Convergence analysis of iterative identification and optimization schemes (original) (raw)
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Simultaneous model identification and optimization in presence of model-plant mismatch
Chemical Engineering Science, 2015
In a standard optimization approach, the underlying process model is first identified at a given set of operating conditions and this updated model is, then, used to calculate the optimal conditions for the process. This "two-step" procedure can be repeated iteratively by conducting new experiments at optimal operating conditions, based on previous iterations, followed by reidentification and re-optimization until convergence is reached. However, when there is a modelplant mismatch, the set of parameter estimates that minimizes the prediction error in the identification problem may not predict the gradients of the optimization objective accurately. As a result, convergence of the "two-step" iterative approach to a process optimum cannot be guaranteed. This paper presents a new methodology where the model outputs are corrected explicitly for the mismatch such that, with the updated parameter estimates the identification and optimization objectives are properly reconciled. With the proposed corrections being progressively integrated over the iterations, the algorithm has guaranteed convergence to the process optimum and also, upon convergence, the final corrected model predicts the process behavior accurately. The proposed methodology is illustrated in a run-to-run optimization framework with a fed-batch bioprocess as a case study. Highlights An iterative optimization algorithm is proposed. The model outputs are corrected iteratively to account for model-plant mismatch. Parameters are estimated to satisfy both identification and optimization objectives. The proposed algorithm is illustrated using a fed-batch bioprocess.
IFAC-PapersOnLine, 2018
Model-plant mismatch commonly arises from simplifications and assumptions during the development of first-principles models. Hence, when employing such models in iterative optimization schemes, structural mismatch may lead to inaccurate prediction of the necessary conditions of optimality. This results in convergence to a predicted optimum which does not coincide with the actual process optimum. The method of simultaneous identification and optimization aims to correct for errors in the predicted gradients of the cost and constraints by adapting the model parameters. In a former implementation of this approach, the gradients have been corrected only locally at the current operating point. To achieve a better prediction of the cost function over a wider range of input conditions, we propose to consider cost measurements from previous batch experiments combined with an optimal experimental design of future experiments. Using this approach, it is possible to achieve a better prediction, especially around the optimum, and to make the gradient correction step less susceptible to uncertainty in local gradient measurements. The improvements are illustrated using a simulated run-to-run optimization study of a cell-culture process.
Interplay between identification and optimization in run-to-run optimization schemes
2002
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.
Identification for Control: Developments in the Iterative Feedback Tuning Framework
2008
The present thesis is concerned with optimization of the closed loop performance of controlled industrial processes. This is achieved through iterative schemes where input/output data is collected from the process during closed loop operation. A presentation of methods for achieving this iterative performance enhancement is given with a clear distinction between model based and data driven approaches. Special attention has been given to simple data driven strategies and the Iterative Feedback Tuning method in particular where a detailed study of methodological developments and tuning properties are given. Based on this analysis new developments for the Iterative Feedback Tuning method has been proposed. In order to extend the application of this data driven tuning approach, the potential of Iterative Feedback Tuning has been analyzed and tested for control structures where this tuning method were novel. Results has been presented which show that the method is applicable for the nonl...
Constrained iterative learning control of batch transesterification process under uncertainty
Research Article , 2020
Biodiesel are fatty acid methyl esters (FAME), which can be produced by the transesterification reaction of vegetable oils with methanol. A batch transesterification process is often associated with model uncertainties and unmeasured disturbances, which may create a detrimental effect on the batch end FAME yield due to plant-model mismatch. Therefore, batch-to-batch iterative learning control (ILC) is necessary to track the desired reference FAME profile under such process variations. This work demonstrates a constrained quadratic programming problem (QPP) based batch-to-batch ILC framework for optimizing the endpoint FAME concentration by controlling the hot water flow profile passing through the reactor jacket under uncertainty. Parametric uncertainties are modeled separately in two case studies, which involve different batch transesterification models differing in the state variables. Case study 1 considers uncertainty in the apparent activation energy and brings out a comparative study between a QPP based ILC and a heuristics based approach. The comparison is shown based on the tracking performance of the ILC in terms of reduction in the batch end tracking error and total root mean square error of the same. Batch-to-batch ILC is superior as it produces faster convergence of the tracking error by saving 6 batches as compared to the heuristics approach. Case study 2 involves the implementation of constrained QPP based ILC algorithm on a proposed 54-state detailed batch transesterification model of canola oil, where uncertainty is modeled as the change in the input triglyceride composition from the base case. The desired reference FAME concentration profile is tracked in 9 batches for fixed uncertainty whereas it takes 15 batches to achieve the stochastic convergence under stochastic disturbance.
Computers & Geosciences, 2012
A new adaptive hybrid optimization strategy, entitled squads, is proposed for complex inverse analysis of computationally intensive physical models. Typically, models are calibrated and model parameters are estimated by minimization of the discrepancy between model simulations characterizing the system and existing observations requiring a substantial number of model evaluations. The new strategy is designed to be computationally efficient and robust in identification of the global optimum (e.g. maximum or minimum value of an objective function). It integrates a global Adaptive Particle Swarm Optimization (APSO) strategy with a local Levenberg-Marquardt (LM) optimization strategy using adaptive rules based on runtime performance. The global strategy optimizes the location of a set of solutions (particles) in the parameter space. The LM strategy is applied only to a subset of the particles at different stages of the optimization based on the adaptive rules. After the LM adjustment of the subset of particle positions, the updated particles are returned to the APSO strategy. Therefore, squads is a global strategy that utilizes a local optimization speedup. The advantages of coupling APSO and LM in the manner implemented in squads is demonstrated by comparisons of squads performance against Levenberg-Marquardt (LM), Particle Swarm Optimization (PSO), Adaptive Particle Swarm Optimization (APSO; the TRIBES strategy), and an existing hybrid optimization strategy (hPSO). All the strategies are tested on 2D, 5D and 10D Rosenbrock and Griewank polynomial test functions and a synthetic hydrogeologic application to identify the source of a contaminant plume in an aquifer. Tests are performed using a series of runs with random initial guesses for the estimated (function/model) parameters. The performance of the strategies are compared based on their robustness, defined as the percentage of runs that identify the global optimum, and their efficiency, 1
Model reduction for process control using iterative nonlinear identification
Proceedings of the 2004 American Control Conference, 2004
Given a complex first principles model of a process, a strategy for model complexity reduction is developed, such that the model obtained is suitable for process control. The system is assumed to have a Volterra representation that can be parametrized in terms of basis functions with fixed poles. The approach taken consists on iteratively using system identification techniques on the complex system model, while at the same time optimizing the inputs used. The results are tested on a copolymerization reactor example.
Computer Aided Chemical Engineering, 2010
Convergence analysis of iterative identification-optimization schemes is a key issue in modeling for optimization of batch processes. In this work, it is formally shown that for convergence is sufficient to guarantee that parametric uncertainty is increasingly reduced on a run-to-run basis. Convergence of a policy iteration algorithm to an optimal policy which satisfies the Hamilton-Jacobi-Bellman equation is thus assured as long as parametric uncertainty is iteratively reduced such that the performance prediction mismatch is driven to zero. The integration of global sensivity analysis with confidence interval boostrapping in the design of a convergent algorithm for model-based policy iteration is proposed. A simple bioprocess is used to exemplify run-to-run improvement.
Integrating Iterative Learning Estimation with Optimal Control for Batch Productivity Enhancement
IFAC-PapersOnLine, 2015
Optimal control has wide applications for the control of batch and semi-batch processes to develop an optimum control input policy by extremizing a performance measure. The deployment of optimal control relies heavily on the accuracy of the process models being used for computation of the optimal profile. Often, the process models do not replicate the plants due to various shortcomings such as assumptions made during model formulations, poor first principles knowledge and limited range of experimental data due to short process development cycles. Moreover, scale-up of the processes from lab to manufacturing scale renders the developed models obsolete. The estimated model parameters can significantly differ from their nominal values which calls for the development of a strategy that updates process models so as to achieve an improved and tight control of batch processes. In this paper, we propose a novel methodology based on iterative learning to gradually update models using on-line measurement data at the end of each successive batch run by minimizing the error between plant and model data. In the proposed methodology, we further integrate Iterative Learning Estimation (ILE) with optimal control to update the optimal control input profile with the advent of measurement after each successive batch run. An important aspect of this integration is to ensure that model updates between batch runs generate feasible optimal control trajectories. Simulations are performed for the temperature control of a batch reactor system to validate the proposed methodology.