Time-Discretization of Nonlinear Systems with Time Delayed Output via Taylor Series

다국어 초록 (Multilingual Abstract)

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.

목차 (Table of Contents)

• 영어 초록
• 1. Introduction
• 2. Discretization of Nonlinear System with Delay-Free Output
• 3. Time-Discretization of Nonlinear System with Time-Delay Output
• 4. Scaling and Squaring Technique (SST)
• 5. Simulation
• 6. Conclusions
• Acknowledgments
• References

참고문헌 (Reference)

1 "Time-Discretization of Nonlinear Systems with Delayed Multi-Input using Taylor Series" 18 (18): 1107-1120, 2004a

2 "Time-Discretization of Nonlinear Control Systems via Taylor Methods" 23 : 763-784, 1999

3 "Time-Discretization of Non-Affine Nonlinear Systems with Delayed Input using Taylor-Series" 18 (18): 1297-1305, 2004b

4 "The Scaling and Squaring Method for the Matrix Exponential Revisited"

5 "System-Theoretic Properties of Sampled-Data Representations of Nonlinear Systems Obtained via Taylor-Lie Series" 67 : 997-1020, 1997

6 "Discretization of Nonlinear Systems with Delayed Multi-Input via Taylor Series and Scaling and Squaring Technique" 19 (19): 1975-1987, 2005

7 "Digital Control of Dynamic Systems." Addison-Wesley 1998

8 "Digital Control" McGraw-Hill 1995

9 "Design and Stability Analysis of Impedance Controller for Bilateral Teleoperation under a Time Delay" 18 (18): 1131-1139, 2004

10 "Control-Relevant Discretization of Nonlinear Systems with Time-Delay Using Taylor-Lie Series" 149-154, 2003

11 "CVT Ratio Control for Improvement of Fuel Economy by Considering Powertrain Response Lag" 17 (17): 1725-1731, 2003

12 "A Single DOF Magnetic Levitation System using Time Delay Control and Reduced-Order Observer" 16 (16): 1643-1651, 2002

13 "A Novel Start-Controlled Phase/Frequency Detector for Multiphase-Output Delay-Locked Loops" 68-71, 2004

14 "A New Approach to State Observation of Nonlinear Systems with Delayed Output" 47 (47): 96-101, Jan.2002

15 "A Class of Sliding Fermat Number Transforms that Admit a Tradeoff Between Complexity and Input?Output Delay" 45 (45): 3094-3096, 1997