scholarly journals Transformed Structural Properties Method to Determine the Controllability and Observability of Robots

2021 ◽  
Vol 11 (7) ◽  
pp. 3082
Author(s):  
Dany Ivan Martinez ◽  
José de Jesús Rubio ◽  
Victor Garcia ◽  
Tomas Miguel Vargas ◽  
Marco Antonio Islas ◽  
...  
Keyword(s):  
Structural Properties ◽  
Approximation Error ◽  
Linearization Method ◽  
Controllability And Observability ◽  
Better Than

Many investigations use a linearization method, and others use a structural properties method to determine the controllability and observability of robots. In this study, we propose a transformed structural properties method to determine the controllability and observability of robots, which is the combination of the linearization and the structural properties methods. The proposed method uses a transformation in the robot model to obtain a linear robot model with the gravity terms and uses the linearization of the gravity terms to obtain the linear robot model; this linear robot model is used to determine controllability and observability. The described combination evades the structural conditions requirement and decreases the approximation error. The proposed method is better than previous methods because the proposed method can obtain more precise controllability and observability results. The modified structural properties method is compared with the linearization method to determine the controllability and observability of three robots.

scholarly journals Two-stage segment linearization as part of the thermocouple measurement chain

2021 ◽  
Vol 54 (1-2) ◽  
pp. 141-151
Author(s):  
Dragan Živanović ◽  
Milan Simić
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Linearization Method ◽  
Linear Segment ◽  
Virtual Instrumentation ◽  
Memory Consumption ◽  
Thermocouple Measurement ◽  
Two Stage ◽  
Approximation Errors ◽  
Input Range

An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

Contralateral Peak Plantar Pressures with a Postoperative Boot

2011 ◽  
Vol 101 (2) ◽  
pp. 127-132 ◽  
Author(s):  
Jamie N. Mieras ◽  
Tanya J. Singleton ◽  
Stephen L. Barrett
Keyword(s):  
Structural Properties ◽  
Plantar Pressure ◽  
Limb Length Discrepancy ◽  
Pressure Reduction ◽  
Length Discrepancy ◽  
Patient Complaints ◽  
Plantar Pressures ◽  
Frequent Use ◽  
Significant Difference ◽  
Better Than

Background: Frequent use of walking boots in podiatric medicine often elicits patient complaints and sequelae from the imposed limb-length discrepancy. This study was designed primarily to determine whether peak plantar pressures are decreased in the contralateral foot when a moderately worn athletic shoe is worn opposite a high-calf walking boot and, if so, secondarily to determine whether a specialized surgical shoe worn on the contralateral foot can also effectively reduce this pressure. The pressure reductions were then compared to determine whether significantly greater plantar pressure reduction was provided by either the athletic shoe or the surgical shoe. Methods: Participants without a foot abnormality walked on a treadmill in four footwear combinations: barefoot bilaterally, high-calf rocker-bottom sole (HCRB) walking boot/ barefoot, HCRB walking boot/athletic shoe, and HCRB walking boot/modified walking boot shoe. Measurements were taken with the participants wearing socks. Peak plantar calcaneal pressures were collected. Results: Peak plantar pressures under the calcaneus opposite the HCRB walking boot were significantly reduced from barefoot pressures when either an athletic shoe or the modified walking boot shoe was worn. However, no significant difference was seen when comparing the reduction by the athletic shoe with that by the modified walking boot. Conclusions: Wearing an athletic shoe on the foot opposite an HCRB walking boot reduces calcaneal pressures; however, wearing a modified device with structural properties of an HCRB walking boot sole is no better than an athletic shoe at reducing peak calcaneal pressures. (J Am Podiatr Med Assoc 101(2): 127–132, 2011)

Approximation Model for Radiation Impedance of a Square Piston Source on an Infinite Planar Baffle

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
John Valacas
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Dimensionless Frequency ◽  
Approximation Model ◽  
Model Accuracy ◽  
Radiation Impedance ◽  
Wide Range ◽  
Finite Sum ◽  
Infinite Planar ◽  
Better Than

Abstract Approximation models based on a finite sum of Bessel functions of the first kind and a pair of simple rational transfer functions are proposed for radiation resistance and reactance of a square piston source mounted on an infinite planar baffle. Model accuracy is better than 1.6% for reactance and 0.5% for resistance within a very wide range of dimensionless frequency k√S (0.1–100). The very low and high frequency behaviors of radiation impedance are incorporated into the models' closed-form expressions so that the approximation error outside the specified frequency range tends to zero.

scholarly journals Approximation and Shape Preserving Properties of the Bernstein Operator of Max-Product Kind

2009 ◽  
Vol 2009 ◽  
pp. 1-26 ◽  
Author(s):  
Barnabás Bede ◽  
Lucian Coroianu ◽  
Sorin G. Gal
Keyword(s):  
Nonlinear Operator ◽  
Approximation Error ◽  
Approximation Order ◽  
Order Of Approximation ◽  
Shape Preserving ◽  
Explicit Constant ◽  
Open Question ◽  
Shape Preserving Properties ◽  
Upper Estimate ◽  
Better Than

Starting from the study of theShepard nonlinear operator of max-prod typeby Bede et al. (2006, 2008), in the book by Gal (2008), Open Problem 5.5.4, pages 324–326, theBernstein max-prod-type operatoris introduced and the question of the approximation order by this operator is raised. In recent paper, Bede and Gal by using a very complicated method to this open question an answer is given by obtaining an upper estimate of the approximation error of the form (with an unexplicit absolute constant ) and the question of improving the order of approximation is raised. The first aim of this note is to obtain this order of approximation but by a simpler method, which in addition presents, at least, two advantages: it produces an explicit constant in front of and it can easily be extended to other max-prod operators of Bernstein type. However, for subclasses of functions including, for example, that of concave functions, we find the order of approximation , which for many functions is essentially better than the order of approximation obtained by the linear Bernstein operators. Finally, some shape-preserving properties are obtained.

scholarly journals A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Linearization Method ◽  
Exact Analytical Solutions ◽  
Successive Linearization Method ◽  
Method Approach ◽  
Better Than

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods.

scholarly journals Controllability and Observability of Linear Discrete-Time Fractional-Order Systems

2008 ◽  
Vol 18 (2) ◽  
pp. 213-222 ◽  
Author(s):  
Said Guermah ◽  
Said Djennoune ◽  
Maamar Bettayeb
Keyword(s):  
Structural Properties ◽  
Fractional Order ◽  
Discrete Time ◽  
Analytical Methods ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
New Concepts ◽  
Controllability And Observability ◽  
Theoretical Results

Controllability and Observability of Linear Discrete-Time Fractional-Order SystemsIn this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

A Novel Non-Uniform BTC and its Application

2014 ◽  
Vol 590 ◽  
pp. 789-794
Author(s):  
Yuan Wei ◽  
Kin Tak U
Keyword(s):  
Image Representation ◽  
Approximation Error ◽  
Least Square ◽  
Construction Quality ◽  
Block Truncation Coding ◽  
Piecewise Polynomials ◽  
Image Partition ◽  
Initial Partition ◽  
Better Than

In this paper, a novel image representation coding based on non-uniform Block Truncation Coding (BTC) is proposed. A given image can automatically be partitioned into different regions with different sizes and the bivariate piecewise polynomials are used to do the Least Square Approximation for the pixel values in each sub-region based on BTC bitmap. When the approximation error and initial partition are specified, a specific image partition result is obtained. The image re-construction quality of the proposed algorithm is better than that of the traditional BTC. Based on this algorithm, an effective denoising scheme of image is implemented and some of the experimental examples are illustrated to prove that the quality of the re-constructed image, the denoising effect are all satisfactory and can be referenced by other researchers.

scholarly journals Error estimates for a multidimensional meshfree Galerkin method with diffuse derivatives and stabilization

2013 ◽  
Vol 9 (17) ◽  
pp. 53-76
Author(s):  
Mauricio Osorio ◽  
Donald French
Keyword(s):  
Differential Equation ◽  
Convergence Rate ◽  
Error Analysis ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Approximation Error ◽  
Neumann Boundary ◽  
Meshfree Method ◽  
General Elliptic ◽  
Better Than

A meshfree method with diffuse derivatives and a penalty stabilization is developed. An error analysis for the approximation of the solution of a general elliptic differential equation, in several dimensions, with Neumann boundary conditions is provided. Theoretical and numerical results show that the approximation error and the convergence rate are better than the diffuse element method.

scholarly journals Composability of global phase invariant distance and its application to approximation error management

2021 ◽  
Author(s):  
Priyanka Mukhopadhyay
Keyword(s):  
Fault Tolerant ◽  
Quantum Algorithms ◽  
Approximation Error ◽  
Optimal Number ◽  
Operator Norm ◽  
Quantum Circuits ◽  
Frobenius Norm ◽  
Invariant Distance ◽  
Composition Product ◽  
Better Than

Abstract Many quantum algorithms can be written as a composition of unitaries, some of which can be exactly synthesized by a universal fault-tolerant gate set like Clifford+T, while others can be approximately synthesized. A quantum compiler synthesizes each approximately synthesizable unitary up to some approximation error, such that the error of the overall unitary remains bounded by a certain amount. In this paper we consider the case when the errors are measured in the global phase invariant distance. Apart from deriving a relation between this distance and the Frobenius norm, we show that this distance composes. If a unitary is written as a composition (product and tensor product) of other unitaries, we derive bounds on the error of the overall unitary as a function of the errors of the composed unitaries. Our bound is better than the sum-of-error bound, derived by Bernstein- Vazirani(1997), for the operator norm. This builds the intuition that working with the global phase invariant distance might give us a lower resource count while synthesizing quantum circuits. Next we consider the following problem. Suppose we are given a decomposition of a unitary, that is, the unitary is expressed as a composition of other unitaries. We want to distribute the errors in each component such that the resource-count (specifically T-count) is optimized. We consider the specific case when the unitary can be decomposed such that the $R_z(\theta)$ gates are the only approximately synthesizable component. We prove analytically that for both the operator norm and global phase invariant distance, the error should be distributed equally among these components(given some approximations) . The optimal number of T-gates obtained by using the global phase invariant distance is less. Furthermore, for approx-QFT the error due to pruning of rotation gates is less when measured in this distance.

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