Balasubrahmanya Srinivasan

Interplay between identification and optimization in run-to-run optimization schemes

The use of measurements to compensate for model uncertainty and disturbances has received increasing attention in the context of process optimization. The standard procedure consists of iteratively using the measurements for identifying the model parameters and the updated model for optimization. However, in the presence of model mismatch, this scheme suffers from lack of synergy between the identification and optimization problems. This paper investigates the performance of run-to-run optimization schemes and proposes to modify the objective function of the identification problem so as to include the cost function and the constraints of the optimization problem. The weights of the various terms in the extended objective function axe based on Lagrange multipliers. The performance improvement obtained with the proposed methodology is illustrated via the simulation of a semi-batch reaction system.

Convergence analysis of run-to-run control for a class of nonlinear systems

In run-to-run control, measurements from previous runs are used to push the outputs of the current run towards desired set points. From a run-to-run perspective, the classical dynamics get integrated by each run, thereby leading to static nonlinear input-output map. This paper shows that, when successive linearization of this nonlinear map is used to adapt the run-to-run controller, convergence may not be achieved. However, convergence can be guaranteed of the controller is based on a linear approximation for which the outputs are in-phase (i.e., within 90/spl deg/) with the true outputs. A convergence proof based on Lyapunov approach is provided. The theoretical aspects are illustrated through the simulated meal-to-meal control of blood glucose concentration in diabetic patients.

Input Filter Design for Feasibility in Constraint-Adaptation Schemes

The subject of real-time, steady-state optimization under significant uncertainty is addressed in this paper. Specifically, the use of constraint-adaptation schemes is reviewed, and it is shown that, in general, such schemes cannot guarantee process feasibility over the relevant input space during the iterative process. This issue is addressed via the design of a feasibility-guaranteeing input filter, which is easily derived through the use of a Lipschitz bound on the plant behavior.While the proposed approach works to guarantee feasibility for the single-constraint case, early sub-optimal convergence is noted for cases with multiple constraints. In this latter scenario, some constraint violations must be accepted if convergence to the optimum is desired. An illustrative example is given to demonstrate these points.

Run-to-run optimization of batch emulsion polymerization

Run-to-run optimization exploits the repetitive nature of batch processes to adapt the operating policy in the presence of uncertainty. For problems where terminal constraints play a dominant role in the optimization, the system can be operated close to the optimum simply by satisfying terminal constraints. The input is parameterized by using the knowledge of the shape of the optimal solution and, in the presence of uncertainty, the input parameters are adapted to meet the terminal constraints. When the number of input parameters is greater than the number of terminal constraints, an adaptation methodology based on a projection matrix derived from the gain matrix between the input parameters and the terminal constraints is proposed. The run-to-run optimization scheme is illustrated in simulation for the minimization of the batch time of an emulsion polymerization process with terminal constraints on conversion and number average molecular weight.

A multi-criteria approach to dynamic optimization

The approach of approximating a differential algebraic optimization problem (DAOP) by a nonlinear program (NLP) and subsequently solving it is considered. In this context, the two distinct objectives to be minimized are: (i) the approximation error and (ii) the predicted cost functional. It is first shown that the minimization of the approximation error by adjusting the collocation points leads to constraining the input space, thereby increasing the minimum predicted cost. This is the main motivation to seek compromise solutions and hence the overall problem is approached from a multicriteria optimization viewpoint. Various preference structures (lexicographic, Pareto and value function) available in the multicriteria literature provide an unified framework for the analysis of existing techniques and the methods proposed here.

Minimal state representation for open fluid-fluid reaction systems

Reaction systems can be represented by first-principles models that describe the evolution of the states (typically concentrations, volume and temperature) by means of conservation equations of differential nature and constitutive equations of algebraic nature. The resulting models often contain redundant states since the various concentrations are not all linearly independent; indeed, the variability observed in the concentrations is caused by the reactions, the mass transferred between phases, the inlet and outlet streams. A minimal state representation is a dynamic model that exhibits the same behavior as the original model but has no redundant state. This paper considers the material balance equations associated with an open fluid-fluid reaction system that involves Sl species, R independent reactions, pl independent inlets and one outlet in the first fluid phase (e.g. the liquid phase) and Sg species, pg independent inlets and one outlet in the second fluid phase (e.g. the gas phase). In addition, there are pm species transferring between the two phases. The (Sl+Sg)-dimensional model is transformed to q = R + 2pm + pl + pg +2 variant states and Sl +Sg -q invariant states. Then, using the concept of accessibility of nonlinear systems, the conditions under which the transformed model is a minimal state representation are derived. It will be shown that the minimal number of concentration measurements needed to reconstruct the full state without kinetic information is R + pm. The simulated chlorination of butanoic acid is used to illustrate the various concepts developed in the paper.

How Important is the Detection of Changes in Active Constraints in Real-Time Optimization?

In real-time optimization, enforcing the constraints that need to be active is important for optimality. In fact, it has been established in the context of parametric variations that, if these constraints are not satisfied, the optimality loss would be O(

Modifier Adaptation for Run-to-Run Optimization of Transient Processes

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A globally convergent run-to-run control algorithm with improved rate of convergence

) – denoting the magnitude of the parametric variations. In contrast, the loss of optimality upon enforcing the correct set of active constraints would be O(

Real-time optimization of nonlinear dynamical systems (M-3)

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