×

Design of delta-sigma modulators via generalized Kalman-Yakubovich-Popov lemma. (English) Zbl 1301.93171

Summary: This paper is concerned with the design of delta-sigma modulators via the generalized Kalman-Yakubovich-Popov lemma. The shaped Noise Transfer Function (NTF) is assumed to have infinite impulse response, and the optimization objective is minimizing the maximum magnitude of the NTF over the signal frequency band. By virtue of the GKYP lemma, the optimization of an NTF is converted into a minimization problem subject to quadratic matrix inequalities, and then an iterative algorithm is proposed to solve this alternative minimization problem. Each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by existing numerical software packages. Moreover, specifications on the NTF zeros are also integrated in the design method. A design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal-to-noise ratio.

MSC:

93E20 Optimal stochastic control
90C15 Stochastic programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Acero, J.; Navarro, D.; Barragan, L. A.; Garde, I.; Artigas, J. I.; Burdio, J. M., FPGA-based power measuring for induction heating appliances using sigma-delta A/D conversion, IEEE Transactions on Industrial Electronics, 54, 1843-1852 (2007)
[2] Aziz, P. M.; Sorensen, H. V.; der Spiegel, J. V., An overview of sigma-delta converters, IEEE Signal Processing Magazine, 13, 61-84 (1996)
[3] Azuma, S. I.; Sugie, T., Optimal dynamic quantizers for discrete-valued input control, Automatica, 44, 396-406 (2008) · Zbl 1283.93168
[4] Azuma, S. I.; Sugie, T., Synthesis of optimal dynamic quantizers for discrete-valued input control, IEEE Transactions on Automatic Control, 53, 2064-2075 (2008) · Zbl 1367.93221
[5] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in systems and control theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[6] Callegari, S.; Bizzarri, F., Output filter aware optimization of the noise shaping properties of \(\Delta \Sigma\) modulators via semi-definite programming, IEEE Transactions on Circuits and Systems I. Regular Papers, 60, 2352-2365 (2013), published online. http://dx.doi.org/10.1109/TCSI.2013.2239091 · Zbl 1468.94321
[7] Chao, K. C.H.; Nadeem, S.; Lee, W. L.; Sodini, C. G., A higher order topology for interpolative modulators for oversampling A/D converters, IEEE Transactions on Circuits and Systems, 37, 309-318 (1990)
[8] Chen, J.; Nett, C. N., Sensitivity integrals for multivariable discrete-time systems, Automatica, 31, 1113-1124 (1995) · Zbl 0831.93018
[9] Dooper, L.; Berkhout, M., A 3.4 W digital-in class-D audio amplifier in 0.14 mu m CMOS, IEEE Journal of Solid-State Circuits, 47, 1524-1534 (2012)
[10] Fu, M.; Xie, L., The sector bound approach to quantized feedback control, IEEE Transactions on Automatic Control, 50, 1698-1711 (2005) · Zbl 1365.81064
[11] Gahinet, P.; Nemirovskii, A.; Laub, A. J.; Chilali, M., LMI control toolbox user’s guide (1995), The Math. Works Inc: The Math. Works Inc Natick, MA
[12] Iwasaki, T.; Hara, S., Generalized KYP lemma: unified frequency domain inequalities with design applications, IEEE Transactions on Automatic Control, 50, 41-59 (2005) · Zbl 1365.93175
[14] Li, X.; Gao, H., A heuristic approach to static output-feedback controller synthesis with restricted frequency-domain specifications, IEEE Transactions on Automatic Control, 59, 1008-1014 (2014) · Zbl 1360.93557
[15] Li, X.; Gao, H., Reduced-order generalized \(H_\infty\) filtering for linear discrete-time systems with application to channel equalization, IEEE Transactions on Signal Processing, 62, 3393-3402 (2014) · Zbl 1393.93078
[17] Li, H.; Jing, X.; Karimi, H. R., Output-feedback-based \(H_\infty\) control for vehicle suspension systems with control delay, IEEE Transactions on Industrial Electronics, 61, 436-446 (2014)
[19] Nagahara, M.; Yamamoto, Y., Frequency domain min-max optimization of noise-shaping delta-sigma modulators, IEEE Transactions on Signal Processing, 60, 2828-2839 (2012) · Zbl 1393.94644
[20] Oppenheim, A. V.; Schafer, R. W.; Buck, J. R., Discrete-time signal processing (1998), Prentice-Hall: Prentice-Hall Upper Saddle River, New Jersey
[22] Quevedo, D. E.; Goodwin, G. C., Multistep optimal analog-to-digital conversion, IEEE Transactions on Circuits and Systems I. Regular Papers, 52, 503-515 (2005)
[23] Schoofs, R.; Steyaert, M. S.J.; Sansen, W. M.C., A design-optimized continuous-time delta-sigma ADC for WLAN applications, IEEE Transactions on Circuits and Systems I. Regular Papers, 54, 209-217 (2007)
[25] Schreier, R.; Temes, G. C., Understanding delta-sigma data converters (2005), IEEE Press/Wiley Interscience: IEEE Press/Wiley Interscience New York
[27] Yang, R.; Liu, G. P.; Shi, P.; Thomas, C.; Basin, M. V., Predictive output feedback control for networked control systems, IEEE Transactions on Industrial Electronics, 61, 512-520 (2014)
[28] Yu, S. H., Analysis and design of single-bit sigma-delta modulators using the theory of sliding modes, IEEE Transactions on Control Systems and Technology, 14, 336-345 (2006)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.