Control of bounded dynamic stochastic distributions using square root models: an applicability study in papermaking systems

Abstract

Following the recent developments on the modelling and control algorithms of the shape of the output probability density function for general dynamic stochastic systems (Wang, 1998a, Proceedings of the IFAC Workshop on AARCT, Cancun, pp. 95-99), this paper presents a square root approximation-based control algorithm, where the B-splines function expansion is used to approximate the square root of the output probability density function in order to guarantee its positiveness. It has been shown that with such an approximation, the system is generally nonlinear. This is true even when the dynamic part of the system is linear. As such, a nonlinear control algorithm has been developed to control the output probability density function of the system. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

Keywords

B-spline neural networks dynamic stochastic systems nonlinear control algorithms papermaking systems probability density function

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References

Åström, K. J. 1970: Introduction to stochastic control theory. New York: Academic Press.

Baki, H. , Kabore, P. and Wang, H. 1999: Bounded distribution control toolbox (MATLAB). Manchester: Department of Paper Science, UMIST.

Baki, H. and Munro, N. 1997: A MATLAB tool-box for parametric uncertain models. In: Colloquium in Robust Control: Theory, Software and Applications, Savoy Place, London, October, London: IEE, pp. 6/1-6/3.

Brown, M. and Harris, C. 1994: Neurofuzzy adaptive modelling and control. Hemel-Hempstead: Prentice-Hall.

Dodson, C. and Wang, H. 1999: Information geometry for statistical parameter estimation in process optimisation algorithms for stochastic systems. Submitted to Journal of Statistical Inference for Stochastic Processes.

Gajic, Z. and Losada, R. 1998: Monotonicity of algebraic Lyapunov iterations for optimal control of jump parameter linear systems. In: Proceedings of the 1998 American Control Conference. Philadelphia: Omnipress, Volume 1, 746-750.

Moore, M. 1997: Practical applications of a novel web monitor for paper machines. In: Proceedings of the 1997 APPITA Conference, Melbourne. Sydney: Australia Tappi.

Smook, G. 1992: Handbook for pulp and paper technologists. Vancouver: Angus Wilde Publications.

Wang, H. , Wang, A. P. and Duncan, S. 1997: Advanced process control for paper and board making. Leatherhead, Surrey: Pira International Ltd.

10.

Wang, H. 1998a: Control of the output probability density functions for a class of nonlinear stochastic systems. In: Proceedings of the IFAC Workshop on AARCT, Cancum, Mexico. Oxford: Elsevier Science, 95-99.

11.

Wang, H. 1998b: Detect unexpected changes of the particle size distribution in paper making white water systems. In: Proceedings of the IFAC Workshop on Online Fault Detection and Supervision in the Chemical Process Industries, Lyon. Oxford: Elsevier Science, 56-60.

12.

Wang, H. 1998c: Robust control of the output probability density functions for multivariable stochastic systems. In: Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida. Philadelphia: Omnipress, 1305-1310.

13.

Wang, H. 1999a: Robust control of the output probability density functionss for multivariable stochastic systems with guaranteed stability. IEEE Transaction on Automatic Control 44, 2103-2107.

14.

Wang, H. 1999b: Model reference adaptive control of the output stochastic distributions for unknown linear stochastic systems. International Journal of Systems Science 30, 707-715.