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Time-Discretization of Nonlinear Systems with Time Delayed Output via Taylor Series
Yuanliang Zhang,Chong Kil-To The Korean Society of Mechanical Engineers 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.7
An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.
Model Algorithm Control for Path Tracking of Wheeled Mobile Robots
Zhang, Yuanliang,Park, Jong-Ho,Chong, Kil-To 한국정밀공학회 2010 International Journal of Precision Engineering and Vol.11 No.5
This paper proposes a model algorithm control (MAC) method for the path tracking control of differentially steered wheeled mobile robots (WMRs) subject to nonholonomic constraints. The continuous dynamic model of the wheeled mobile robot is presented and used as the model to be controlled. The MAC controller is designed based on the sampled-data representation of the system. In this paper the case that there exists time delay in the control input is also considered. A time discretization method using the Taylor series and the zero-order-hold (ZOH) assumption is proposed to discretize the continuous dynamic model of the WMR. This time discretization method is especially useful in the case of the time delayed system. It can provide finite dimensional and more accurate discretized form model of the mobile robot with input time delay and convert it into a general nonlinear time discretizedform to which the MAC controller can be applied. Simulations are conducted to show the performance and feasibility of the proposed control strategy. In these simulations the WMR is controlled to track two difference reference paths such as the "8" shape path and the circular path. The bounded inertial parameters uncertainties and some disturbance are also considered in the model of the control system.
Hybrid discretization method for time-delay nonlinear systems
Zhang, Zheng,Kostyukova, Olga,Zhang, Yuanliang,Chong, Kil-To 대한기계학회 2010 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.24 No.3
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable.
Model Algorithmic Control for Multi-Input Nonlinear Time-delay System
Yuanliang Zhang(장원량),Kil To Chong(정길도) 제어로봇시스템학회 2008 제어로봇시스템학회 국내학술대회 논문집 Vol.2008 No.10
In this paper a digital controller for nonlinear MIMO system with time-delayed input is proposed. A nonlinear system with multi-input time-delay is discretized by using Taylor’s discretization method. And the discretized system can be converted to a general nonlinear system. For this reason, general nonlinear controller synthesis can be applied to the discretized time-delay system. We adopted MAC controller synthesis for this study. computer simulations are conducted to verify the performance of the proposed method. The results of simulation show good performance of the proposed controller synthesis.
Yuanliang Zhang,Kil To Chong 대한전기학회 2006 International Journal of Control, Automation, and Vol.4 No.3
A new discretization method for calculating a sampled-data representation of a nonlinear continuous-time system is proposed. The proposed method is based on the well¬known Taylor series expansion and zero-order hold (ZOH) assumption. The mathematical structure of the new discretization method is analyzed. On the basis of this structure, a sampled-data representation of a nonlinear system with a time-delayed input is derived. This method is applied to obtain a sampled-data representation of a non-affine nonlinear system, with a constant input time delay. In particular, the effect of the time discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. 'Hybrid' discretization schemes that result from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method parameters to meet CPU time and accuracy requirements are examined as well. The performance of the proposed method is evaluated using a nonlinear system with a time-delayed non-affine input.
An GPS/DR Navigation System Using Neural Network for Mobile Robot
Yuanliang Zhang,정길도 한국정밀공학회 2014 International Journal of Precision Engineering and Vol.15 No.12
Dead reckoning (DR) is frequently used for mobile robot navigation as it can provide precise short term navigation information butthe errors of a DR system can accumulate over time. A global positioning system (GPS) can be used for outside navigation andlocalization but the error of a single GPS receiver is still big even though an error intentionally introduced into the system called theselective availability policy (SA) was already removed. Standard differential GPS (DGPS) can provide an accuracy of less than onemeter but it is too expensive for the mass market aside from the need of having a base station to provide differential data. This paperproposes a new GPS/DR fusion method based on the data characteristics of a cheap single GPS receiver and use neural networkto estimate the output of the GPS receiver to provide precise navigation information to the mobile robot. Simulation results validatedthe performance of the proposed method and showed its potential use in outdoor mobile robot navigation.
Navigation of Mobile Robot Using Low-cost GPS
Yuanliang Zhang,홍동표 한국정밀공학회 2015 International Journal of Precision Engineering and Vol.16 No.4
A method of fusing data from a Global Positioning System (GPS) and a Dead Reckoning (DR) system for outdoor navigation of aWheeled Mobile Robot (WMR) is proposed. The low-cost GPS receiver cannot be utilized by itself for navigating the mobile robot. Since, it produces an error of approximately 10-20 meters. DR can provide precise navigation data to the mobile robot but its errorsaccumulate over time. Since, all the previous data are utilized to calculate the current position information. DR needs to becomplemented by other navigation sensors to navigate the mobile robot. The proposed GPS/DR data fusion method is based on thecharacteristics of the single GPS receiver output. The fused data provides accurate and robust navigation information to the outdoormobile robot. Simulations were conducted using real GPS data which were then compared with the results using a Kalman filter thatverified the potential of the proposed GPS/DR data fusion method.
Time-Discretization of Nonlinear Systems with Time Delayed Output via Taylor Series
Zhang Yuanliang,Kil To Chong 대한기계학회 2006 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.20 No.7
An output time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via a digital computer. A new method for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed in this paper. This method is applied to the sampled-data representation of a nonlinear system with a constant output time-delay. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. In addition, 'hybrid' discretization schemes resulting from a combination of the 'scaling and squaring' technique with the Taylor method are also proposed, especially under conditions of very low sampling rates. A performance of the proposed method is evaluated using two nonlinear systems with time-delay output.