s-to-z Transformation Tool for Discretization

Abstract

The signals/systems in nature are analog in terms of their sources. These continuous-time signals/systems need to be discretized in order to be used in digital systems (processing, storage etc.). For this aim, different methods have been developed and continue to be developed. In the work carried out; a software tool with a user-friendly interface has been designed that performs discretization of continuous-time systems with different methods in a fast, accurate and effective manner, presents single or comparative results (parameters, responses, etc.) both numerically and graphically.

Keywords

• s-to-z transform
• s-to-z transformation
• s-to-z mapping
• s-z transform
• discretization

References

1. Katz P., (1981). Digital Control using Microprocessors. New Jersey: Prentice Hall.
2. Franklin G.F., Powell J.D., Workman M.L., (1998). Digital Control of Dynamic Systems. 3rd ed. California: Addison-Wesley Longman.
3. Al-Alaoui M.A., Novel stable higher order s-to-z transforms, IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, 48 No. 11 (2001) 1326-1329. doi: 10.1109/81.964421
4. Al-Alaoui M.A., Linear phase low pass IIR digital differentiators, IEEE Transactions on Signal Processing, 55 No. 2 (2007) 697-706. doi: 10.1109/TSP.2006.885741
5. Al-Alaoui M.A., Novel approach to analog-to-digital transforms, IEEE Transactions on Circuits and Systems-I: Regular Papers, 54 No. 2 (2007) 338-350. doi:10.1109/TCSI.2006.885982
6. Ádám T., Dadvandipour S., Futás, J., Influence of discretization method on the digital control system performance, Acta Montanistica Slovaca, 8 No. 4 (2003) 197-200.
7. Mirković D., Petković P., Litovski V., A second order s-to-z transform and its implementation to IIR filter design, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 33 No. 5 (2014) 1831-1843. doi: 10.1108/COMPEL-03-2014-0058
8. Paarmann L.D., Mapping from the s-domain to the z-domain via the magnitude-invariance method, Signal Processing, 69 No. 3 (1998) 219-228. doi: 10.1016/S0165-1684(98)00104-2

9. Paarmann L.D., Atris Y.H., Mapping from the s-domain to the z-domain via the phase-invariance method, Signal Processing, 86 No. 2 (2006) 223-229. doi: 10.1016/j.sigpro.2005.05.007
10. Schneider A.M., Kaneshige J.T., Groutage F.D., Higher order s-to-z mapping functions and their application in digitizing continuous-time filters, Proceedings of the IEEE, 79 No. 11 (1991) 1661-1674. doi: 10.1109/5.118990
11. James J.R., A survey of knowledge-based systems for computer-aided control system design, 1987 American Control Conference, Minneapolis (1987) 2156-2161. doi: 10.23919/ACC.1987.4789669
12. Kessler P., Schaufelberger W., Minitools for education in control system analysis and design, IFAC Proceedings Volumes, 24 No. 4 (1991) 441-446. doi: 10.1016/S1474-6670(17)54312-8
13. Prendergast D.P., Eydgahi A.M., 'EDCON': an educational control system analysis and design program, IEEE Transactions on Education, 36 No. 1 (1993) 42-44. doi: 10.1109/13.204814
14. Palopoli L., Abeni L., Buttazzo G., Conticelli F., Di Natale M., Real-time control system analysis: an integrated approach, Proceedings 21st IEEE Real-Time Systems Symposium, Orlando (2000) 131-140. doi: 10.1109/REAL.2000.896003
15. Lincoln B., Cervin A., JITTERBUG: a tool for analysis of real-time control performance, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas (2002) 1319-1324. doi: 10.1109/CDC.2002.1184698
16. Ang K.H., Chong G., Li Y., PID control system analysis, design, and technology, IEEE Transactions on Control Systems Technology, 13 No. 4 (2005) 559-576. doi: 10.1109/TCST.2005.847331
17. Vatansever F., Hatun M., Sistem analizi eğitim simülatörü tasarımı, 2nd International Symposium on Innovative Technologies in Engineering and Science (ISITES2014), Karabuk (2014) 546-550.
18. Hatun M., Vatansever F., Discrete time system simulator, 3rd International Symposium on Innovative Technologies in Engineering and Science (ISITES2015), Valencia (2015) 1807-1814.
19. Vatansever F., The design of transform simulator, 5th International Symposium on Innovative Technologies in Engineering and Science (ISITES2017), Baku (2017) 289-293.
20. Díaz J.M., Costa-Castelló R., Muñoz R., Dormido S., An interactive and comprehensive software tool to promote active learning in the loop shaping control system design, IEEE Access, 5 (2017) 10533-10546. doi: 10.1109/ACCESS.2017.2712520
21. Vatansever F., Yalcin N.A., e-Signals & Systems: A web-based educational tool for signals and systems, Computer Applications in Engineering Education, 25 No. 4 (2017) 625-641. doi: 10.1002/cae.21826
22. The MathWorks Inc. (2018). MATLAB , App Designer.
23. Vatansever F., (2018). Sayısal Hesaplama ve Programlama. Ankara: Seçkin Yayıncılık.
24. Hori N., Cormier R., Kanai K., On matched pole-zero discrete-time models, IEE Proceedings D: Control Theory and Applications, 139 No. 3 (1992) 273-278. doi: 10.1049/ip-d.1992.0036
25. Hartley T.T., Comments on “On the nature of the Boxer-Thaler and Madwed integrators and their applications in digitizing a continuous-time system”, IEEE Transactions on Automatic Control, 37 No. 5 (1992) 702-704. doi: 10.1109/9.135524
26. Al-Alaoui M.A., Novel approach to designing digital differentiators, Electronics Letters, 28 No. 15 (1992) 1376-1378. doi: 10.1049/el:19920875
27. Al-Alaoui M.A., Novel digital integrator and differentiator, Electronics Letters, 29 No. 4 (1993) 376-378. doi: 10.1049/el:19930253
28. Al-Alaoui M.A., Novel IIR differentiator from the Simpson integration rule, IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, 41 No. 2 (1994) 186-187. doi: 10.1109/81.269060
29. Al-Alaoui M.A., A class of second-order integrators and low-pass differentiators, IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, 42(4) (1995) 220-223. doi: 10.1109/81.382477
30. Al-Alaoui M.A., A class of numerical integration rules with first order derivatives, ACM Signum Newsletter, 31 No. 2 (1996) 25-44. doi: 10.1145/230922.230930
31. Al-Alaoui M.A., Filling the gap between the bilinear and the backward-difference transforms: an interactive design approach, International Journal of Electrical Engineering & Education, 34 No. 4 (1997) 331-337. doi: 10.1177/002072099703400405
32. Al-Alaoui M.A., Al-Alaoui operator and the α-approximation for discretization of analog systems, Facta Universitatis, Ser.: Elec. and Energ., 19 No. 1 (2006) 143-146. doi: 10.2298/FUEE0601143A
33. Al-Alaoui M.A., Al-Alaoui operator and the new transformation polynomials for discretization of analogue systems, Electrical Engineering, 90 No. 6 (2008) 455-467. doi: 10.1007/s00202-007-0092-0
34. Al-Alaoui M.A., Class of digital integrators and differentiators, IET Signal Processing, 5 No. 2 (2011) 251-260. doi: 10.1049/iet-spr.2010.0107
35. Al-Alaoui M.A., Baydoun M., Yaacoub E., Confluence of pattern recognition and signal processing: application of Al-Alaoui pattern recognition algorithm to digital filters design, IET Signal Processing, 9 No. 6 (2015) 498-505. doi: 10.1049/iet-spr.2014.0377
36. Auger F., Some new developments on the Al-Alaoui and the Pei and Hsu s-to-z transforms, IEEE Transactions on Signal Processing, 57 No. 6 (2010) 471-475. doi: 10.1109/TCSII.2010.2048350
37. Chen C.M., Liu F.H., The discrete-time equivalent of an analogue controller by a compensated approach, International Journal of Systems Science, 32 No. 3 (2001) 287-294. doi: 10.1080/002077201300029566
38. Chen C.M., Liu F.H., The discrete-time equivalent of an analogue controller by the parabolic approach, Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 215 No. 1 (2001) 29-36. doi:10.1243/0959651011539178
39. Georgiev V., Some applied aspects of rational higher order s-z transformations, Radioengineering, 7 No. 1 (1998) 19-26.
40. Gupta M., Jain M., Kumar B., Novel class of stable wideband recursive digital integrators and differentiators, IET Signal Processing, 4 No. 5 (2010) 560-566. doi: 10.1049/iet-spr.2009.0030
41. Gupta M., Jain M., Kumar B., Recursive wideband digital integrator and differentiator, International Journal of Circuit Theory and Applications, 39 No. 7 (2011) 775-782. doi: 10.1002/cta.658
42. Gupta M., Jain M., Kumar B., Wideband digital integrator and differentiator, IETE Journal of Research, 58 No. 2 (2012) 166-170. doi: 10.4103/0377-2063.96175
43. Hamming R.W., (1989). Digital Filters. 3rd ed. New Jersey: Prentice Hall.
44. Kowalczuk Z., Discrete approximation of continuous-time systems: a survey, IEE Proceedings–G (Circuits, Devices and Systems), 140 No. 4 (1993) 264-278. doi: 10.1049/ip-g-2.1993.0045
45. Le Bihan J., Novel class of digital integrators and differentiators, Electronics Letters, 29 No. 11 (1993) 971-973. doi: 10.1049/el:19930647
46. Ngo N.Q., A new approach for the design of wideband digital integrator and differentiator, IEEE Transactions on Circuits and Systems–II: Express Briefs, 53 No. 9 (2006) 936-940. doi: 10.1109/TCSII.2006.881806
47. Papamarkos N., Chamzas C., A new approach for the design of digital integrators, IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications, 43 No. 9 (1996) 785-791. doi: 10.1109/81.536749
48. Šekara T.B., Stojić M.R., Application of the α-approximation for discretization of analogue systems, Facta Universitatis, Ser.: Elec. and Energ., 18 No. 3 (2005) 571-586. doi: 10.2298/FUEE0503571S
49. Šekara T.B., New transformation polynomials for discretization of analogue systems, Electrical Engineering, 89 No. 2 (2006) 137-147. doi: 10.1007/s00202-005-0322-2
50. Tseng C.-C., Digital integrator design using Simpson rule and fractional delay filter, IEE Proceedings of Vision, Image and Signal Processing, 153 No. 1 (2006) 79-85. doi: 10.1049/ip-vis:20045208
51. Upadhyay D.K., Recursive wideband digital differentiators, Electronics Letters, 46 No. 25 (2010) 1661-1662. doi: 10.1049/el.2010.2113
52. Upadhyay D.K., Class of recursive wideband digital differentiators and integrators, Radioengineering, 21 No. 3 (2012) 904-910.
53. Upadhyay D.K., Recursive wideband linear phase digital differentiators and integrators, 2015 International Conference on Computing Communication Control and Automation, Pune (2015) 927-931. doi: 10.1109/ICCUBEA.2015.184
54. Upadhyay D.K., Singh R.K., Recursive wideband digital differentiator and integrator, Electronics Letters, 47 No. 11 (2011) 647-648. doi: 10.1049/el.2011.0420
55. Wang C.-H., Lin M.-Y., Teng C.-C., On the nature of the Boxer-Thaler and Madwed integrators and their applications in digitizing a continuous-time system, IEEE Transactions on Automatic Control, 35 No. 10 (1990) 1163-1167. doi: 10.1109/9.58563