RTO Loop under Uncertainties

Typically the model-based RTO loop is shown in Figure . Once the plant operation has reached steady-state, the plant data () are gathered and validated to avoid gross errors in the process measurements and at the same time, the measurements may be reconciled using material and energy balances to ensure the data set used for model updating is self-consistent. These validated measurements () are used to estimate the model parameters () to ensure the model represents the plant, as accurately as possible, at the current operating point. Then, the optimum controller setpoints () are calculated using the updated model, and are transferred to the advanced process controllers after they are checked by the command conditioning subsystem.

  
Figure: RTO Loop under Uncertainties

Within such an RTO loop, there are various uncertainties that may affect the RTO predictions. They fall into the following four types:

1)

Manipulation uncertainty; this term in the paper refers to various process disturbances which can be classified into two subsets: internal disturbances and external disturbances. In general, internal disturbances are fluctuations in temperatures, flows, and levels that caused by some certain coupling relationships within the system; external disturbances include ambient condition changes, upstream quality variations, etc. For example, consider a typical distillation column control system, the fluctuation of column bottom level belongs to internal disturbance, and the variations of feedstock flowrate and quality, the environment temperature changes belong to external disturbance. The manipulation uncertainty information can be partially obtained from process measurement data. A better mathematical description of manipulation uncertainty is probability density function, which gives the probability distribution within a certain variation range.

2)

Measurement uncertainty; that is measurement error. They are closely related to the sensors in a control system. Basically they can be classified into random measurement noise and gross error such as process leaks, biased instrumentation and so on. Random measurement noise usually are normal distributed with zero mean, certain variance matrix and have no correlation in time, and gross error can be described as independent, discrete random event. Some statistical process control techniques are applied to reduce the measurement uncertainty, such as data reconciliation is aimed at adjusting the values of measured variables and, if possible, estimate the unmeasured variables so that they are consistent with the process constraints (i.e., mass and energy balance), and gross error detection are used to identify the presence of any gross errors so that suitable corrective actions can be taken.

3)

Model uncertainty; the model in RTO systems is usually non-linear, first-principle model, which describes the process steady-state behavior. Model uncertainty includes model structure uncertainty and model parameter uncertainty. Since selecting a appropriate model structure requires the profound recognitions of process mechanism, the model parameter uncertainty in RTO systems receive more attention, although both of them can result in the plant/model mismatch, which has been analyzed systematically in Zhang and Forbes (1998). Model parameter uncertainty comes from process changes, for example, exchanger fouling, catalysts deactivation, etc. In order to reflect such process changes, some selective model parameters are updated off-line or on-line based on some plant experiments or on-line measurements to compensate for plant/model mismatch. Apparently, the parameter estimates can be affected by manipulation uncertainty and measurement uncertainty, further manipulation uncertainty and measurement uncertainty affect the RTO predictions through model parameter uncertainty. Similarly, model parameter uncertainty can be described as a certain probability density function (for on-line adjustable model parameters) or a possible range of variation (for off-line updated model parameters).

4)

Market uncertainty; any industrial production can't continue without purchase and sale. Market uncertainty include a few uncertain economic indexes related to operating profit, such as prices of products and utilities, feedstock availability, customers' demands, product quality specification and so forth. Forecasting market uncertainty is difficult, however, they also can be described by some variation range, which can be extracted from the historical market information.

For the purpose of this paper, the RTO loop is simplified to include only three main parts based on the assumptions that the process measurements are assumed to be corrupted only by random, stationary measurement noise and the process controllers are assumed to be capable of implementing the calculated setpoints. As shown in Figure , the parts of interest are described as the model updater, model-based optimizer and the plant, where is manipulation uncertainty, is measurement uncertainties, are model uncertainties represented by the fixed (off-line updated) and adjustable (on-line updated) model parameters, respectively, as well as is market uncertainty. By linear approximation of the simplified RTO loop, the small deviation of the RTO prediction can be written as (Forbes and Marlin, 1996),

close-loop case:

open-loop case:

where

as is a set of adjustable model parameters estimated from available process measurements (), and process measurements are decided by process operation, process disturbances () and sensor noise ().

  
Figure: Simplified RTO Loop

Consider that the RTO loop is closed only intermittently when RTO predictions pass some certain of conditions, the open-loop linear approximation of the RTO loop is used in this paper for results analysis. In addition, the uncertainties and are not addressed in this paper, then the deviation of RTO predictions will be given by:

 

where is the new RTO prediction, is the current operating point.