Presence Of Plant-model Mismatch Research Articles

Robust batch-to-batch optimization with global sensitivity analysis for microbial fermentation processes under model-plant mismatch

This paper studies the optimization of product yield for the microbial fermentation process in the presence of model-plant mismatch. The typical “two-step” optimization method involves modifying the model by adjusting its parameters and subsequently utilizing the updated model to optimize product output. However, due to estimability and overfitting problems, it is often impractical to update all available parameters. Therefore, we propose a robust batch-to-batch optimization method with global sensitivity analysis. First, the parameters to be identified are determined through global sensitivity analysis. Then, the robust batch-batch optimization method is employed to optimize the yield of fermentation products. Compared with previous parameter selection methods, global sensitivity analysis considers the complex correlation between parameters, allowing for a more comprehensive evaluation of the impact of multiple parameters and their interactions on the model. Furthermore, compared with previous studies, the robust batch-to-batch optimization method assigns weights to each variable in the identification objective function based on experience and model output variance, significantly reducing the uncertainty of the next optimal batch run. Simultaneously, the method is robust to the uncertainty in initial conditions, ensuring a more stable process when running in large batches. A penicillin fermentation case study verifies the convergence and robustness of the method.

Safe chance constrained reinforcement learning for batch process control

Reinforcement Learning (RL) controllers have generated excitement within the control community. The primary advantage of RL controllers relative to existing methods is their ability to optimize uncertain systems independently of explicit assumption of process uncertainty. Recent focus on engineering applications has been directed towards the development of safe RL controllers. Previous works have proposed approaches to account for constraint satisfaction through constraint tightening from the domain of stochastic model predictive control. Here, we extend these approaches to account for plant-model mismatch. Specifically, we propose a data-driven approach that utilizes Gaussian processes for the offline simulation model and use the associated posterior uncertainty prediction to account for joint chance constraints and plant-model mismatch. The method is benchmarked against nonlinear model predictive control via case studies. The results demonstrate the ability of the methodology to account for process uncertainty, enabling satisfaction of joint chance constraints even in the presence of plant-model mismatch.

Semi-infinite programming yields optimal disturbance model for offset-free nonlinear model predictive control

Offset-free nonlinear model predictive control (NMPC) can eliminate the tracking offset associated with the presence of plant-model mismatch or other persistent disturbances by augmenting the plant model with disturbances and employing an observer to estimate both the states and disturbances. Despite their importance, a systematic approach for the generation of suitable disturbance models is not available.We propose an optimization-based method to generate disturbance models based on sufficient observability conditions and generalize the theory of offset-free NMPC by allowing for (i) more measured variables than controlled variables and (ii) unmeasured controlled variables. Based on the sufficient conditions, we formulate a generalized semi-infinite program, which we reformulate and solve as a simpler semi-infinite program using a discretization algorithm. The solution furnishes the optimal disturbance model, which maximizes the set of those state, manipulated variable, and disturbance realizations, for which a sufficient observability condition is satisfied. The disturbance model is generated offline and can be used online for offset-free NMPC.We apply the approach using three case studies ranging from small scale chemical reactor cases to a medium scale polymerization reactor case. The results demonstrate the validity and usefulness of the generalized theory and show that the model generation approach successfully finds suitable disturbance models for offset-free NMPC.

Homothetic tube-based robust offset-free economic Model Predictive Control

This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system’s state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system.

Real-time optimization via modifier adaptation of closed-loop processes using transient measurements

Real-time optimization (RTO) has the ability to boost the performance of a process whilst satisfying the constraints by using process measurements, driving the operating conditions towards optimality. Modifier adaptation (MA) is a methodology of RTO which can find the optimal operating point of a process even in the presence of plant-model mismatch. This work presents an extension to MA through the combination of two established frameworks, allowing for the optimization of a controlled process using transient measurements whilst using a steady-state open-loop model. In addition, an approach for model-based gradient estimation, despite the mismatch between the degrees of freedom of the closed-loop plant and the available open loop model is suggested that does not necessitate amending the model. The proposed scheme is illustrated on a case study of a CSTR and a distillation column, detailing how the gradient can be estimated.

An Application of Modifier Adaptation with Quadratic Approximation on a Pilot Scale Plant in Industrial Environment

The goal of this work is to identify the optimal operating input for a lithiation reaction that is performed in a highly innovative pilot scale continuous flow chemical plant in an industrial environment, taking into account the process and safety constraints. The main challenge is to identify the optimum operation in the absence of information about the reaction mechanism and the reaction kinetics. We employ an iterative real-time optimization scheme called modifier adaptation with quadratic approximation (MAWQA) to identify the plant optimum in the presence of plant-model mismatch and measurement noise. A novel NMR PAT-sensor is used to measure the concentration of the reactants and of the product at the reactor outlet. The experiment results demonstrate the capabilities of the iterative optimization using the MAWQA algorithm in driving a complex real plant to an economically optimal operating point in the presence of plant-model mismatch and of process and measurement uncertainties.

Gaussian processes modifier adaptation with uncertain inputs for distributed learning and optimization of wind farms

A modifier adaptation scheme based on Gaussian processes is presented to optimize the control inputs of a wind farm. Often an approximate model of the wind farm is available, however due to the high complexity of the process plant-model mismatch is prevalent. For example the mechanics of wakes is not well-understood, which may have a profound impact on the power production of wind farms. Therefore, Gaussian process (GP) regression is exploited to account for this deviation. A distributed learning approach is used to learn the plant-model mismatch of each individual turbine considering explicitly the uncertainty of the uncontrolled inputs, like the wind direction. Afterwards, a distributed optimization scheme using alternating direction method of multipliers is applied to iteratively attain the wind farm optimum despite the presence of plant-model mismatch.

Estimation technique for offset-free economic MPC based on modifier adaptation

Economic model predictive control formulations that combine online optimizing control with offset-free methodologies such as modifier adaptation have been proposed recently. These new algorithms are able to achieve asymptotic optimal performance despite the presence of plant-model mismatch. However, there is a major requirement stemming from the modifier-adaptation part, namely, the necessity to know the static plant gradients at the sought (and therefore still unknown) steady-state operating point. Hence, for implementation purposes, the algorithms need to be enhanced with plant gradient estimation techniques. This work proposes to estimate modifiers directly, based on steady-state perturbations and using Broyden’s approximation. The proposed economic MPC algorithm has been tested in simulation on the Williams-Otto reactor and provides plant optimality upon convergence.

An Automatic Tuning Method for Model Predictive Control Strategies

The proposed auto-tuning method is a layer of receding horizon optimization problem whose objective function is able to consider the performance/robustness through the trade-off representation combining the responses of the process variables and the control actions. The tuning parameters are evaluated based on a closed-loop simulation in the presence of model-plant mismatch, which is compared to the desired tunnel response in the time domain. The method is tested for two types of model predictive control, and its flexibility and suitability for different scenarios of fit criteria are presented. The results point to the feasibility of the applications of the method, keeping the system close to the ideal setting and highlighting the importance of evaluating the behavior of control actions in the tuning problem.

A note on efficient computation of privileged directions in modifier adaptation

In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially perturbed in all input directions. To ease this gradient estimation task, it has been proposed to exploit the sensitivity of the model gradient with respect to the model parameters to find a reduced input subspace that is spanned by a few privileged directions for gradient estimation. The computation of gradient sensitivities to parametric variations requires the evaluation of double derivatives with respect to both the inputs and the parameters. In this short note, we propose an approach for computing the privileged directions using only single derivatives with respect to the inputs. We show that this approach results in significant reduction in computational costs without compromising the quality of the privileged directions.

Using a neural network for estimating plant gradients in real-time optimization with modifier adaptation

In the presence of structural plant-model mismatch, standard real-time optimization (RTO) schemes are prone to compute an operation point that does not coincide with the plant optimum. Modifier Adaptation (MA) methods are RTO variants that have the ability to reach plant optimality even in the case of structural plant-model mismatch. However, MA implementations require plant gradient information, which is challenging to obtain. This work proposes a method for estimating plant gradients based on neural networks (radial basis function network - RBFN). Our method is applied for obtaining the gradients of a gas lifted oil well network, which is then optimized using MA. The results show that, even with measurement noise, the gradients are estimated within an adequate precision and the MA method is able to increase production of the well network, reaching the plant optimum without any constraint violations despite the presence of plant-model mismatch.

Mixed stochastic-deterministic tube MPC for offset-free tracking in the presence of plant-model mismatch

This paper presents a stochastic-tube model predictive control (MPC) strategy that systematically handles plant-model mismatch, guarantees stability in the presence of changing operating conditions, and ensures offset-free tracking for all reachable operating conditions. The key notion of this work is to separate the system uncertainty into two distinct sources of additive bounded state error. The first source is a non-random uncertainty that represents mismatch between the linear model of the controller and the true plant (as well as other types of persistent disturbances). The second source represents random fluctuations due to either the intrinsic stochastic variability of the system, or exogenous disturbances. Recursive feasibility and stability of the stochastic-tube MPC strategy is guaranteed by defining the terminal invariant set to include the effect of changes in the steady-state operating conditions. Offset-free tracking is achieved with a disturbance estimator that can be tuned independently of the controller. To reduce the conservatism inherent to robust control performance, a new filter model for deterministic disturbances is proposed that predicts uncertainty in the future evolution of the disturbances based on a bound on how quickly the plant-model mismatch can vary. The stochastic-tube MPC strategy is demonstrated on two simulation case studies—a benchmark DC-DC converter and an industrially-motivated fluidized-bed catalytic cracking unit.

Iterative Real-Time Optimization Scheme for Optimal Operation of Chemical Processes under Uncertainty: Proof of Concept in a Miniplant

Real-time optimization (RTO) has gained growing attention during the past few years as a useful approach to boost process performance while safety and environmental constraints are satisfied. Despite the increasing acceptance of RTO in traditional industries such as petrochemical and refineries, its application to novel chemical processes remains limited. This can be partially explained by the fact that only inaccurate models are available and the performance of the traditional RTO scheme suffers in the presence of plant-model mismatch. During the past few years, the so-called modifier-adaptation schemes for real-time optimization have been gaining popularity as an efficient tool to handle plant-model mismatch. So far, there are only few published works regarding experimental implementations. In this contribution, a reliable RTO scheme that is able to deal with model uncertainty and measurement noise is applied to a novel transition metal complex catalyzed process that is performed in a continuously opera...

Experimental validation of predictor-corrector approach based control schemes on the laboratory scale non-linear system

In this work, the authors have designed and implemented predictor-corrector approach based control schemes for a single input-single output nonlinear system. The controller output is computed in two steps. The first step explicitly uses a non-linear model or multiple-linear models weighted using fuzzy membership function to compute the value of the controller output. The second step is based on the measurement, where the value of the controller output computed in first step is updated. The extensive simulation studies show that the set-point tracking and disturbance rejection capability of the proposed control schemes are found to be satisfactory in the absence and presence of Model-plant mismatch. The performances of the proposed control schemes have been compared with that of a gain-scheduled PI controller. In addition, the control schemes are experimentally validated on the laboratory scale conical tank experimental setup.

Active Perturbation in Modifier Adaptation for Real Time Optimization to Cope with Measurement Delays

Iterative optimization is a technique where the model-based optimization problem is iteratively updated to drive the plant to its optimal operating point in the presence of plant-model mismatch. Modifier adaptation (MA) is a state-of-the-art iterative optimization approach which can be used in the presence of both structural and parametric plant-model mismatch. Availability of plant measurements is key for the successful application of MA. In the process industries, analytical sensors cannot always be installed directly at the location of interest. A remote positioning of a measurement device leads to a significant delay in receiving the measurements, since the transportation of the sample to the sensor requires additional time. This leads to a waiting time between two successive iterations during which the standard iterative optimization techniques remain idle. In this contribution, the issue of a pure time delay caused by the remote positioning of a sensor is addressed. We propose an active perturbation strategy to obtain more information by perturbing the plant during the waiting time to improve the estimation of the plant gradient, which reduces the time to reach the plant-optimum. The performance of the proposed strategy is analyzed based on the simulation results from a chemical engineering case study.

Modifier adaptation for real-time optimization of a gas lifted well network

This work studies the steady-state optimization of a Gas Lift Oil Well Network. The optimization approach used is based on the methodology proposed by (Gao et al., 2016), which is a Modifier Adaptation (MA) with gradient estimation from fitted surfaces. The methodology uses plant data to locally approximate the cost and constraint functions of the plant by quadratic functions and then estimates the plant gradients based on the approximated functions. The proposed scheme is simulated using a phenomenological model of the oil well, which was introduced by (Krishnamoorthy et al., 2016). The optimization results showed that the MA scheme is able to increase production, reaching the plant optimum, despite the presence of plant-model mismatch without any constraint violations. Furthermore, it was able to provide good quadratic approximations of both cost and constraint functions.

Implementation of an economic MPC with robustly optimal steady-state behavior

Designing an economic model predictive control (EMPC) algorithm that asymptotically achieves the optimal performance in presence of plant-model mismatch is still an open problem. Starting from previous work, we elaborate an EMPC algorithm using the offset-free formulation from tracking MPC algorithms in combination with modifier-adaptation technique from the real-time optimization (RTO) field. The augmented state used for offset-free design is estimated using a Moving Horizon Estimator formulation, and we also propose a method to estimate the required plant steady-state gradients using a subspace identification algorithm. Then, we show how the proposed formulation behaves on a simple illustrative example.

Speed-up of Iterative Real-Time Optimization by Estimating the Steady States in the Transient Phase using Nonlinear System Identification

Iterative Real-Time Optimization (RTO) has gained increasing attention in the context of model-based optimization of the operating points of chemical plants in the presence of plant-model mismatch. In all iterative RTO schemes, it is necessary to wait until the plant has reached a steady-state to obtain the required information on plant performance and constraint satisfaction which leads to slow convergence in the case of processes with slow dynamics. It has recently been proposed to use a linear black-box model that is identified online to predict the steady-state values of the plant during the transient between different stationary operating points; these values are then employed in the modifier adaptation with quadratic approximation to drive the process to its optimum (Gao et al., 2016). In this contribution, this idea is extended by integrating nonlinear system identification into iterative RTO. Specifically, a Nonlinear Output Error (NOE) model is proposed to describe the dynamics of the process, thus providing a faster prediction of the steady-state of the plant. A robust scheme for the estimation of the model parameters is proposed. The performance of the strategy is illustrated by simulation studies of a continuous stirred-tank reactor. By means of the proposed methodology a fast convergence to the plant optimum can be achieved despite plant-model mismatches.

Real-time optimization of a novel hydroformylation process by using transient measurements in modifier adaptation

This paper deals with the use of transient measurements in the steady-state optimization of a hydroformylation process in the presence of plant-model mismatch. The key idea is to predict steady states from the measurements obtained during the transients of the process. The predicted steady states are then employed in the modifier adaptation with quadratic approximation algorithm to drive the operation of the process to its economic optimum. Simulation results show the promising performance of the proposed scheme.

Handling Model Plant Mismatch in State Estimation Using a Multiple-Model-Based Approach

Accurate state estimates are important for the success of model predictive control (MPC). State estimates are obtained using a model, but, in real plants, there will always be model plant mismatch (MPM), which affects these estimates. In this work, we present a multiple-model (MM)-based approach to obtain unbiased state estimates in the presence of MPM. Necessary assumptions on the source of mismatch and models used are presented. It is shown that unbiased output estimates do not guarantee unbiased state estimates. Our approach is shown to provide unbiased state estimates when all the assumptions are met using a froth flotation system. A model-identification-based control approach using our multiple model estimation approach with a conventional MPC was tested on the froth flotation system and was found to successfully provide offset-free reference tracking when all the necessary assumptions for unbiased state estimation were met. A nonlinear offset-free MPC was also tested on the froth flotation system bu...