Optimal control of a nonlinear fed-batch fermentation process using model predictive approach

Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).     

A multiple model predictive control strategy in the PLS framework

For chemical processes with a wide range of operating conditions, a switched multiple model predictive control (MMPC) strategy in the partial least squares (PLS) framework is proposed. Interactive MIMO systems can be automatically decoupled with inputs and outputs paired in their dynamic PLS models. Based on the identified PLS models, companion controllers are designed to form the MMPC strategy. A novel switching criterion based on output statistics is proposed to assure each model/control pair works in its operating region spanned by the identification data sets. The control results of disturbance rejection and setpoint tracking in a two-phase chemical reactor process are presented to demonstrate the capability and effectiveness of the proposed MMPC strategy.     

An integrated advanced process control framework using run-to-run control,virtual metrology and fault detection

This paper develops a new advanced process control (APC) system for the multiple-input multiple-output (MIMO) semiconductor processes using the partial least squares (PLS) technique to provide the run-to-run control with the virtual metrology data, via the gradual mode or the rapid mode depending on the current system status, in order to deal with metrology delays and compensate for different types of system disturbances. First, we present a controller called the PLS-MIMO double exponentially weighted moving average (PLS-MIMO DEWMA) controller. It employs the PLS method as the model building/estimation technique to help the DEWMA controller generate more consistent and robust control outputs than purely using the conventional DEWMA controller. To cope with metrology delays, the proposed APC system uses the pre-processing metrology data to build up the virtual metrology (VM) system that can provide the estimated process outputs for the PLS-MIMO DEWMA controller. Lastly, the Fault Detection (FD) system is added based upon the principal components of the PLS modeling outcomes, which supplies the process status for the VM mechanism and the PLS-MIMO DEWMA controller as to how the process faults are responded. Two scenarios of the simulation study are conducted to illustrate the APC system proposed in this paper.     

Fault tolerant control for a dearomatisation process

In this paper, a fault tolerant control (FTC) for a dearomatisation process in the presence of faults in online product quality analysers is presented. The FTC consists of a fault detection system (FDI) and a logic for triggering predefined FTC actions. FDI is achieved by combining several process data driven approaches for detecting faults in online quality analysers. The FTC exploits the diagnostic information in adapting a quality controller (MPC) to the faulty situation by manipulating tuning parameters of the MPC to produce both proactive and reactive strategies. The proposed FTC was implemented, tested offline and validated onsite at the Naantali oil refinery. The successful testing and plant validation results are presented and discussed.     

PLS based dEWMA run-to-run controller for MIMO non-squared semiconductor processes

This paper focuses on the modification of the PLS (partial least squares) modeling. The new method allows incorporation of a dEWMA (double exponentially weighted moving average) control algorithm into the standard run-to-run controller design for semiconductor processes. The resulting structure of the PLS model can extract the strongest relationship between the input and the output variables. It is particularly useful for inherent noise suppression. In addition, the resulting non-square MIMO control system can be decomposed into a multi-loop control system by employing pre-compensators and post-compensators of the PLS model, which is constructed from the input and output loading matrices. Subsequently, the conventional dEWMA controller can be separately and directly applied to each SISO control loop. The performance of the proposed method is illustrated through a chemical–mechanical polishing process in the manufacturing of the semiconductor.     

Model selection for partial least squares based dimension reduction

Partial least squares (PLS) has been widely applied to process scientific data sets as an effective dimension reduction technique. The main way to determine the number of dimensions extracted by PLS is by using the cross validation method, but its computation load is heavy. Researchers presented fixing the number at three, but intuitively it’s not suitable for all data sets. Based on the intrinsic connection between PLS and the structure of data sets, two novel algorithms are proposed to determine the number of extracted principal components, keeping the valuable information while excluding the trivial. With the merits of variety with different data sets and easy implementation, both algorithms exhibit better performance than the previous works on nine real world data sets.     

Model predictive control: Recent developments and future promise

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.     

Nonlinear one-step-ahead control using neural networks: Control strategy and stability design

A nonlinear one-step-ahead control strategy based on a neural network model is proposed for nonlinear SISO processes. The neural network used for controller design is a feedforward network with external recurrent terms. The training of the neural network model is implemented by using a recursive least-squares (RLS)-based algorithm. Considering the case of the nonlinear processes with time delay, the extension of the mentioned neural control scheme to d-step-ahead predictive neural control is proposed to compensate the influence of the time-delay. Then the stability analysis of the neural-network-based one-step-ahead control system is presented based on Lyapunov theory. From the stability investigation, the stability condition for the neural control system is obtained. The method is illustrated with some simulated examples, including the control of a continuous stirred tank reactor (CSTR).     

Robust model predictive control of integrating time delay processes

This work focuses on the solution to the problem of model predictive control of time delay processes with both integrating and stable modes and model uncertainty. The controller is developed for the practical case of zone control and input target tracking. The method is based on a state-space model that is equivalent to the analytical form of the step response model corresponding to the system transfer function. Here, this model is extended to the time delay system. The proposed controller is evaluated through simulation of the of two control reactor systems and the results confirms the robustness of the proposed approach.     

Neural network control of multivariable processes with a fast optimisation algorithm

A radial basis function (RBF) neural network model based predictive control scheme is developed for multivariable nonlinear systems in this paper. A fast convergence algorithm is proposed and employed in multidimensional optimisation in the control scheme to reduce the computing time and save required computer memory. The scheme is applied to a simulated two-input two-output nonlinear process for set-point tracking control. Simulation results demonstrate the effectiveness of the control strategy and the fast learning algorithm for multivariable non-linear processes. Comparison of the performance with PID control is included.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.     

On optimality of nonlinear model predictive control

In this note the optimality property of nonlinear model predictive control (MPC) is analyzed. It is well known that the MPC approximates arbitrarily well the infinite horizon (IH) controller as the optimization horizon increases. Hence, it makes sense to suppose that the performance of the MPC is a not decreasing function of the optimization horizon. This work, by means of a counterexample, shows that the previous conjecture is fallacious, even for simple linear systems.     

Non-singular optimal control for fed-batch fermentation processes with a differential-algebraic system model

The problem of optimal control for fed-batch fermentation processes is studied with nonlinear differential-algebraic system modelling. A non-singular optimal control strategy has been developed as a result of the necessary condition analysis of non-singularity of the Hamiltonian function established for the processes. Proof of the optimality of the proposed feeding policy is given. The difficulty associated with singularity of the fed-batch operation mode can thus be avoided. The ethanol fermentation process from glucose by S. cerevisiae is taken as an example for the optimization application. It has been found that previous investigations by some authors, with different optimization methods, led to overestimation of the product formation from the process. A constraint is thus put on the specific productivity, which if unconstrained is responsible for the existing inaccurate predictions. This constraint takes into account the stoichiometry involved in the fermentation. Our simulation study has shown that a realistic result can be achieved with the proposed non-singular optimization scheme.     

基于小波网络的非线性系统建模与控制

提出了种基于小波网络的非线性系统的建模和控制方法。使用小波网络对未知控制系统建立一步预测模型,基于Ｄｓａｖｉｄｏｎ最小二乘法得到自适应控制律。小波网络的权值由广义递推最小二乘法来学习,尺度参数和平移参数通过稳定的Ｄａｖｉｄｏｎ最小二乘法来获得。仿真结果表明了该方法的有效性。     

Incorporating state estimation into model predictive control and its application to network traffic control

Model predictive control (MPC) is of interest because it is one of the few control design methods which preserves standard design variables and yet handles constraints. MPC is normally posed as a full-state feedback control and is implemented in a certainty-equivalence fashion with best estimates of the states being used in place of the exact state. This paper focuses on exploring the inclusion of state estimates and their interaction with constraints. It does this by applying constrained MPC to a system with stochastic disturbances. The stochastic nature of the problem requires re-posing the constraints in a probabilistic form. Using a gaussian assumption, the original problem is approximated by a standard deterministically-constrained MPC problem for the conditional mean process of the state. The state estimates’ conditional covariances appear in tightening the constraints. ‘Closed-loop covariance’ is introduced to reduce the infeasibility and the conservativeness caused by using long-horizon, open-loop prediction covariances. The resulting control law is applied to a telecommunications network traffic control problem as an example.     

Oxygen control for an industrial pilot-scale fed-batch filamentous fungal fermentation

Industrial filamentous fungal fermentations are typically operated in fed-batch mode. Oxygen control represents an important operational challenge due to the varying biomass concentration. In this study, oxygen control is implemented by manipulating the substrate feed rate, i.e. the rate of oxygen consumption. It turns out that the setpoint for dissolved oxygen represents a trade-off since a low dissolved oxygen value favors productivity but can also induce oxygen limitation. This paper addresses the regulation of dissolved oxygen using a cascade control scheme that incorporates auxiliary measurements to improve the control performance. The computation of an appropriate setpoint profile for dissolved oxygen is solved via process optimization. For that purpose, an existing morphologically structured model is extended to include the effects of both low levels of oxygen on growth and medium rheological properties on oxygen transfer. Experimental results obtained at the industrial pilot-scale level confirm the efficiency of the proposed control strategy but also illustrate the shortcomings of the process model at hand for optimizing the dissolved oxygen setpoints.     

Optimization of fed-batch fermentation processes with bio-inspired algorithms

The optimization of the feeding trajectories in fed-batch fermentation processes is a complex problem that has gained attention given its significant economical impact. A number of bio-inspired algorithms have approached this task with considerable success, but systematic and statistically significant comparisons of the different alternatives are still lacking. In this paper, the performance of different metaheuristics, such as Evolutionary Algorithms (EAs), Differential Evolution (DE) and Particle Swarm Optimization (PSO) is compared, resorting to several case studies taken from literature and conducting a thorough statistical validation of the results. DE obtains the best overall performance, showing a consistent ability to find good solutions and presenting a good convergence speed, with the DE/rand variants being the ones with the best performance. A freely available computational application, OptFerm, is described that provides an interface allowing users to apply the proposed methods to their own models and data.     

On the effect of measurement errors in regression-adjusted monitoring of multistage manufacturing processes

A critical challenge in multistage process monitoring is the complex relationships between quality characteristics at different stages. A popular method to deal with this problem is regression adjustment in which each quality characteristic is regressed on its preceding quality characteristics and the resulting residual is monitored to detect changes in local variations. However, the performance of this method depends on the accuracy of the regression coefficient estimation. One source of the estimation errors is measurement errors which commonly exist in practice. To provide guidance on the use of regression-adjusted monitoring methods, this study investigates the effect of measurement errors on the bias of regression estimation theoretically and numerically. Two estimators, the ordinary least squares (OLS) estimator and the total least squares (TLS) estimator, are compared, and insights regarding their performance are obtained.