloted simulations, and results confirmed the linear analysis. The RSF control law design has potential to improve handling qualities by allowing higher bandwidth and better disturbance rejection with reduced risk of closed-loop instability.

A Unified Design Approach to Repetitive Learning Control for Systems Subject to Fractional Uncertainties

2017 ◽  
Vol 140 (6) ◽  
Author(s):  
Mingxuan Sun ◽  
He Li ◽  
Yanwei Li
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Tracking Error ◽  
Estimation Method ◽  
Learning Control ◽  
Closed Loop System ◽  
Repetitive Learning ◽  
Context Of Learning ◽  
Asymptotical Convergence ◽  
Synthesis Approach

Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.

scholarly journals A Circular Light Bulb Economy: Framework for Sustainable End-of-life Management of Modern Light Bulb

2019 ◽  
pp. 1-9
Author(s):  
S. Selvam ◽  
Shivinder Singh Chandok ◽  
Harsh Singh
Keyword(s):  
Pilot Study ◽  
Best Practices ◽  
Circular Economy ◽  
Closed Loop ◽  
Relevant Literature ◽  
Light Bulb ◽  
Closed Loop System ◽  
Comprehensive Review ◽  
The Impact

This paper presents a framework that focuses on transitioning from a linear light bulb economy to a circular light bulb economy by developing a closed-loop system of reuse. The conceptual framework is based on a pilot study conducted in India and strengthened by a comprehensive review and analysis of relevant literature. Accordingly, the proposed paradigms are a result of best practices identified during the pilot study. The results demonstrate the financial viability of the pilot study conducted over a period of three years. Additionally, the results provide evidence of the impact of the circular economy on economic growth, employment opportunity, and reduction in environmental waste. The discussion also identifies the barriers to the adoption of a circular economy framework including the role of attitude towards the environment and the skill gap in labor.

scholarly journals Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

2020 ◽  
Vol 71 (1) ◽  
pp. 1-10
Author(s):  
Miroslav Pokorný ◽  
Tomáš Dočekal ◽  
Danica Rosinová
Keyword(s):  
Closed Loop ◽  
Fuzzy Controller ◽  
Fitness Function ◽  
Fuzzy Model ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Fuzzy Aggregation ◽  
Takagi Sugeno

AbstractUsing the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.

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