(369p) Plant Friendly Input Design for System Identification

The problem of designing an experiment that is maximally informative for estimation of the unknown parameters has been well studied in the statistics literature. System identification is the process of generating a dynamic model of a system using data and process knowledge. It is common practice to perturb the system of interest and use the resulting data to build the model. The problem of input design is to synthesize an input signal that is maximally informative for generating good quality dynamic models.

Identification in process industries is carried out on operating plants and hence it is important to ensure that the experiment is least hostile to operating conditions or equivalently, the input signal should be ?plant friendly?. Plant friendly identification is a challenging problem of immense importance to the process engineering community [1].

Plant friendliness requirements often require that input move sizes, input and output amplitudes or energies and experiment time is kept to a minimum [1,2]. System identification theory and practice however requires persistent excitation, high signal to noise levels and long periods of testing and hence the two demands are often conflicting. Thus, the problem is inherently multi-objective in nature and trade-offs between the two were quantified by solving appropriate multi-objective optimization problems in recent publications by the authors [3,4].

Some of the recent work by the authors on plant friendly identification focused on reducing input move sizes [4,5]. It is often the case that output constraints are more relevant for plant friendly identification. In this contribution, we focus on constraints in the output space. Such constraints could be of the form of limiting output energies, output magnitudes. The theory of Tchebysheff systems has been used to parameterize the feasible set for optimal input design problems [5,6]. In this contribution, we extend this approach to the design of plant friendly input designs. The decision variables are parameterized in terms of linear functions of parital auto-correlation sequences or equivalently in terms of mo- ment points. Using the theory of Tchebysheff systems, the feasible set is represented by linear constraints. The problem is thus converted to a Semi Definite Program that can be solved efficiently [7].

We calculate tight lower and upper bounds on the probability that the output amplitudes satisfy the given constraints for all input sequences with the given partial auto-correlation sequences. The quality of the relaxation can be determined by the use of multivariate Tchebysheff inequalities and semi-definite programming [8].

References:

1. ?Plant friendly system identification: A challenge for the process industries? Daniel E. Rivera, Hyunjin Lee, Martin W. Braun and Hans D. Mittelmann, 13th International Symposium on System Identification (SYSID), Rotterdam, The Netherlands, pg 917-922, 2003.

2. Rivera, D.E., H. Lee, H.D. Mittelmann, and M.W. Braun, "Constrained multisine input signals for plant-friendly identification of chemical process systems," Journal of Process Control, Vol. 19, No. 4, pgs. 623 - 635.

3. S. Narasimhan, R. Srinivasan and R. Rengaswamy (2003). Multi-objective input signal design for plant-friendly identification, proceedings of SYSID2003. Rotterdam, Netherlands

4. S. Narasimhan and R. Rengaswamy, ?Multi-objective optimal input design for plant friendly identification?, proceedings of the American Control Conference, 2008.

5. S. Narasimhan and R. Rengaswamy, ?Plant friendly input design: convex relaxation and quality?, under review.

6. M. Zarrop, ?A Chebyshev System Approach to Optimal Input Design?, IEEE Transactions on Automatic Control, vol 24, 687-698,1979.

7. J. Lfberg, ?Yalmip : A toolbox for modeling and optimization in MATLAB,? in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. [Online]. Available: http://control.ee.ethz.ch/ joloef/yalmip.php

8. D. Bertsimas and I. Popescu. Optimal inequalities in probability theory: A convex programming approach. SIAM J. Optim., 15:780?804, 2005.