The Experts below are selected from a list of 36207 Experts worldwide ranked by ideXlab platform
Geok Soon Hong - One of the best experts on this subject based on the ideXlab platform.
-
Experimental implementation of Taylor Series expansion error compensation on a bi-axial CNC machine.
The International Journal of Advanced Manufacturing Technology, 2010Co-Authors: A N Poo, Geok Soon Hong, Feng HuoAbstract:In this paper, a new model-based Taylor Series expansion error compensation (TSEEC) strategy is proposed to improve the contouring accuracy for computer numerically controlled (CNC) machines. In TSEEC, the contour error compensation problem is formulated as a Taylor Series expansion problem, in which the value of the contour error is expanded around the reference points and the compensation components are calculated as the deviations from the reference points. Simulations show that, with perfect knowledge of the axial dynamics, zero contour errors can be achieved with TSEEC for both linear and circular contours. Due to modeling errors, external disturbances, and measurement noise, some modifications and experimentation need to be made to determine suitable parameters for implementation of the TSEEC scheme on a real machine. These measurements include a low-pass filter, a choice of a compensation target, and a compensation gain. Experimental results show the effectiveness of TSEEC in reducing contour errors and demonstrate the superiority of TSEEC over inverse feedforward compensation and cross-coupled control in improving the contouring accuracy.
-
Taylor Series expansion error compensation for a bi axial cnc machine
Systems Man and Cybernetics, 2008Co-Authors: A N Poo, Geok Soon HongAbstract:In this paper, an approach using the Taylor Series expansion is explored for error compensation in bi-axis CNC machines. The objective is to improve the contouring accuracy in these machines. The contour errors that will occur if the desired reference inputs are directly applied to the control loops are first predicted using the known axial dynamic models. The Taylor Series expansion is then used to obtain an expression of the contour error around the current tool position. A robust numerical method is devised which is then used to compute the modified reference components along individual axes for cancellation of the predicted contour errors. Simulation results show that, with perfect knowledge of the machine's dynamic models, the proposed strategy can perfectly cancel out the contour errors for both linear and circular contours despite the mismatches in the axes dynamics.
A N Poo - One of the best experts on this subject based on the ideXlab platform.
-
Experimental implementation of Taylor Series expansion error compensation on a bi-axial CNC machine.
The International Journal of Advanced Manufacturing Technology, 2010Co-Authors: A N Poo, Geok Soon Hong, Feng HuoAbstract:In this paper, a new model-based Taylor Series expansion error compensation (TSEEC) strategy is proposed to improve the contouring accuracy for computer numerically controlled (CNC) machines. In TSEEC, the contour error compensation problem is formulated as a Taylor Series expansion problem, in which the value of the contour error is expanded around the reference points and the compensation components are calculated as the deviations from the reference points. Simulations show that, with perfect knowledge of the axial dynamics, zero contour errors can be achieved with TSEEC for both linear and circular contours. Due to modeling errors, external disturbances, and measurement noise, some modifications and experimentation need to be made to determine suitable parameters for implementation of the TSEEC scheme on a real machine. These measurements include a low-pass filter, a choice of a compensation target, and a compensation gain. Experimental results show the effectiveness of TSEEC in reducing contour errors and demonstrate the superiority of TSEEC over inverse feedforward compensation and cross-coupled control in improving the contouring accuracy.
-
Taylor Series expansion error compensation for a bi axial cnc machine
Systems Man and Cybernetics, 2008Co-Authors: A N Poo, Geok Soon HongAbstract:In this paper, an approach using the Taylor Series expansion is explored for error compensation in bi-axis CNC machines. The objective is to improve the contouring accuracy in these machines. The contour errors that will occur if the desired reference inputs are directly applied to the control loops are first predicted using the known axial dynamic models. The Taylor Series expansion is then used to obtain an expression of the contour error around the current tool position. A robust numerical method is devised which is then used to compute the modified reference components along individual axes for cancellation of the predicted contour errors. Simulation results show that, with perfect knowledge of the machine's dynamic models, the proposed strategy can perfectly cancel out the contour errors for both linear and circular contours despite the mismatches in the axes dynamics.
Yury A. Litmanovich - One of the best experts on this subject based on the ideXlab platform.
-
Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion
Giroskopiya i Navigatsiya, 2020Co-Authors: Yury A. Litmanovich, Central ScientificAbstract:There are two basic approaches to strapdown attitude computation, namely, the traditional Taylor Series expansion approach and the Picard iterative method. The latter was recently implemented in a recursive form basing on the Chebyshev polynomial approximation and resulted in the so-called functional iterative integration approach. Up to now a detailed comparison of these two approaches with arbitrary number of gyroscope samples has been lacking for the reason that the first one is based on the simplified rotation vector equation while the second one uses the exact form. In this paper, the mainstream algorithms are considerably extended by the Taylor Series expansion approach using the exact differential equation and recursive calculation of high-order derivatives, and the functional iterative integration approach is re-implemented on the normal polynomial. This paper applies the two approaches to solve the strapdown attitude problem, using the attitude parameter of quaternion as a demonstration. Numerical results under the classical coning motion are reported to assess all derived attitude algorithms. It is revealed that in the low and middle relative conic frequency range all algorithms have the same order of accuracy, but in the range of high relative frequency the algorithm by the functional iterative integration approach performs the best in both accuracy and robustness if the Chebyshev polynomials and a larger number of gyroscope samples are to be used. The main conclusion applies to other attitude parameters as well.
-
Strapdown Attitude Computation: Functional Iterative Integration versus Taylor Series Expansion.
arXiv: Numerical Analysis, 2019Co-Authors: Yuanxin Wu, Yury A. LitmanovichAbstract:This paper compares two basic approaches to solving ordinary differential equations, which form the basis for attitude computation in strapdown inertial navigation systems, namely, the Taylor Series expansion approach that was used in its low-order form for deriving all mainstream algorithms and the functional iterative integration approach developed recently. They are respectively applied to solve the kinematic equations of major attitude parameters, including the quaternion, the Rodrigues vector and the rotation vector. Specifically, the mainstream algorithms, which have relied on the simplified rotation vector without exception, are considerably extended by the Taylor Series expansion approach using the exact rotation vector and recursive calculation of high-order derivatives. The functional iterative integration approach is respectively implemented on both the normal polynomial and the Chebyshev polynomial. Numerical results under the classical coning motion are reported to assess all derived attitude algorithms. It is revealed that in the relative frequency range when the coning to sampling frequency ratio is below 0.05-0.1 (depending on the chosen polynomial truncation order), all algorithms have the same order of accuracy if the same number of samples are used to fit the angular velocity over the iteration interval; in the range of higher relative frequency, the group of Quat/Rod/RotFIter algorithms (by the functional iterative integration approach combined with the Chebyshev polynomial) perform the best in both accuracy and robustness, thanks to the excellent numerical stability and powerful functional representation capability of the Chebyshev polynomial.
Mohammad Mehdi Fateh - One of the best experts on this subject based on the ideXlab platform.
-
on the Taylor Series asymptotic tracking control of robots
Robotica, 2019Co-Authors: Seyed Mohammad Ahmadi, Mohammad Mehdi FatehAbstract:Achieving the asymptotic tracking control of electrically driven robot manipulators is a challenging problem due to approximation/modelling error arising from parametric and non-parametric uncertainty. Thanks to the specific property of Taylor Series systems as they are universal approximators, this research outlines two robust control schemes using an adaptive Taylor Series system for robot manipulators, including actuators' dynamics. First, an indirect adaptive controller is designed such as to approximate an uncertain continuous function by using a Taylor Series system in the proposed control law. Second, a direct adaptive scheme is established to employ the Taylor Series system as a controller. In both controllers, not only a robustifying term is constructed using the estimation of the upper bound of approximation/modelling error, but the closed-loop stability, as well as the asymptotic convergence of joint-space tracking error and its time derivative, is ensured. Due to the design of the Taylor Series system in the tracking error space, our technique clearly has an advantage over fuzzy and neural network-based control methods in terms of the small number of tuning parameters and inputs. The proposed methods are simple, model free in decentralized forms, no need for uncertainty bounding functions and perfectly capable of dealing with parametric and non-parametric uncertainty and measurement noise. Finally, simulation results are introduced to confirm the efficiency of the proposed control methods.
-
task space asymptotic tracking control of robots using a direct adaptive Taylor Series controller
Journal of Vibration and Control, 2018Co-Authors: Seyed Mohammad Ahmadi, Mohammad Mehdi FatehAbstract:This paper presents a robust task-space control approach using a direct adaptive Taylor Series controller for electrically driven robot manipulators. In an adaptive Taylor Series control scheme, the parameters of controller are directly tuned in order to reduce the task-space tracking error in the presence of structured and unstructured uncertainty. Also, the upper bound of approximation error is estimated to form a robustifying term and the asymptotic convergence of task-space tracking error and its time derivative is proven based on the stability analysis. Simulation results are included to verify the effectiveness of the proposed control method.
Duran M Toksari - One of the best experts on this subject based on the ideXlab platform.
-
Taylor Series approach to fuzzy multiobjective linear fractional programming
Information Sciences, 2008Co-Authors: Duran M ToksariAbstract:This paper presents the use of a Taylor Series for fuzzy multiobjective linear fractional programming problems (FMOLFP). The Taylor Series is a Series expansion that a representation of a function. In the proposed approach, membership functions associated with each objective of fuzzy multiobjective linear fractional programming problem transformed by using a Taylor Series are unified. Thus, the problem is reduced to a single objective. Practical applications and numerical examples are used in order to show the efficiency and superiority of the proposed approach.
