Closed-loop state estimation

Sundaramoorthy and Rao designed and implemented a DDC scheme on a batch fluid-bed dryer, which was drying wet sawdust [32]. The system was described by a state-space model with parameters that were estimated from experimental data. The performance of the designed controller was checked by closed-loop simulation and then the scheme was implemented online using the heater power supply as the final control element to regulate the inlet-air temperature. 

As discussed in Section 8.3.2, in addition to the fast and frequent on-hne measurement, some measurements may be available at infrequent and/or irregular times and with significant delays. For example, there may be a combination of MWDs and PSDs measured off-line by chromatographic methods and monomer concentrations measured in real time by spectroscopic methods. In these cases, the so-called multi-rate state estimators maybe applied. In these estimators, the fast measurements are used to estimate the state variables that are observable, while estimation of the non-observable variables is obtained in open-loop mode. When the (infrequent) measurement becomes available, the close-loop estimator is used. Ellis et al. [102] and Mutha etal. [108] used a multi-rate EKF to estimate monomer conversion and average molecular weights in the solution polymerization ofMMA. 

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. 

The optimization provides the amounts of monomers and CTAs in the reactor at any overall conversion. These profiles are independent of the kinetics of the process and can be regarded as master curves. Once the trajectories of the amounts of monomers and CTAs as a function of the conversion are calculated, the implementation of the closed-loop strategy (Figure 6.14) reduces to tracking these profiles. To do so, on-line measurements of the overall conversion and of the free amount of monomers and CTA are necessary. Reaction calorimetry plus state estimation is probably the easiest, cheapest, and most robust option from an industrial perspective. 

In summary, the simplicity of measurement makes turbidity spectra methods attractive for on-line monitoring of particle size distribution, particular / if the distribution is known to be monomodal. In this case average particle size, determined by turbidimetry may be sufficient for continuous monitoring and control. This has been shown by Hamielec and coworkers (10) who, by techniques of state estimation, have used turbidity data to estimate other states of an emulsion system, and applied closed-loop control accordingly. 

For the five mixtures, the cumulative mesoporous volume, Feds, and mesoporous surface area, S edB, and are both linear decreasing functions of the micropore content y (Figure 2b). The cumulative specific surface area SedB is definitely a better estimator of the mesoporous surface than the specific surface S xt computed Ifom the t-plot. The lUPAC classification states that mesopores are pores whose width is larger that 2 nm. In the case of the cylindrical pore model retained for the pore size distribution, this is equivalent to radii larger than 1 nm. It should however be stressed that the calculation of the cumulative surface and volume of the mesopores must not be continued at lower pressures than the closing of the hysteresis loop (gray zones of Figures 3a and 3b). If a black box analysis tool is used and if the calculation is systematically continued down to 1 nm, severe overestimation of the mesopores surface and volume may occur. 

The differences in the motion of the two loops seen in the simulations appeared to originate from differences between the two subunits in the crystal structure that made the closing of the loop in subunit II less probable than in subunit I. These seemed to hinder full relaxation of all the bonds and angles in the loop in subunit II to their equilibrium values, so that, during much of the simulation time, only 9 residues moved in subunit II, whereas 11 moved in subunit I. This discrepancy appears to arise from crystal contacts, which keep the loop in subunit II in a defined open conformation in the crystal structure, whereas the loop in subunit I is disordered and exposed to solvent. Sulfate and phosphate ions are able to bind in the active site of subunit I but not subunit II in the crystal. These differences suggest that the loop in subunit I may undergo motions that are more representative of those of the active enzyme in solution than the loop in subunit II, which exists in a somewhat artificial state that restricts its motion. Therefore, the effect of gating on the rate constant of the reaaion was estimated from the motion of the loop in subunit I. 

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