I intend to determine the Transfer matrix of a TRMS by system identification. In this context, which input would be better and why, chirp or PRBS ??
Dear Biswajit,
To obtain a consistent model, it is important to excite the process with all frequencies in its operating range. The input signal applied must therefore be rich in frequencies (have a broad spectrum). In general, a pseudo-random periodic signal (PRBS) is applied.
When we have a MIMO system, it is important to apply decorrelated signals to avoid introducing identification bias. A common idea of exchanging inputs one by one is a bad method because it introduces an identification bias and does not account for the normal operation of the system. It is important to follow a certain rigorous procedure to identify such a process.
For more information please see links and attached files in topics
-APPLICATION OF PSEUDO RANDOM BINARY SEQUENCE (PRBS ...
eprints.utm.my/11483/1/MaimunHujaHusinMFKE2008.pdf
- System Modeling 101 - Semantic Scholar
https://pdfs.semanticscholar.org/.../ac4034e57f6df2b79dcbdab684...
- Robustness estimation of self-sensing active magnetic bearings via ...
citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.474.2526&rep=rep1&type...
Best regards
Dear Lafifi, thank you for your reply. However, my question still remains un answered. A chirp input signal also contains multiple frequencies as does PRBS. The only difference is that PRBS has discrete time steps while chirp input has continuous time steps.
Hi Biswajit,
Thank you for inviting me into this discussion.
While Prof. Lafifi has provided an overview of PRBS excitation, my own feeling is that there is no firm reply to your question due to the strong nonlinearities involved. Any reply is certainly system-specific, and I would draw your attention to the exact nature of the TRMS, as described by Feedback (check out http://doc.es.aau.dk/fileadmin/doc.kom.aau.dk/labs_facillities/control/manuals/330074M5.PDF for some details).
The following observations are immediate:
Under the circumstances, excitation that is required for a reasonably accurate linear identification algorithm to converge effectively will have to be introduced by the experimenter - it is not present by default !
How effective the excitation is likely to prove (PRBS, chirp, or anything else for that matter !) is decided by the point around which you wish to linearise the TRMS system model. Depending on this fact, the TRMS system modes may be strongly excited by a white disturbance signal, may be weakly excited by the same, or may not be excited at all !!
Don't overlook the fact that commonly implemented real-time identification employs linear models for which effectiveness of PRBS, chirp, etc. are well understood. But a strongly nonlinear system is a different cup of tea altogether !
And if you wish to use a non-linear identification model such as the extended Kalman filter or the unscented Kalman filter, then the reply to your question is even more subjective, and requires careful examination of the filter properties !!
Cheers !
-Sanjay
The excitation signal choice represents a fundamental problem of system identification. Most of the existing methods for identifying these models assume that the input signal is of the white noise type. This signal is very interesting from the theoretical point of view because of its statistical properties. But, its practical use is not recommended. To overcome this problem, we can apply the pseudo-random binary sequence (PRBS) which is widely used for the identification of linear systems. The parameters are set taking into account only the dynamics of the system to be identified. Therefore, it can not be applied in the case of non-linear systems because they also require a judicious choice of excitation amplitudes to cover the entire operating range of the system to identify. Consequently, the chirp signal can be used in the case of non linear system.
About non-linear identification using PRBS. You can use an amplitude modulated PRBS (APRBS). Nelles O. Nonlinear System Identification overviews the procedure in chapter 17. Based on a standard PRBS, count the number of steps, divide the input interval into as many levels. For each change in the PRBS, randomly pick one level; do NOT pick the same level twice. Now you have an APRBS that can be used for non-linear system ID.
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