Abstract
This chapter deals with fundamental limitations for sampled-data (SD) feedback systems. By the term SD, we refer to a system with both continuous-time and discrete-time signals — as is the case of digital control of an analogue plant — but which is studied in continuous-time. This contrasts with the approach taken in §3.4 in Chapter 3, where we were concerned only with the sampled behavior of the system. In this chapter, the full intersample behavior will be taken into account.
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Notes and References
The contents of this chapter are largely based on Freudenberg et al. (1995). In this paper, integral constraints on S° and T° of the Bode-type have also been derived. Extensions of these results to multirate SD systems have been reported in Xie & Middleton (1996), while applications to the analysis of robustness properties of zero shifting control schemes have been presented in Freudenberg, Middleton & Braslavsky (1994), from which the example in §6.5 was taken; see also Braslavsky (1995) for a detailed discussion. More on performance limitations for SD systems may be found in Araki (1993), Feuer & Goodwin (1994) and Zhang & Zhang (1994).
Fundamental sensitivity functions were first introduced in Goodwin & Salgado (1994) to study SD systems considering full intersample behavior. A frequency domain framework embodying all harmonics has been presented in Araki et al. (1993). Recent references on the frequency response of SD systems include Yamamoto & Araki (1994), Hagiwara, Ito & Araki (1995), Rosenvasser (1995), and Yamamoto & Khargonekar (1996).
A rigorous and self-contained derivation of the key sampling formula that yields (6.7) may be found in Braslavsky, Meinsma, Middleton & Freudenberg (1995).
For further reading on SD systems see the recent books by Chen & Francis (1995) and Feuer & Goodwin (1996).
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© 1997 Springer-Verlag London Limited
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Seron, M.M., Braslavsky, J.H., Goodwin, G.C. (1997). Extensions to Sampled-Data Systems. In: Fundamental Limitations in Filtering and Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0965-5_6
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DOI: https://doi.org/10.1007/978-1-4471-0965-5_6
Publisher Name: Springer, London
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