High-performance conversions between continuous- and discrete-time systems

In this paper, a new algorithm for converting an S-domain model to a Z-domain model is proposed. The resultant Z-domain model is much closer to the original S-domain model than that obtained from conventional conversion schemes such as Tustin approximation with or without frequency pre-warping, zero-pole mapping equivalent, and Triangle hold equivalent. The proposed algorithm adopts the standard recursive least squares approach, and it has the following advantages. First, the computation is trivial and can be easily implemented online. Second, it can handle both parametric and non-parametric models, while conventional conversion methods can only handle parametric models. Third, it is very flexible and applicable to Z- to S-domain model conversion, sampling rate selection, re-sampling, time delay system conversion, and model order selection. The superior performance of the method is demonstrated with several simulation examples in this paper.

[1]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[2]  Benjamin C. Kuo,et al.  Digital Control Systems , 1977 .

[3]  P. Eykhoff.  System Identification Parameter and State Estimation , 1974 .

[4]  J. Schoukens,et al.  Parametric identification of transfer functions in the frequency domain-a survey , 1994, IEEE Trans. Autom. Control..

[5]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[6]  K. S. Rattan.  Digitalization of existing continuous control systems , 1984 .

[7]  D Tabak,et al.  Digitalisation of control systems , 1971 .

[8]  J. P. Keller,et al.  A new approach to the discretization of continuous-time controllers , 1990, 1990 American Control Conference.

[9]  Bernhard P. Lampe,et al.  Application of Laplace transformation for digital redesign of continuous control systems , 1999, IEEE Trans. Autom. Control..

[10]  Tongwen Chen,et al.  A technique for optimal digital redesign of analog controllers , 1996, IEEE Trans. Control. Syst. Technol..

[11]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[12]  B. Francis,et al.  H/sub 2/-optimal sampled-data control , 1991 .

[13]  E W. Djaja,et al.  Technique for enhancing the performance of discretized controllers , 1999 .

[14]  K. S. Rattan.  Compensating for computational delay in digital equivalent of continuous control systems , 1989 .

[15]  Masayoshi Tomizuka,et al.  Analysis of multi-rate discrete equivalent of continuous controller , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[16]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[17]  L. S. Shieh,et al.  A new approach to the digital redesign of continuous-time controllers , 1992 .

[18]  B. Lampe,et al.  Parametric transfer functions for sampled-data systems with time-delayed controllers , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.