(242k) Optimization-Based Design of Plant-Friendly Input Signals for Data-Centric Estimation and Control

In recent years, the increasing need for reliable, high performance estimation and control in the process industries has spurred significant interest in data-centric dynamic modeling frameworks such as Just-in-Time modeling (Cybenko, 1996), lazy learning (Bontempi et al., 1999), and Model-on-Demand (MoD) estimation (Stenman, 1999). The significant appeal of these data-centric approaches is that they enable nonlinear estimation and control, while reducing the structural decisions made by the user and maintaining reliable numerical computations (Braun et. al, 2000). The performance of these methods, however, is highly dependent upon the availability of quality, informative databases, and consequently, good experimental designs are an imperative.

Multisine signals are deterministic, periodic signals whose power spectra can be directly specified by the user; these have been demonstrated to provide a flexible, powerful framework for identification testing in the process industries. Prior research on multisine input signals geared for MoD estimation (Braun et al., 2000, 2002) was somewhat ad hoc in that the signals designed to minimize crest factor (a measure of how evenly distributed a signal is over a span), were analyzed a posteriori to determine their adequacy for data-centric estimation purposes. While this work demonstrated that criteria such as crest factor still has relevance in the data-centric modeling context, a more important consideration in signal design for these kinds of estimation methods is to achieve uniform coverage of regressors in the database. This paper examines the development of signal designs specifically geared for data-centric frameworks that also satisfy plant-friendliness constraints during identification testing, an important practical consideration.

The basic approach relies on applying principles arising from geometric discrepancy theory (Matousek, 1999) as a means for achieving uniformity of the data in a regressor space. This is accomplished by replacing the crest factor objective with a discrepancy function made up of trigonometric polynomials arising from Weyl's Theorem that insure that the points are equidistant on a state-space. The optimization-based multisine design problem calls for minimizing this discrepancy function on the anticipated outputs of the system, subject to the restrictions of an orthogonal ?zippered? spectrum (used to enable multi-channel implementation) and simultaneously enforcing plant-friendliness time-domain constraints on upper/lower limits, move sizes, and rates of change in either (or both) input and output signals. The optimization problem is solved using a state-of-the-art NLP solver (KNITRO 3.1) which uses an interior point trust region SQP method to solve these types of challenging constrained optimization problems.

The power and usefulness of this problem formulation are demonstrated by applying it to dynamic modeling and control of the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy (1980). The signal is designed with a modified ?zippered? power spectrum that uses correlated harmonics that promote the presence of low-gain directionality information in the data (Lee et al., 2003). In addition to the use of a Weyl-based objective function and the plant-friendliness constraints noted previously, the optimization problem includes a search for all the Fourier coefficients and phases in the signal, including those of the correlated harmonics. Such a problem formulation involves very little user intervention, which further enhances its practical usefulness. Compared to minimum crest factor signals with the same number of harmonics and frequency grid, the use of the Weyl-based objective and the ability to search for all phases and amplitudes with the optimizer clearly results in a much more uniformly distributed coverage of the output state-space, and a much improved dataset for data-centric estimation purposes. The resulting benefit of these signals for control purposes is demonstrated by evaluating their effectiveness in a MoD-based Model Predictive Controller, as described in Braun et al. (2000).

References:

Bontempi, G., M. Biratari and H. Bersini (1999). Lazy learning for local modeling and control design. Int. J. of Control, 72(7), 643-658.

Braun, M.W., D.E. Rivera, and A. Stenman (2000), Model-On-Demand Model Predictive Control for Nonlinear Process Systems, AIChE 2000 Annual Meeting, Paper 256h, pgs. 1 - 40, November 2000.

Braun, M.W., R. Ortiz-Mojica and D.E. Rivera (2002). Application of minimum crest factor multisinusoidal signals for ?plant-friendly? identification of nonlinear process systems, Control Engineering Practice, 10, 301-313.

Cybenko, G. (1996). Just-in-time learning and estimation. In: Identification, Adaptation, Learning (S. Bittani and G.Picci, Eds.).pp.~423-434. NATO ASI. Springer.

Lee, H., D.E. Rivera, and H.D. Mittelmann (2003), Constrained minimum crest factor multisine signals for plant-friendly identification of highly interactive systems, 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands, pgs. 947-952.

Matousek, J. (1999). Geometric Discrepancy: An Illustrated Guide. Springer-Verlag. Berlin.

Stenman, Anders (1999). Model on Demand: Algorithms, Analysis and Applications. PhD thesis. Dept. of Electrical Engineering, Linkoping University, Sweden.

Weischedel, K. and T.J. McAvoy (1980). Feasibility of decoupling in conventionally controlled distillation column. Ind. Eng. Chem. Fund. 19, 379-384.