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Article
Publication date: 17 August 2012

Sajjad Shoja Majidabad and Heydar Toosian Shandiz

The purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete‐time domain for robot manipulators.

Abstract

Purpose

The purpose of this paper is to develop sliding mode control with linear and nonlinear manifolds in discrete‐time domain for robot manipulators.

Design/methodology/approach

First, a discrete linear sliding mode controller is designed to an n‐link robot based on Gao's reaching law. In the second step, a discrete terminal sliding mode controller is developed to design a finite time and high precision controller. The stability analysis of both controllers is presented in the presence of model uncertainties and external disturbances. Finally, sampling time effects on the continuous‐time system outputs and sliding surfaces are discussed.

Findings

Computer simulations on a three‐link SCARA robot show that the proposed controllers are robust against model uncertainties and external disturbance. It was also shown that the sampling time has important effects on the closed loop system stability and convergence.

Practical implications

The proposed controllers are low cost and easily implemented in practice in comparison with continuous‐time ones.

Originality/value

The novelty associated with this paper is the development of an approach to finite time and robust control of n‐link robot manipulators in discrete‐time domain. Also, obtaining an upper bound for the sampling time is another contribution of this work.

Details

International Journal of Intelligent Computing and Cybernetics, vol. 5 no. 3
Type: Research Article
ISSN: 1756-378X

Keywords

Article
Publication date: 7 April 2022

Linhai Zhu, Liu Jinfu, Yujia Ma, Mingliang Bai, Weixing Zhou and Daren Yu

This paper aims to establish a multi-input equilibrium manifold expansion (EME) model for gas turbine (GT). It proposes that the extension of model input dimension is realized…

Abstract

Purpose

This paper aims to establish a multi-input equilibrium manifold expansion (EME) model for gas turbine (GT). It proposes that the extension of model input dimension is realized based on similarity theory and affine structure in the framework of single-input EME model. The study aims to expand the scope of application of the EME model so that it can be used for the control or fault diagnosis of GTs.

Design/methodology/approach

In this paper, the concepts of corrected equilibrium manifold expansion (CEME) model and multi-cell equilibrium manifold expansion (MEME) model are first proposed. This paper uses theoretical analysis and simulation experiments to demonstrate the effectiveness of the bilayer equilibrium manifold expansion (BEME) model, which is a combination of the CEME and the MEME models. Simulation experiments include confirmatory experiments and comparative experiments.

Findings

The paper provides a new sight into building a multiple-input EME (MI-EME) model for GTs. The proposed method can build an accurate and robust MI-EME model that has superior performance compared with widely used nonlinear models including Wiener model (WM), Hammerstein model (HM), Hammerstein–Wiener model (HWM) and nonlinear autoregressive with exogenous inputs (NARX) network model. In terms of accuracy, the maximum error percentage of the proposed model is just 1.309%, far less than WM, HM and HWM. In terms of the stability of model calculation, the range of the mean error percentage of the proposed model is just a quarter of that of NARX network model.

Originality/value

The paper fulfills the construction of a novel multi-input nonlinear model, which has laid a foundation for the follow-up research of model-based GT fault detection and isolation or GT control.

Details

Aircraft Engineering and Aerospace Technology, vol. 94 no. 8
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 2 January 2018

Azadeh Ahifar, Abolfazl Ranjbar Noee and Zahra Rahmani

The purpose of this paper is to design a synergetic controller to precisely and quickly track reference signals in robot manipulators. Having smooth control signal this controller…

Abstract

Purpose

The purpose of this paper is to design a synergetic controller to precisely and quickly track reference signals in robot manipulators. Having smooth control signal this controller enables the nonlinear robot system to track desired references in presence of disturbances in a finite time.

Design/methodology/approach

A new synergetic manifold is introduced here, followed by adding a nonlinear exponential term to it have a precise tracking within a finite time of the desired references with disturbances. Previously the nonlinear term was inserted in the main synergetic equation which makes it complicated due to its hard mathematical approach. Using Lyapunov function, the stability of the system in the presence of disturbances is proved. The validity of the resulted system is confirmed by simulating it in Simulink.

Findings

Using a terminal synergetic controller with new manifold proposed in this work enables system’s state variables to track desired reference signal in the presence of disturbances from any initial condition with proper precision and rate. Simulation results show that compared to similar methods it provides a more proper speed and a finite time convergence with high precision and speed.

Originality/value

Providing fast and precise convergence, the proposed controller can be used in robot manipulator systems which need fast response and also have a precise performance such as in printing 3D objects and any industrial process.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 8 April 2021

Bhumeshwar Patle, Shyh-Leh Chen, Brijesh Patel, Sunil Kumar Kashyap and Sudarshan Sanap

With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a…

Abstract

Purpose

With the increasing demand for surveillance and smart transportation, drone technology has become the center of attraction for robotics researchers. This study aims to introduce a new path planning approach to drone navigation based on topology in an uncertain environment. The main objective of this study is to use the Ricci flow evolution equation of metric and curvature tensor over angular Riemannian metric, and manifold for achieving navigational goals such as path length optimization at the minimum required time, collision-free obstacle avoidance in static and dynamic environments and reaching to the static and dynamic goals. The proposed navigational controller performs linearly and nonlinearly both with reduced error-based objective function by Riemannian metric and scalar curvature, respectively.

Design/methodology/approach

Topology and manifolds application-based methodology establishes the resultant drone. The trajectory planning and its optimization are controlled by the system of evolution equation over Ricci flow entropy. The navigation follows the Riemannian metric-based optimal path with an angular trajectory in the range from 0° to 360°. The obstacle avoidance in static and dynamic environments is controlled by the metric tensor and curvature tensor, respectively. The in-house drone is developed and coded using C++. For comparison of the real-time results and simulation results in static and dynamic environments, the simulation study has been conducted using MATLAB software. The proposed controller follows the topological programming constituted with manifold-based objective function and Riemannian metric, and scalar curvature-based constraints for linear and nonlinear navigation, respectively.

Findings

This proposed study demonstrates the possibility to develop the new topology-based efficient path planning approach for navigation of drone and provides a unique way to develop an innovative system having characteristics of static and dynamic obstacle avoidance and moving goal chasing in an uncertain environment. From the results obtained in the simulation and real-time environments, satisfactory agreements have been seen in terms of navigational parameters with the minimum error that justifies the significant working of the proposed controller. Additionally, the comparison of the proposed navigational controller with the other artificial intelligent controllers reveals performance improvement.

Originality/value

In this study, a new topological controller has been proposed for drone navigation. The topological drone navigation comprises the effective speed control and collision-free decisions corresponding to the Ricci flow equation and Ricci curvature over the Riemannian metric, respectively.

Details

Industrial Robot: the international journal of robotics research and application, vol. 48 no. 3
Type: Research Article
ISSN: 0143-991X

Keywords

Article
Publication date: 16 August 2022

Zibo Li, Zhengxiang Yan, Shicheng Li, Guangmin Sun, Xin Wang, Dequn Zhao, Yu Li and Xiucheng Liu

The purpose of this paper is to overcome the application limitations of other multi-variable regression based on polynomials due to the huge computation room and time cost.

Abstract

Purpose

The purpose of this paper is to overcome the application limitations of other multi-variable regression based on polynomials due to the huge computation room and time cost.

Design/methodology/approach

In this paper, based on the idea of feature selection and cascaded regression, two strategies including Laguerre polynomials and manifolds optimization are proposed to enhance the accuracy of multi-variable regression. Laguerre polynomials were combined with the genetic algorithm to enhance the capacity of polynomials approximation and the manifolds optimization method was introduced to solve the co-related optimization problem.

Findings

Two multi-variable Laguerre polynomials regression methods are designed. Firstly, Laguerre polynomials are combined with feature selection method. Secondly, manifolds component analysis is adopted in cascaded Laguerre polynomials regression method. Two methods are brought to enhance the accuracy of multi-variable regression method.

Research limitations/implications

With the increasing number of variables in regression problem, the stable accuracy performance might not be kept by using manifold-based optimization method. Moreover, the methods mentioned in this paper are not suitable for the classification problem.

Originality/value

Experiments are conducted on three types of datasets to evaluate the performance of the proposed regression methods. The best accuracy was achieved by the combination of cascade, manifold optimization and Chebyshev polynomials, which implies that the manifolds optimization has stronger contribution than the genetic algorithm and Laguerre polynomials.

Details

Engineering Computations, vol. 39 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 26 August 2014

Andrzej Zawadzki

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic…

Abstract

Purpose

The purpose of this paper is to aim to an application of element of the theory of differential geometry for building the state space transformation, linearizing nonlinear dynamic system into a linear form.

Design/methodology/approach

It is assumed that the description of nonlinear electric circuits with concentrated parameters or electromechanical systems is given by nonlinear system of differential equations of first order (state equations). The goal is to find transformation which leads nonlinear state equation (written in one coordinate system) to the linear in the other – sought coordinate system.

Findings

The necessary conditions fulfilled by nonlinear system undergoing linearization process are presented. Numerical solutions of the nonlinear equations of state together with linearized system obtained from direct transformation of the state space are included (transformation input – the state of the nonlinear system).

Originality/value

Application of first order exact differential forms for determining the transformation linearizing the nonlinear state equation. Simple linear models obtained with the use of the linearizing transformation are very useful (mainly because of the known and well-mastered theory of linear systems) in solving of various practical technical problems.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Open Access
Article
Publication date: 28 February 2023

Nadia Mohdeb

In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.

Abstract

Purpose

In this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.

Design/methodology/approach

The design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.

Findings

The author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.

Practical implications

The author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.

Originality/value

The authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Article
Publication date: 1 April 1984

J.L. CASTI

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few…

Abstract

It is often observed in practice that the essential behavior of mathematical models involving many variables can be captured by a much smaller model involving only a few variables. Further, the simpler model very often displays oscillatory behavior of some sort, especially when critical problem parameters are varied in certain ranges. This paper attempts to supply arguments from the theory of dynamical systems for why oscillatory behavior is so frequently observed and to show how such behavior emerges as a natural consequence of focusing attention upon so‐called “essential” variables in the process of model simplification. The relationship of model simplification and oscillatory behavior is shown to be inextricably intertwined with the problems of bifurcation and catastrophe in that the oscillations emerge when critical system parameters, i.e. those retained in the simple model, pass through critical regions. The importance of the simplification, oscillation and bifurcation pattern is demonstrated here by consideration of several examples from the environmental, economic and urban areas.

Details

Kybernetes, vol. 13 no. 4
Type: Research Article
ISSN: 0368-492X

Article
Publication date: 12 July 2011

Tina Thiessen and Wolfgang Mathis

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

Abstract

Purpose

This paper seeks to give an outline about the geometric concept of electronic circuits, where the jump behavior of nonlinear circuits is emphasized.

Design/methodology/approach

A sketch of circuit theory in a differential geometric setting is given.

Findings

It is shown that the structure of circuit theory can be given in a much better way than by means of a description of circuits using concrete coordinates. Furthermore, the formulation of a concrete jump condition is given.

Originality/value

In this paper, an outline is given about the state of the art of nonlinear circuits from a differential geometric point of view. Moreover, differential geometric methods were applied to two example circuits (flip flop and multivibrator) and numerical results were achieved.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 August 2017

Daniel Mejia, Diego A. Acosta and Oscar Ruiz-Salguero

Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus…

Abstract

Purpose

Mesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions.

Design/methodology/approach

A Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg–Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: α with 0 ≤ α ≤ 1) and angle distortion (weight: 1 − α).

Findings

The present study parameterization algorithm has linear complexity [𝒪(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets.

Originality/value

The devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones.

Details

Engineering Computations, vol. 34 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

1 – 10 of 342