Discrete time subharmonic modelling and analysis. (English) Zbl 1090.93003
Summary: Traditionally the Volterra time and frequency domain analysis tools cannot be applied to severely nonlinear systems. In this paper, a new method of building a time-domain NARX MISO model for a class of severely SISO nonlinear systems that exhibit subharmonics is introduced and it is shown how this allows the Volterra time and frequency domain analysis to be extended to this class of nonlinear systems. The new approach is based on decomposing the original single input based on a Fourier analysis to provide a set of modified input signals which have the same period as the output signal. A MISO NARX model can then be constructed from the decomposed multiple inputs and the single output signal. The resulting MISO model is shown to meet the basic requirement for the existence of a Volterra series representation from which important frequency domain properties can be derived, explained and discussed. This is done by first introducing the derivation of generalized frequency response functions (GFRFs) from time domain MISO NARX models. The steady state response synthesis problem using the input spectrum and the MISO GFRFs is then investigated in order to verify the effectiveness and accuracy of the MISO modelling approach for severely nonlinear systems. Finally a new frequency domain analysis method is introduced for systems that exhibit subharmonic oscillations.
MSC:
| 93A30 | Mathematical modelling of systems (MSC2010) |
| 93B50 | Synthesis problems |
References:
| [1] | DOI: 10.1109/PROC.1971.8525 · doi:10.1109/PROC.1971.8525 |
| [2] | Billings SA, Proceedings of the IEEE, Pt.D 127 pp pp. 272–285– (1980) |
| [3] | DOI: 10.1142/S0218127401003164 · doi:10.1142/S0218127401003164 |
| [4] | DOI: 10.1080/00207728908910143 · Zbl 0674.93066 · doi:10.1080/00207728908910143 |
| [5] | Billings SA, Proceedings of the 7th IFAC Symposium on Identification and Parameter Estimation pp pp. 193–210– (1985) |
| [6] | DOI: 10.1080/00207179008953572 · Zbl 0721.93041 · doi:10.1080/00207179008953572 |
| [7] | Billings SA, J. Mech Systems and Signal Processing 3 pp pp. 319–339– (1989) |
| [8] | Billings SA, Proc. IEE, Pt. D 130 pp pp. 193–199– (1983) |
| [9] | DOI: 10.1080/00207728808964057 · Zbl 0669.93015 · doi:10.1080/00207728808964057 |
| [10] | DOI: 10.1109/TCSI.2003.813965 · Zbl 1368.94174 · doi:10.1109/TCSI.2003.813965 |
| [11] | DOI: 10.1093/imamci/1.3.243 · Zbl 0668.93042 · doi:10.1093/imamci/1.3.243 |
| [12] | DOI: 10.1016/0022-460X(70)90074-X · Zbl 0198.52302 · doi:10.1016/0022-460X(70)90074-X |
| [13] | DOI: 10.1016/S0022-460X(03)00258-X · doi:10.1016/S0022-460X(03)00258-X |
| [14] | DOI: 10.1109/PROC.1974.9572 · doi:10.1109/PROC.1974.9572 |
| [15] | Greenman J, Physica D–Nonlinear Phenomena 190 pp pp. 136–151– (2004) · Zbl 1040.92046 · doi:10.1016/j.physd.2003.08.008 |
| [16] | Hsu HP, Outline of Fourier Analysis (1967) |
| [17] | Hung G, Mathematical Biosecience 37 pp pp. 135–190– (1977) |
| [18] | Kim KI, IEEE Transactions ASSP 36 pp pp 1758–1769– (1988) |
| [19] | DOI: 10.1109/78.403342 · doi:10.1109/78.403342 |
| [20] | Lang ZQ, IEEE Transactions on circuits and systems Ii-Analog and Digital Signal Processing 47 pp pp. 28–38– (2000) |
| [21] | DOI: 10.1080/00207176508905543 · doi:10.1080/00207176508905543 |
| [22] | Peyton Jones JC, Int. J. Control 50 pp pp. 1925–1940– (1989) |
| [23] | Rugh WJ, Nonlinear System Theory–The Volterra/Wiener Approach (1981) |
| [24] | Schetzen M, The Volterra and Wiener Theories of Non-linear System (1980) · Zbl 0501.93002 |
| [25] | Subba Rao T, Proceedings of the 7th IFAC Symposium on Identification and Parameter Estimation (1985) |
| [26] | DOI: 10.1080/00207170010030144 · Zbl 1038.93066 · doi:10.1080/00207170010030144 |
| [27] | Tommaseo G, European Physical Journal D 28 pp pp. 39–48– (2004) |
| [28] | DOI: 10.1016/S0029-8018(02)00144-0 · doi:10.1016/S0029-8018(02)00144-0 |
| [29] | Velazquez JLP, Physica D–Nonlinear Phenomena 186 pp pp. 205–220– (2003) |
| [30] | Volterra V, Theory of Functionals (1930) |
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