Abstract
This chapter provides an overview of wavelets from a process control perspective. The time-frequency localization and multiresolution properties of wavelets are discussed in the context of control applications. We also discuss various control problems where wavelets could be particularly advantageous. We illustrate the benefits of wavelet formulations by presenting wavelet domain approaches to basis reduction and frequency domain tuning in model predictive control problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alpert, B.K. (1992). Wavelets and Other Bases for Fast Numerical Linear Algebra. In Wavelets: A Tutorial in Theory and Applications, Edited by Charles Chui. pp 181–216. Academic Press, San Diego, CA.
Bakshi R.B. and Stephanopoulos G. (1992). Representation of Process Trends Part III: Multi-Scale Extraction of Trends from Process Data. Submitted toComputers ê? Chem. Engng.
Bakshi R.B. and Stephanopoulos G. (1993). Wave-Net: A Multiresolution, Hierarchical Neural Network with Localized Learning. AIChE Journal, 39, pp. 57–81.
Beylkin G., Coifman R. and Rokhlin V. (1991). Fast Wavelet Transforms and Numerical Algorithms I. Communications on Pure and Applied Mathematics, 44, pp.141–183.
Carrier J.F. and Stephanopoulos G. (1992). Multiresolution Theory for Model Identification and Control. Presented at the AIChE Annual Meeting, Miami Beach, FL.
Coifman R., Meyer Y. and Wickerhauser V. (1992). Wavelet Analysis and Signal Processing. In Wavelets and their Applications, Edited by Mary B. Ruskai, pp. 153–178. Jones and Bartlett Publishers, Boston, MA.
Daubechies I. (1988). Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics, 41, pp. 909–996.
Daubechies I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia, PA.
Elias-Juarez A. and Kantor J.C. (1992). On the Application of Wavelets to Model Predictive Control. Presented at the American Control Conference, Chicago, IL.
Joshi, A. and Motard R.L. (1991). Linear Time-Frequency Analysis in Automated Fault Detection. Presented at the AIChE Annual Meeting, Los Angeles, CA.
Lee J. H., Chikkula Y., Yu Z. H. and Kantor J.C. (1992a). Improving the Computational Efficiency of the Model Predictive Control Algorithm Using the Wavelet Transformation. Submitted to International Journal of Control.
Lee J.H. and Yu Z.H. (1992b). Robust Tuning of Model Predictive Controllers. Accepted for publication in Computers é4 Chem. Engng.
Lee J.H., Gelormino M.S. and Morari M. (1992c). Model Predictive Control of Multi-Rate Sampled-Data Systems: A State-Space Approach. International Journal of Control, 55, pp. 153–191.
Leonard J.A. and Kramer M.A. (1991). Radial Basis Function Networks for Classifying Process Faults.IEEE Control Systems, pp. 55,31–38, April, 1991.
Leonard J.A. and Kramer M.A. and Ungar L.H. (1992). A Neural Network Architecture that Computes Its Own Reliability. Computers é4 Chem. Engng, 16, 819–35.
Liandrat J., Perrier V. and Tchamitchian Ph. (1992). Numerical Resolution of Nonlinear Partial Differential Equations Using the Wavelet Approach. In Wavelets and their Applications, Edited by Mary B. Ruskai, pp. 227–238. Jones and Bartlett Publishers, Boston, MA.
Mallat S. (1989a). Multiresolution Approximation and Wavelet Orthonormal bases of L 2 (R). Transactions of the American Mathematical Society, 315, pp. 69–87.
Mallat S. (1989b). A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 pp.674–693.
Meyer Y. (1985). Principe d’incertitude, bases hilbertiennes et algèbres d’ opérateurs. Séminaire Bourbaki, no. 662.
Meyer Y. (1986). Ondelettes et functions splines. Séminaire Equations aux Derivees Partielles, Ecole Polytechnique, Paris, France.
Nikolaou M. and Yong You (1992). Solution of Partial Differential Equations Using Wavelets. Presented at the AIChE Annual Meeting, Miami Beach, FL.
Palavajjhala S., Motard R.L. and Babu Joseph (1993). Improving Robustness and Performance of QDMC Using Blocking and Condensing in the Wavelet Domain. Submitted toI& EC Research.
Rawlings, J.B. and Muske K.R. (1991). The Stability of Constrained Receding Horizon Control. Submitted to IEEE Trans. Automatic Control.
Stephanopoulos G. and Carrier J.F. (1991). Generation and Validation of Models for the Design of Process Controllers. Presented at the AIChE Annual Meeting, Los Angeles, CA.
Strang G. (1989). Wavelets and Dilation Equations: A Brief Introduction. SIAM Review, 31, pp.614–627.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Chikkula, Y., Lee, J.H. (1994). Application of Wavelets in Process Control. In: Motard, R.L., Joseph, B. (eds) Wavelet Applications in Chemical Engineering. The Kluwer International Series in Engineering and Computer Science, vol 272. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2708-4_6
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2708-4_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-9461-7
Online ISBN: 978-1-4615-2708-4
eBook Packages: Springer Book Archive