×

Adaptive control of Wiener type nonlinear systems. (English) Zbl 0765.93042

Summary: This study is concerned with the problem of adaptive control of a Wiener type nonlinear process. It is assumed that the linear dynamic part of the process can be represented by a pulse transfer function of known order, with stable inverse followed by a known time delay. The memoryless nonlinarity is one-to-one on a compact set and belongs to one of two classes: (1) piecewise linear with known breakpoints, or (2) smooth function (in which case an approximation is made). It is represented by linear splines. The output signal from the linear part is not available for measurement.
The global stability of the proposed model reference adaptive control scheme is established subject to the assumption that the nonlinearity can be represented exactly by the linear spline function with a given set of breakpoints. Otherwise, there will be a residual tracking error which depends on the nonlinearity approximation error, but the boundedness of all signals can be assured. The proposed scheme is used for adaptive control of the pH-process in a continuous flow reactor.

MSC:

93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Anbumani, K.; Sarma, I.G.; Patnaik, L.M., Self-tuning control of nonlinear systems characterized by Hammerstein models, (), 78-83 · Zbl 0561.93036
[2] Billings S. A. Identification of nonlinear systems—A Survey. IEEE Proc., {\bf127,} 272-285.
[3] Butler, J.N., ()
[4] Goodwin, G.C.; Sin, K.S., ()
[5] Jaakola, P., Adaptive ph-controllers, (), (in Finnish)
[6] Kreisselmeier, C.; Narenda, K.S., Stable model reference adaptive control in the presence of bounded disturbances, IEEE trans. aut. control, AC-27, 1169, (1982) · Zbl 0498.93036
[7] Kung, M.C.; Womack, B.F., Discrete time adaptive control of linear systems with preload nonlinearity, Automatica, 20, 477, (1984) · Zbl 0539.93053
[8] Lancaster, P.; Salkansas, K., ()
[9] Niemi, A.; Jutila, P.K., Process models and control of acidity: computer applications in the analysis of chemical data and plants, CHEMDATA77, Finland, (1977), (1986)
[10] Pajunen, G.A., Application of a model reference adaptive technique to the identification and control of Wiener type nonlinear processes, Acta polytechnica scandinavica, (1984), Electrical Engineering Series No. 52, Helsinki
[11] Richter, J.D.; Fourier, C.D.; Ash, R.H.; Marcikic, S., Waste neutralization control—digital simulation spots nonlinearities, Instrumentation technology, 35, (1974)
[12] Sung, D.J.T.; Lee, T.T., Model reference adaptive control for linear dynamic systems having a polynomial input, IEEE trans. aut. control, AC-32, 1106, (1981)
[13] Zhang, J.; Lang, S., Indirect adaptive suboptimal control for linear dynamic systems having polynomial nonlinearities, IEEE trans. aut. control, AC-33, 389, (1988) · Zbl 0643.93040
[14] Zhang, J.; Lang, S., Explicit self-tuning control for a class of nonlinear systems, Automatica, 25, 593, (1989) · Zbl 0694.93053
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.