Constraint Control

Some MVC permit the definition of hard and soft constraints. In addition to their meaning as described above, often a soft constraint is used as a more conservative limit on a hard constraint. The controller will violate soft constraints if this is the only way that it can satisfy all the hard constraints. 

Constraint controllers fall into three categories. 

Process Control A Practical Approach Myke King 2011 John Wiley Sons Ltd. ISBN 978-0-470-97587-9 

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Fig. 17. Examples of selective control strategy (a) reactor hot spot (b) level override (c) prioritized and (d) constraint controls, where...

Fig. 20. Example of constraint control operating window for a distillation column, where (-----) is the vessel pressure limit, and ( ) represents constant...

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. 

Constraint control strategies, 20 675-676 Constraint method, in multiobjective optimization, 26 1033 Constructed wetland, defined, 3 759t Constructed wetlands effluent treatment, 9 436 37 Construction... 

For a given subset of chemicals, where cp CP, these constraints control the production of different processes based on the upper and lower demands of the petrochemical market for the final products. In constraint (4.3), defining the binary variables yp cm for each process m Mpet is required for the process selection requirement as y ( m will equal 1 only if process m is selected or zero otherwise. Furthermore, if only process m is selected, its production level must be at least equal to the process minimum economic capacity B for each m Mpet, where Ku is a valid upper bound.. This can be written for each process m as follows ... 

Multivariate envelope-based constraint control can lower overall excess oxygen. This can be achieved by monitoring both carbon dioxide and water and by performing constraint limit checks on excess oxygen, hydrocarbons, stack temperature, and opacity. 

Several schemes suggest themselves for using these bounds. Obviously one can develop any network he or she chooses subject to safety constraints, controllability constraints, etc., and... 

First note that the next nearest neighbor constraint controls both the distribution of A1 atoms among 6R types and the arrangement of A1 atoms in 6R s with two A1 atoms (P vs. M ). The number of next nearest Al, A1 pairs is minimized by taking the distribution to be as narrow as possible. Thus for 1 < Si/Al < 2, only 6R s with 3 Al (M ) and 2 Al (M or P ) are considered and for 2 < Si/Al < 3, only 6R s with 2 Al and 1 Al are considered. A single order parameter describes the 6R ensemble, namely the ratio of to P, designated as Kjjp. 

In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study. 

Keywords Real-time optimization, constraint control, constraint adaptation. 

In this work, a constraint-adaptation scheme is combined with a constraint controller. Special emphasis is placed on selecting the set points and the manipulated variables used in the constraint controller at each RTO period. The effect of the constraint controller on the feasibility of intermediate operating points is studied, rmder the assumption of an ideal constraint controller. 

The paper is organized as follows. Section 2 formulates the optimization problem. The RTO scheme combining constraint adaptation and constraint control is presented in Section 3. The behavior of the proposed scheme, with and without the constraint controller, is illustrated for a simple quadratic programming (QP) problem in Section 4. Finally, Section 5 concludes the paper. 

For the combination with constraint control, constraint adaptation (6-7) is preferred because it gives the ability to vary the set points passed to the constraint... 

At the constraint-control level, the variables are considered as time-dependent signals. In this work, the constraint controller is designed so as to track the iteratively-updated active constraints by varying the process inputs along the constraint-seeking directions. 

More precisely, the manipulated variables (MVs) in the constraint controller correspond to the corrections 5Uj(/) g ffi" along the directions V°, from the model optimum u. Observe that the MVs may change from RTO period to RTO period, e.g. when the active set of (5-6) changes. At each time instant, the inputs Uj(/) are then reconstructed from the values of (/), based on the knowledge of u and, as ... 

The set points in the constraint controller correspond to the active constraints, e M", determined at the RTO level. Finally, the controlled variables (CVs) are the active constraints G (/) = g for the plant. 

At the initial time of the A -th RTO period, the constraint controller is started from j) = j-u j. At the terminal time of that period, the constraint... 

Figure 1. Scheme eombining constraint adaptation and constraint control. 

Set k= 0. Initialize B. Start from a feasible (conservative) operating point (without the constraint controller). 

Formulate a square constraint-control problem where the MVs are the values of 5uj(/), the CVs are the active constraints G (i), and the set points are the values G . of the active constraints identified in Step 3. 

Apply the constraint controller to the plant and get the corresponding to the new steady-state operation. Go to Step 2. 

The approach assumes that all the constrained variables can be measured or estimated on-line at a sampling period much smaller than the time constant of the controlled plant. Notice that the decision variables u in the RTO problem may very well be set points of feedback controllers acting directly on the plant manipulated variables. In this case, the constraint controller can be viewed as a primary controller in a cascade control configuration that corrects the set points produced at the RTO level. 

The constraint-control problem is a multivariable square control problem, and various controllers can be used, such as a discrete integral controller or a model predictive controller. 

In this simple QP problem, an ideal constraint controller is assumed, i.e. the controller determines 5uj(/j) such that G u, V ,5uj(/j)jJ = G. The objective here is to illustrate the effect of constramt control on the feasibility of the steady-state intermediates. 

An optimization scheme combining constraint adaptation with constraint control has been proposed. This scheme presents two important features (i) the constraint controller tracks the active constraint determined at the RTO level by adapting the inputs in the subspace of constraint-seeking directions, and (ii) the set points for the active constraints in the constraint controller are updated at each iteration and reach the actual constraint bormds upon convergence. 

In future work, this combined scheme will be compared to other existing approaches (e.g. Ying and Joseph, 1999). The combination of more involved RTO schemes with constraint control (e.g. Gao and Engell, 2005) will also be considered. 

A. Maarleveld and J. E. Riinsdorp, 1970, Constraint control on distillation columns, Automatica, 6, 51-58. 

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