Multivariable Controller Performance Monitoring

CPM of multivariable control systems has attracted significant attention because of its industrial importance. Several methods have been proposed for performance assessment of multivariable control systems. One approach is based on the extension of minimum variance control performance bounds to multivariable control systems by computing the interactor matrix to estimate the time delay [103, 116]. The interactor matrix [103, 116] can be obtained theoretically from the transfer function via the Markov parameters or estimated from process data [114]. Once the interactor matrix is known, the multivariate extension of the performance bounds can be established. 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak 

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SJ Qin and J Yu. Multivariable controller performance monitoring. In Prep. IFAC ADCHEM 2006, pages 593-600, Gramado, Brazil, 2006. 

Martin, E. B., Morris, A. J., and Zhang, J. (1996). Process performance monitoring using multivariate statistical process control. IEE Proc. Control Theory 143, 132. 

The monitoring uses formulas that take into account feed flow rates, targets calculated by the optimization layer of multivariable control, controlled variables upper and lower limits and other parameters. The economic benefits are based on the degrees of freedom and the active constraints at the steady state predicted by the linear model embedded in the controller. In order to improve the current monitoring, parameters dealing with process variability will be incorporated in the formulas. By doing this, it will be also possible to quantify external disturbances that affect the performance of the advanced control systems and identify regulatory control problems. 

An overview of single-loop CPM is presented in Section 9.1. Section 9.2 surveys CPM tools for multivariable controllers. Monitoring of MPC performance and a case study based on MPC of an evaporator model and a supervisory knowledge-based system (KBS) is presented in Section 9.3 to illustrate the methodology. The extension of CPM to web and sheet processes is discussed in Section 10.3. 

TJ Harris, CT Seppala, and LD Desborough. A review of performance monitoring and assessment techniques for univariate and multivariate control systems. J. Process Control, 9 1-17, 1999. 

It is not the intention here to reproduce the detailed theory of model predictive control (MFC) or how it used for multivariable control (MVC). This has become an almost obligatory section in modem control texts. There are also numerous papers, marketing material and training courses. In this book its description is limited to its general principles focus instead is on how to apply it and monitor its performance. 

Several statistics from the models can be used to monitor the performance of the controller. Square prediction error (SPE) gives an indication of the quality of the PLS model. If the correlation of all variables remains the same, the SPE value should be low, and indicate that the model is operating within the limits for which it was developed. Hotelling s 7 provides an indication of where the process is operating relative to the conditions used to develop the PLS model, while the Q statistic is a measure of the variability of a sample s response relative to the model. Thus the use of a multivariate model (PCA or PLS) within a control system can provide information on the status of the control system. 

Multivariate envelope-based constraint control can lower overall excess oxygen. This can be achieved by monitoring both carbon dioxide and water and by performing constraint limit checks on excess oxygen, hydrocarbons, stack temperature, and opacity. 

The test samples should always be analyzed in random order to avoid the introduction of unwanted biases and time trends. A way to monitor such unwanted effects is to utilize quality control (QC) samples as a means to effectively examine system performance. QC samples are often made by pooling together subaliquots of biological test samples (29-31). This way a representative bulk sample is generated that should contain all metabolites present in the test samples. QC samples are typically analyzed through the analytical batch and data from the QC injections are scrutinized as a separate dataset by both multivariate analysis but also as typical LC-MS data. Data should pass certain criteria to ensure adequate quality of the dataset, that is, the number of zero values (which should be less than 40%), the CV% of the peak areas (should be less than 30% for a trustworthy peak), the number of peaks that pass the 30% CV filter (which should be higher than 70% in the dataset), the repeatability of retention times and peak areas, and so forth (29). 

J Schaefer and A Cinar. Multivariable MPC system performance assessment, monitoring, and diagnosis. J. Process Control, 14(2) 113-129, 2004. 

Kourti, T., and J. F. MacGregor, 1996. Multivariate Statistical Process Control methods for Monitoring, Diagnosing Process and Product Performance. J. Qual. Tech. 28 409-428. 

In future, multivariate analysis should be used more and more in everyday (scientific) life. Until recently, experimental work resulted in a very hmited amount of data, the analysis of which was quite easy and straightforward. Nowadays, it is common to have instmmentation producing an almost continuous flow of data. One example is process monitoring performed by measuring the values of several process variables, at a rate of one measurement every few minutes (or even seconds). Another example is quality control of a final product of a continuous process on which an FT-IR spectmm is taken every few minutes (or seconds). 

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