Process state estimation, prediction, and

Since biological processes are generally very complicated, they have not been fully described using mathematical models. However, hybrid process modeling based on all the available knowledge and information provided by means of mathematical models, heuristic knowledge or even by data sets has been shown to be useful for process state estimation, prediction and control [50, 51]. 

Dors, M., Simutis, R., Ltibbert, A. (1995) Hybrid process modeling for advanced process state estimation, prediction and control exemplified at a production scale mammalian cell culture. In Recent Advances in Biosensors, Bioprocess Monitoring, and Bioprocess Control, K.R. Rogers, A. Mulchandani, W. Zhou, Eds., ACS Symposium Series, American Chemical Society, Washington, D.C. (this vol.)... 

Hybrid Process Modeling for Advanced Process State Estimation, Prediction, and Control Exemplified in a Production-Scale Mammalian Cell Culture... 

Advanced process state estimation, prediction, and control via hybrid process modeling, 144-154 Aminophenols, use as sensor for subnanomolar concentrations, 70-80 Analyte concentrations, measurement using fluorescent lifetime, 99-108... 

Constraint control strategies can be classified as steady-state or dynamic. In the steady-state approach, the process dynamics are assumed to be much faster than the frequency with which the constraint control appHcation makes its control adjustments. The variables characterizing the proximity to the constraints, called the constraint variables, are usually monitored on a more frequent basis than actual control actions are made. A steady-state constraint appHcation increases (or decreases) a manipulated variable by a fixed amount, the value of which is determined to be safe based on an analysis of the proximity to relevant constraints. Once the appHcation has taken the control action toward or away from the constraint, it waits for the effect of the control action to work through the lower control levels and the process before taking another control step. Usually these steady-state constraint controls are implemented to move away from the active constraint at a faster rate than they do toward the constraint. The main advantage of the steady-state approach is that it is predictable and relatively straightforward to implement. Its major drawback is that, because it does not account for the dynamics of the constraint and manipulated variables, a conservative estimate must be taken in how close and how quickly the operation is moved toward the active constraints. 

State estimators are basically just mathematical models of the system that are solved on-line. These models usually assume linear DDEs, but nonlinear equations can be incorporated. The actual measured inputs to the process (manipulated variables) are fed into the model equations, and the model equations are integrated. Then the available measured output variables are compared with the predictions of the model. The differences between the actual measured output variables and the predictions of the model for these same variables are used to change the model estimates through some sort of feedback. As these differences between the predicted and measured variables are driven to zero, the model predictions of all the state variables are changed. 

Why is any of this of interest If it is known that some data are normally distributed and one can estimate p and a, then it is possible to state, for example, the probability of finding any particular result (value and uncertainty range) the probability that future measurements on the same system would give results above a certain value and whether the precision of the measurement is lit for purpose. Data are normally distributed if the only effects that cause variation in the result are random. Random processes are so ubiquitous that they can never be eliminated. However, an analyst might aspire to reducing the standard deviation to a minimum, and by knowing the mean and standard deviation predict their effects on the results. 

Since both the on-line dynamic optimization and the model-based control strategy rely on process models, the knowledge of current states and/or model parameters is required. However, in most industrial processes, state variables are not all measurable and some parameters are not known exactly. As a consequence, there is a need for estimating these states and parameters. In this work, two Extended Kalman Filters (EKF) are implemented. The first one is applied to predict the reactant concentration, which will be used for on-line dynamic optimization, from its delayed measurement. The other one is applied to estimate the unknown heat of reaction, which will be used for model-based controller, from the frequently available measurements of temperature. 

Figure 3 shows the predicted behavior of the pH of the solution as a function of leachant renewal frequency for the same system parameters. As can be seen, the higher the flow rate, the sooner steady state is achieved, and the closer the leachant composition to that of the original solution. In particular, the pH curve for the static case ( = 0) shows that the solution pH has not reached steady state yet after 28-days leaching. Approach to steady state under the static leaching conditions can be a very lengthy process. However, an equilibrium pH value can be estimated by use of the solution electroneutrality condition as applied to the reactions modeled. Indeed, at all times ... 

The success of MPC is based on a number of factors. First, the technique requires neither state space models (and Riccati equations) nor transfer matrix models (and spectral factorization techniques) but utilizes the step or impulse response as a simple and intuitive process description. This nonpara-metric process description allows time delays and complex dynamics to be represented with equal ease. No advanced knowledge of modeling and identification techniques is necessary. Instead of the observer or state estimator of classic optimal control theory, a model of the process is employed directly in the algorithm to predict the future process outputs. 

In the recent years Simulated Moving Bed (SMB) technology has become more and more attractive for complex separation tasks. To ensure the compliance with product specifications, a robust control is required. In this work a new optimization bas adaptive control strategy for the SMB is proposed A linearized reduced order model, which accounts for the periodic nature of the SMB process is used for online optimization and control purposes. Concentration measurements at the raffinate and extract outlets are used as the feedback information together with a periodic Kalman filter to remove model errors and to handle disturbances. The state estimate from the periodic Kalman filter is then used for the prediction of the outlet concentrations over a pre-defined time horizon. Predicted outlet concentrations constitute the basis for the calculation of the optimal input adjustments, which maximize the productivity and minimize the desorbent consumption subject to constraints on product purities. 

Corresponding estimates for auxiliary parametric functions that the user may define. Such estimates may include alternative parameters, predicted process states, and performance measures for processes designed with the given models and data. 

In the classical concept of predictive control, the trajectory (or set-point) of the process is assumed to be known. Control is implemented in a discrete-time fashion with a fixed sampling rate, i.e. measurements are assumed to be available at a certain frequency and the control inputs are changed accordingly. The inputs are piecewise constant over the sampling intervals. The prediction horizon Hp represents the number of time intervals over which the future process behavior will be predicted using the model and the assumed future inputs, and over which the performance of the process is optimized (Fig. 9.1). Only those inputs located in the control horizon H, are considered as optimization variables, whereas the remaining variables between Hr+1 and Hp are set equal to the input variables in the time interval Hr. The result of the optimization step is a sequence of input vectors. The first input vector is applied immediately to the plant. The control and the prediction horizon are then shifted one interval forward in time and the optimization run is repeated, taking into account new data on the process state and, eventually, newly estimated process parameters. The full process state is usually not measurable, so state estimation techniques must be used. Most model-predictive controllers employed in industry use input-output models of the process rather than a state-based approach. 

One alternative to the direct online measurement of polymer properties is to use a process model in conjunction with optimal state estimation techniques to predict the polymer properties. Indeed, several online state estimation techniques such as Kalman filters, nonlinear extended Kalman filters (EKF), and observers have been developed and applied to polymerization process systems. ° In implementing the online state estimator, several issues arise. For example, the standard filtering algorithm needs to be modified to accommodate time-delayed offline measurements (e.g., MWD, composition, conversion). The estimation update frequency needs to be optimally selected to compensate for the model inaccuracy. Table 5 shows the extended Kalman filter algorithm with delayed offline measurements. Fig. 2 illustrates the use of online state estimator... 

NaLS) by copper(II) yields assemblies in which Cu2+ ions constitute the counter ion atmosphere of the micelle (Fig. 4.8). These may be photoreduced to the monovalent state by suitable donor molecules incorporated in the micellar interior. An illustrative example is that where D = N,N -dimethyl 5,11-dihydroindolo 3,3-6 carbazole(DI). When dissolved in NaLS micelles, DI displays an intense fluorescence and the fluorescence lifetime measured by laser techniques is 144 ns. Introduction of Cu2+ as counterion atmosphere induces a 300 fold decrease in the fluorescence yield and lifetime of DI. The detailed laser analysis of this system showed that in Cu(LS) micelles there is an extremely rapid electron transfer from the excited singlet to the Cu2+ ions. This process occurs in less than a nanosecond and hence can compete efficiently with fluorescence and intersystem crossing165. This astonishing result must be attributed to a pronounced micellar enhancement of the rate of the transfer reaction. It is, of course, a consequence of the fact that within such a functional surfactant unit regions with extremely high local concentrations of Cu2+ prevail. (Theoretical estimates predict the counterion concentration in the micellar Stem layer to be between 3 and 6 M). 

---