Multivariable robust control

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

This tutorial uses the MATLAB Control System Toolbox for linear quadratie regulator, linear quadratie estimator (Kalman filter) and linear quadratie Gaussian eontrol system design. The tutorial also employs the Robust Control Toolbox for multivariable robust eontrol system design. Problems in Chapter 9 are used as design examples. 

Then the multivariable IMC controller is set equal to the invertible part times a filter matrix which slows up the closedloop response to give the system more robustness. The filter acts as a tuning parameter (tike setting the closedloop time constant in the SISO case in Chap. 8). 

The final test of the proposed nonlinear robust controllers to be presented in this chapter is its implementation in a highly nonlinear reactor an non-isothermal homopolymerization carried out in a CSTR. In this case, we develop a multivariable version of the nonlinear regulator, in contrast to the SISO versions used in the previous examples. 

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... 

APC resides in a separate computer/server, linked to the DCS system. The platform used in Pearl GTL for APC is the Shell proprietary package SMOCPro (Shell Multivariable Optimising Control) in combination with RQEPro (Robust Quality Estimator). In total approximately 70 SMOC controllers and 100 Quality Estimators are being developed for Pearl GTL. 

Chu, C.C. (1985) Hoo-Optimization and Robust Multivariable Control, PhD Thesis, University of Minnesota, Minneapolis, MN. 

Lehtomaki, N.A., Sandell, Jr., N.R. and Athans, M. (1981) Robustness Results in Linear-Quadratic Gaussian Based Multivariable Control Designs, IEEE Trans, on Automat. Contr., AC-26(1), pp. 75-92. 

Chapter 16 covers the analysis of multivariable processes stability, robustness, performance. Chapter 17 presents a practical procedure for designing conventional multiloop SISO controllers (the diagonal control structure) and briefly discusses some of the full-blown multivariable controller structures that have been developed in recent years. 

In Chap. 15 we reviewed a tittle matrix mathematics and notation. Now that the tools are available, we will apply them in this chapter to the analysis of multivariable processes. Our primary concern is with closedloop systems. Given a process with its matrix of openloop transfer functions, we want to be able to see the effects of using various feedback controllers. Therefore we must be able to find out if the entire closedloop multivariable system is stable. And if it is stable, we want to know how stable it is. The last question considers the robustness of the controller, i.e., the tolerance of the controller to changes in parameters. If the system becomes unstable for small changes in process gains, time constants, or deadtimes, the controller is not robust. 

A bioprocess system has been monitored using a multi-analyzer system with the multivariate data used to model the process.27 The fed-batch E. coli bioprocess was monitored using an electronic nose, NIR, HPLC and quadrupole mass spectrometer in addition to the standard univariate probes such as a pH, temperature and dissolved oxygen electrode. The output of the various analyzers was used to develop a multivariate statistical process control (SPC) model for use on-line. The robustness and suitability of multivariate SPC were demonstrated with a tryptophan fermentation. 

One final comment should be made about model-based control before we leave the subject. These model-based controllers depend quite strongly on the validity of the model, particularly its dynamic fidelity. If we have a poor model or if the plant parameters change, the performance of a model-based controller is usually seriously affected. Model-based controllers are less robusf than the more conventional PI controllers. This lack of robustness can be a problem in the single-input, singleoutput (SISO) loops that we have been examining. It is an even more serious problem in multivariable systems, as we discuss in Chapters 12 and 13. 

The detergent drying process is a large-scale process, and in modem installations digital control systems are used to control the plant. However, the control of product properties such as density and blown powder moisture tends not to be fully automated, partly due to the multivariable uature of the product properties and lack of robust measurement systems. Therefore, there tends to be a human operator responsible for the starting-up, center lining, and shutting down of the process. 

Glover (1986) studied the robust stabilization of a linear multivariable open-loop unstable system modelled as (G+A) where G is a known rational transfer function and A is a perturbation (or plant uncertainty). G is decomposed as G/+G2, where G, is antistable and G2 is stable (Figure 1). The controller and the output of the feedback system are denoted by K and y respectively. Gi is strictly proper and K is proper. Glover (1986) argued that the stable projection G2 does not affect the stabilizability of the system, since it can be exactly cancelled by feedback. The necessary and sufficient condition for G to be robustly stabilized is to stabilize its antistable projection G/. 

Wise, B.M. and Ricker, N.L., (1991), Recent advances in multivariate statistical process control improving robustness and sensitivity. Proceedings of IFAC ADCHEM Symposium, 125. 

Al-Haj Ali et al. [5,6] developed different types of linear time invariant models by system identification, which adequately represent the fluidized-bed drying dynamics. MBC techniques such as IMC and model predictive control (MPC) were used for the designing of the control system. Simulations with multivariable MPC strategy provided robust, fast, stable, and non-oscillatory closed loop responses. A stationary form of Kalman filter was designed to estimate the particle moisture content (state observer). Performance studies showed that the Kalman filter provided satisfactory estimates even in the presence of significant noise levels and inaccurate initial states feed to the observer. 

Principles and Characteristics As already indicated in Chp. 1.2.3, Raman scattering induced by radiation (UV/VIS/NIR lasers) in gas, liquid or solid samples contains information about molecular vibrations. Raman specfioscopy (RS) was restricted for a long time primarily to academic research and was a technique rarely used outside the research laboratory. Within an industrial spectroscopy laboratory, two of the more significant advances in recent years have been the allying of FT-Raman and FTIR capabilities, coupled with the availability of multivariate data analysis software. Raman process control (in-line, on-line, in situ, onsite) is now taking off with various robust commercial instrumental systems equipped with stable laser sources, stable and sensitive CCD detectors, inexpensive fibre optics, etc. With easy interfacing with process streams and easy multiplexing with normal (remote) spectrometers the technique is expected to have impact on product and process quality. 

Experimentally, however, the spectra are easy to observe, thick samples being tractable in either transmission or reflection without preparation. As the spectra seldom possess many narrow features that could be unduly affected by instrumental or other factors, robust methods for quantitation were possible. With the arrival of cheap instrumental computing from the 1980s onwards and the development of multivariate analysis methodology, NIR spectroscopy has undergone considerable expansion in use. It is now widely applied to automated, rapid and precise quantitative analyses in agriculture, industrial process control and noninvasive medical examinations. A typical and early example was determination of the protein content of grain and flour. 

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