(520b) An Integrated Methodology for Plant-Friendly Input Signal Design and Control-Relevant Estimation of Highly Interactive Processes

An effective, integrated methodology for control-relevant identification of multivariable systems, satisfying process operating constraints and conducted within an acceptable time period, has long been coveted in the process industries. Highly interactive processes such as high purity distillation represent a particularly challenging class of systems in this regard, because of their inherent difficulty in obtaining low-gain directionality information using conventional open-loop identification tests. In addition, control-relevant model estimation procedures are needed that capture the level of process directionality required for high performance model-based controllers, such as Model Predictive Control. In this talk, we present an integrated methodology for input signal design, experimental testing, and control-relevant parameter estimation (CRPEP) that addresses the challenges associated with highly interactive chemical processes under conditions that may involve significant noise and ?plant-friendly? operating restrictions.

The procedure involves the use of properly designed multisine signals, spectral analysis, and control-relevant curvefitting of the resulting frequency responses to parsimonious discrete-time models useful for Model Predictive Control. The key component of the multisine design procedure applied to highly interactive systems lies in the specification of the power spectrum. Here we apply a modified orthogonal (?zippered?) power spectrum with correlated harmonics that promotes the presence of low gain information in the data. The authors have extended the design procedure presented in Lee et al. (2003) for specifying the phases and magnitude of correlated harmonics to consider user-specified (real or complex-valued) input directions, beyond the [1?1] input direction that typically describes the low gain direction in problems such as high-purity distillation. The magnitude of the correlated harmonics can be further adjusted so that the output spans of the low gain direction are comparable to those of the high gain direction of the system. The multisine signal design procedure takes advantage of a priori knowledge of either steady-state or dynamic process gain directionalities in determining the character of these correlated harmonics.

A frequency response of the plant is generated by applying nonparametric identification procedures such as spectral analysis to the input/output data obtained during experimental testing. This response needs to be curvefit to a model useful for Model Predictive Control purposes. The control-relevant parameter estimation procedure consists of an iterative frequency response curvefitting problem with pre and post weighting functions, which are systematically defined from the nominal model, the nominal closed-loop transfer functions, and the setpoint and disturbance directions to be faced by the control system (Gaikwad and Rivera, 1997; Bayard, 1994). We have enhanced the control-relevant parameter estimation algorithm so that it can take advantage of directionality information provided by the correlated harmonics. A full Matrix Fraction Description (MFD) model representation (de Callafon et al, 1996) utilized in the curvefitter allows independent poles to be specified for individual transfer function elements, giving greater flexibility in the representation of the multivariable system structure. Because control requirements are systematically incorporated in the curvefitting algorithm, the appropriate level of gain directionality information needed for desired closed-loop performance is automatically captured in the final parametric model.

The synergism provided by the integrated methodology is illustrated in a series of meaningful case studies. One is the nonlinear 2x2 Weischedel-McAvoy (1980) high-purity distillation problem, while the other is a conceptual 3x3 highly interactive system (Koung and MacGregor, 1994). In these case studies we illustrate that for equivalent noise levels and experimental test duration, the integrated algorithm will produce models leading to improved closed-loop MPC performance in comparison to models from classical input signal designs such as PRBS or standard zippered multisine that are estimated with unweighted methods (such as ARX or unweighted curvefitting). Alternatively, we show that standard/unweighted methods could give a desirable result, but only after requiring significantly longer identification tests that those resulting from signals proposed in this work. Ultimately, the goal of this work is to develop a system identification framework that is able to produce a nominal model for control design for large, nonlinear, multivariable process systems, such as those frequently encountered in advanced control implementations in the petrochemical and refining industries.

References:

Bayard, D. S. (1994), High-order multivariable transfer function curve fitting: Algorithms, sparse matrix methods and experimental results, Automatica, 30(9), pp. 1439?1444.

de Callafon, R., D. de Roover, and P. Van den Hof (1996), Multivariable least squares frequency domain identification using polynomial matrix fraction descriptions, 35th IEEE Conference on Decision and Control, Kobe, Japan, vol. 2, pp. 2030?2035.

Gaikwad, S. and D. Rivera (1997), Multivariable frequency-response curve fitting with application to control-relevant parameter estimation, Automatica, 33(4), pp. 1169?1174.

Koung, C.W. and J.F. MacGregor (1994), Identification for robust multivariable control: the design of experiments. Automatica, 30(10), 1541?1554.

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.

Lee, H., D. E. Rivera, and H. D. Mittelmann (2003), A Novel Approach to Plant-Friendly Multivariable Identification of Highly Interactive Systems, paper 436a, 2003 AIChE Annual Meeting, San Francisco, CA, Nov. 16-21.

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