Nonlinear Multirate Model-Algorithmic Control. 2. Experimental Application to a Polymerization Reactor

Abstract

This paper experimentally implements the nonlinear multirate model-algorithmic controller to regulate the reactor temperature, which is measured at a fast sampling rate, and the numberaverage molecular weight of the polymer, which is measured at an extremely slow sampling rate. A detailed model of the continuous free-radical methyl methacrylate polymerization reactor was developed from first principles to construct the multirate controller algorithm. The performance of the controller was examined by varying the tunable controller parameters, where it was shown that the controller can adequately track step changes in the output set points under active input constraints. Decreasing the tunable controller parameters deteriorated the control of the number-average molecular weight but improved the control of the temperature. Overall, the nonlinear multirate controller was an efficient and effective method to deal with the difficult problem of multirate output measurements.

Mw Control of Continuous Polymer Reactors

“…As it can be seen in the figure: (i) the behavior of the discrete controller with small sampling period-delay ( = 5 min) approaches the behavior of the controller with continuous MW measurements, and (ii) the discrete controller with long sampling period-delay ( = 90 min) regulates the MW in about 380 minutes (1.7 residence times). In terms of natural residence time units, the proposed MW controller with = 90 min (about 1 half of the residence time) regulates the MW with similar convergence time than the ones obtained with full-model -based and appropriately tuned control schemes (Niemiec et al, 2002). In other words, the proposed MW control scheme can perform the same task with less modeling requirements and more robustness with respect to model uncertainty.…”

“…The modeling requirements of the volume, temperature and monomer loops (19a-b) are: two steady-state approximated constants (a T , a j ) for the temperature loop, and calorimetric parameters (densities and heat capacities) for the monomer loop. These modeling requirements are fewer than the ones of previous polymer reactor control studies with MW measurements (Adebekun and Schork, 1989;Ellis et al, 1994;Niemiec et al, 2002).…”

“…Sometimes nonlinear chemical process and polymer reactor estimation and control problems are addressed on the basis of Euler-type discretization (Tatiraju et al, 1999;Niemiec et al, 2002). By doing so, the implementation is simplified at the cost of limiting the estimation and/or control capability to handle DD MW measurements.…”

“…with the unstable steady-state being the setpoint, and the closed-loop reactor-control system was subjected to step changes in the reactor and jacket feed temperatures step changes shown in Figure 1 (at t = 100 min: T e from 315 to 320 K, and T je from 328 to 330 K). Two sampling periods-delays were tested: (i) = 5 min, to evaluate the recovery target towards the continuous MW measurements case (10), and (ii) = 90 min, in accordance to previous polymer reactor control studies (Niemiec et al, 2002) where the long sampling period-delay is about one half of the nominal residence time. Following the tuning guidelines of section 4 and the ones from (Alvarez and González, 2006), the MW control gains were set as follows: = 5 min, o = 3, o = (1/10) min -1 c = 1.5, c = (1/100) min -1 = 90 min, o = 1, o = (1/90) min -1 c = 0.71, c = (1/140) min -1…”

“…The state-of-the-art can be seen elsewhere (Richards and Congalidis, 2006), and here it suffices to mention that several control approaches have been employed, including linear PI controllers (Ellis et al, 1994) as well as nonlinear geometric (Adebekun and Schork, 1989;Niemiec et al, 2002), model predictive (MPC) (Mutha et al, 1997), and calorimetric (Alvarez et al, 2004) control techniques, including open-loop (Adebekun and Schork, 1989), extended Kalman filter (EKF) (Ellis et al, 1994;Mutha et al, 1997), and Luenberger (L) (Tatiraju et al, 1999) nonlinear observers. Most of the MW control and/or estimation schemes have been driven by size exclusion chromatography (SEC) (Ellis et al, 1994) and gel permeation chromatography (GPC) (Niemiec et al, 2002) measurements, which typically involve low sampling rates and long delays. This feature and the detailedmodel dependency of the control schemes affect the functioning, and imply complexity, reliability, and cost drawbacks for industrial applicability.…”