Observer-based non-linear control of a fed-batch autoinductive fermentation process

Optimal regulatory control of an autoinductive recombinant culture in a fed-batch reactor is considered. End point optimization results in a three-stage process: biomass growth, inducer synthesis and product synthesis. It is shown that in the last stage the substrate concentration should be maintained constant. This is achieved using an input—output linearizing controller accompanied by a novel non-linear state observer for the estimation of unmeasured state variables on the basis of on-line off-gas carbon dioxide concentration measurements. Experimental runs of luminous recombinant E. coli strain in a laboratory fermenter demonstrate the rapid convergence of the observer estimates as well as the effectiveness and robustness of the overall control system.     

Modelling and adaptive control of fed-batch penicillin fermentation

This paper describes a study to investigate the application of state estimation and parameter adaptive control in fed-batch fermentation for penicillin production. A model of the penicillin fermentation process is outlined and shown to be capable of matching industrial data. The penicillin mould biomass is controlled to a reference trajectory by applying self-tuning control to an estimate of biomass, obtained from measurements of carbon dioxide production rate and fermenter volume and by using the fermentation model with an extended Kalman filter. The manipulated variable, sugar feed to the fermenter, is calculated by an adaptive algorithm. Simulation results compare the performance of self-tuning control with that obtained using digital Proportional plus Integral control.     

乙醇补料发酵技术研究进展

作为一种可再生的清洁能源,燃料乙醇的开发利用备受关注,对其发酵工艺的研究也日益深入。近年来,补料发酵工艺逐渐应用于燃料乙醇的生产研究中,并以其降低基质抑制和减轻纤维素稀酸水解液中有毒成分的影响等优点而显示了良好的发展潜力,但由于发酵过程的复杂性和对补料控制策略的研究尚不深入等存在的问题,使该技术在燃料乙醇规模化生产中的应用受到制约。本文介绍了国内外乙醇补料发酵研究的主要进展,着重概述补料发酵技术在乙醇两大重要发酵工艺——纤维素乙醇工艺和超高浓度乙醇发酵工艺中的应用以及补料调控策略等,并提出该领域进一步研究应留意的方向,如应加强乙醇补料发酵动力学和控制理论、新型传感器与在线监测技术等方面的研究。     

微生物发酵过程优化控制技术进展

微生物发酵过程优化控制技术是发酵工程的重要技术。综述了近年来微生物发酵过程优化控制技术的研究现状,讨论了机理分析建模、黑箱建模、混合建模等发酵过程建模方法,对基于模型的优化控制策略进行了分析。指出了基于混合模型和多目标优化策略建立动态优化控制器,是微生物发酵过程优化控制的有效方法,并给出了实现优化控制需要解决的关键问题。     

Adaptive multirate estimation and control of nutrient levels in a fed-batch fermentation using off-line and on-line measurements

A multirate adaptive estimation algorithm developed earlier (Gudi et al., 1995) is extended to perform estimation of nutrient levels using frequent on-line measurements of the carbon dioxide evolution rate (CER) and off-line, infrequent and delayed measurements of the biomass and substrate concentrations. It has been shown that the algorithm can be designed to track changing substrate yield coefficients as well. The estimation algorithm has been verified using simulations and industrial data from a fed-batch fermentation involving a Streptomyces specie. It has been coupled with a nonlinear control law designed to track prespecified optimal nutrient trajectories. The resulting closed loop control scheme is evaluated using simulation runs.     

Plasmid stability analysis in a non-homogeneous bioreactor for a recombinant fed-batch fermentation

Fed-batch fermentation for tryptophan synthetase by a recombinant Escherichia coli strain has been analyzed through a model incorporating segregational loss of the plasmid pPLc23trpAl and imperfect macromixing of the broth. These features become significant in large fermentation vessels, where fluid circulation in the bioreactor influences the rates of cell growth and productivity. A simple model consisting of two interacting reactors describes the degree of macromixing, which is characterized by the respective (internal) dilution rates. Controlled imperfect macromixing is superior to other methods in arresting, and even reversing, the normal decline in the concentration of recombinant cells, thereby providing a method to exploit the non-homogeneity of the broth in large bioreactors. Some physical implications are discussed.     

基于KTA-LSSVM的青霉素发酵过程预测建模

为解决青霉素发酵过程预测建模中存在的输入变量选择问题,提出了基于核目标度量（kernel target alignment,KTA）和最小二乘支持向量机（least squares support vector machines,LSSVM）的青霉素发酵过程预测模型。首先,在分析影响青霉素产物浓度相关因素的基础上选取输入变量,采用KTA对输入变量进行尺度缩放,然后,利用Pensim仿真平台数据,采用混沌粒子群算法对LSSVM的参数寻优,建立青霉素发酵过程的KTA-LSSVM预测模型。青霉素浓度预测的KTA-LSSVM模型均方根误差为0.0179,LSSVM模型的均方根误差为0.0276,实验结果表明,本文提出的模型预测精度高,推广性能好。     

Analysis of fed-batch fermentation processes by graphical methods

Graphical methods are used for many types of engineering calculations. Their appeal is often related to calculational simplicity, but probably the increased understanding that accompanies a graphical calculation method is chiefly responsible for their popularity. In the present work existing graphical concepts which have been used in chemical reaction engineering and fermentation technology have been extended to allow the calculation of biomass and product formation for a variety of fermentation processes. Comparisons in productivity are made among chemostat, batch, fed batch with variable and constant feed rate, and cyclic fed-batch operations.     

Mathematical modeling of fed-batch butanol fermentation with simultaneous pervaporation

A mathematical model was developed to describe a fed-batch acetone-butanol-ethanol (ABE) fermentation with simultaneous pervaporation. The model predicted satisfactorily batch or fed-batch fermentation with or without pervaporalion by introducing a parameter reflecting cell activity loss during fed-batch fermentation with pervaporation. The model also predicted the effect of membrane area, membrane thickness, and sweep air flow rate on glucose consumption rate and residual butanol concentration in the fermentation broth. Glucose consumption rate increased by 30% by either doubling the membrane area or decreasing membrane thickness by half.     

一种提高发酵单位的SVM与RGA相结合的优化控制策略

An optimal control strategy is proposed to improve the fermentation titer, which combines the support vector machine (SVM) with real code genetic algorithm (RGA). A prediction model is established with SVM for penicillin fermentation processes, and it is used in RGA for fitting function. A control pattern is proposed to overcome the coupling problem of fermentation parameters, which describes the overall production condition. Experimental results show that the optimal control strategy improves the penicillin titer of the fermentation process by 22.88%, compared with the routine operation.     

Robust and optimal control approach for exothermic reactor stabilization

In this paper, the possibility to stabilise open-loop unstable exothermic reactors with temperature measurements is studied. Moreover, the reactors are considered to be multi-input multi-output systems with parametric uncertainties. Robust static output feedback and optimal controllers are designed for stabilization of the exothermic reactors into their open-loop unstable steady states. Stabilization of reactors is simulated using designed controllers. The possibility of using both types of controllers for energy savings is studied and measured by coolant consumption. The approach is tested with a representative example. Obtained simulations results confirm that the robust static output feedback controllers outperform optimal controllers when systems with parametric uncertainties are controlled.     

基于最优控制方法的聚合物驱注入浓度优化

针对聚合物驱提高原油采收率技术,建立了确定最佳注入浓度的最优控制模型。性能指标为一定时间内原油开采所获得的利润,约束条件包括非线性渗流力学偏微分方程组、积分不等式约束和控制变量的边界约束。利用二维分布参数系统最优控制的必要条件获得了原最优控制问题的伴随问题以及目标泛函的梯度。给出了求解该最优控制问题的一种基于梯度的数值方法,并通过研究实例表明了所提出方法的有效性。     

A simultaneous approach for singular optimal control based on partial moving grid

Singular optimal control plays an important role in process engineering, including optimal operation of batch and semi-batch reactions. However, for many practical applications, accurate solution of singular optimal control profiles is still an open issue. In particular, numerical optimization must deal with an ill-conditioned problem that often leads to very slow convergence or failure. Starting from the nested approach in our previous work in 2016, this study develops a more efficient strategy for singular control through a heuristic approach for the outer problem. The approach includes three stages. Starting from a coarse distribution of finite elements, sufficiently many finite elements are inserted where control profiles are steep and fixed gridpoints are inserted on the basis of error estimation of state profiles. Then, moving gridpoints are inserted where the modified switching function is violated. Initial junctions are obtained by moving the latest inserted gridpoints. Moreover, further mesh refinements are considered based on switching point detection and a moving grid point update strategy, until modified switching conditions are satisfied over the whole-time span. A key feature of this approach is that only a subset of finite elements needs to move during optimization. Complexity of the optimization formulation is considerably decreased compared to our previous work. This approach is demonstrated on eight classical singular control problems with known solutions, as well as six complex singular control problems drawn from the chemical engineering literature.     

一种求解最优控制问题的变时间节点控制向量参数化方法

控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域,将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的,其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点,提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系,得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试,结果表明所提出方法能够更好地逼近最优控制轨迹。     

青霉素发酵过程的模型仿真与补料优化

补料分批式青霉素发酵的机理模型已得到深入研究,但是模型往往难以用于补料的优化和批次内的控制。为了对模型进行优化控制,针对Birol等提出的青霉素发酵非结构动力学模型,合理调整了温度和pH变化的影响,得到了青霉素发酵过程的简化机理模型。反应基质的补料是青霉素优化控制的关键,选择对补料速率进行优化来提高青霉素的产量。由于机理模型具有非线性和约束条件,采用序贯二次规划算法来进行求解,其中将补料轨线进行分段处理提高了优化效率。优化计算结果表明改进的补料过程可以提高青霉素的浓度和产量。     

Development of a computer algorithm based on a conjugate gradient approach for optimization of fed-batch fermentations

The problem of optimization of fed-batch fermentations using the substrate feed rate as the control variable is singular in nature. Previous approaches, including the boundary condition iteration method and transformation to a nonsingular problem using a different control variable, do not work well for solving optimization of systems governed by more than four differential equations. The applicability of a first-order conjugate gradient algorithm for optimizing fed-batch fermentations was tested for systems of varing complexity. This approach does not need any variable transformation ora priori knowledge of the control arc sequence. Constraints on the feed rate are handled in a simple and direct manner. The algorithm worked very well for three, four, and five-dimensional singular systems. The correctness of the optimal profile was judged by observing the variation in the sign of the gradient of the Hamiltonian. The gradient was found to be zero during the singular period and had the appropriate sign on the boundary arcs. The optimization method based on conjugated gradient approach can be complementary to the boundary condition iteration method for determination of the exact optimum profile.     

分批补料发酵过程多目标优化的分布式强化学习策略

发酵过程优化问题通常包含有互相冲突的多重优化目标,另外反应本身具有诸多复杂性。提出一种基于Pareto的分布式Q学习多目标策略,用以求解赖氨酸分批补料发酵过程流加速率轨迹的Pareto最优解。该策略中,Q学习算法和Pareto排序法将结合来产生非支配解集,并使之逼近真实的Pareto前沿,利用奖赏机制来描述多重目标之间的关系,并同时使用多组含有随机初始值的agent共同作用改善搜索能力。将所提出的方法应用于赖氨酸分批补料发酵过程的优化中,并与粒子群优化进行了对比,验证策略的性能。     

Robust adaptive control of yeast fed-batch cultures

Model-based control of bioprocesses is a difficult task due to the challenges associated with biological system modeling and the lack of on-line measurements. In this study, two robust controllers using minimal a priori process knowledge and minimal measurement information are designed to maximize biomass productivity in aerobic cultures of Saccharomyces cerevisiae. This latter objective can be achieved through the regulation of the ethanol concentration at a low constant value. The linearization of Sonnleitner’s model allows simple transfer function models to be derived, which describe the relation between the ethanol concentration, the substrate feed and an exponential disturbance – image of the substrate demand for cell growth – in the different operating (respirative and respiro-fermentative) regimes. The two controllers are based on these linear models and use a RST structure, but differ in the way the exponential growth disturbance is handled. In the first controller, the disturbance is represented by a linear model, whereas in the second controller, the disturbance is measured on-line via the oxygen transfer rate signal and a feedforward control action is used to cancel the disturbance effect on the ethanol concentration. Particular attention is paid to the robustification of the controllers to measurement noise, neglected high frequency dynamics and uncertain stoichiometry coefficients using the observer polynomial. Tests in simulation show the controller performance.     

Further developments in the new approach to boundary condition iteration in optimal control

In solving the boundary value problem resulting from the use of Pontryagin's maximum principle, a transformation matrix is used to relate the sensitivity of the final state to the initial state. This avoids the need to solve the (n × n) differential equation to give the transition matrix, and yields very rapid convergence to the optimum. To ensure convergence, iterative dynamic programming (IDP) is used for a number of passes to yield good starting conditions for this boundary condition iteration procedure. Clipping technique is used to handle constraints on control. Five optimal control problems are used to illustrate and to test the procedure.     

Multi-rate observer design and optimal control to maximize productivity of an industry-scale fermentation process

Chemical industries focus primarily on profitable operations, resulting in growing attention and advances in the field of digital twins and optimal control algorithms. However, most industries still struggle due to a lack of physical sensors, infrequent measurements, and asynchronous sampling. Thus, in this work, we have designed a multi-rate state observer for state estimation from plant measurements and developed a model predictive controller (MPC) that maximized the profitability of an industry-scale fermentation process (fermenter volume < 378,500 L). Additionally, as the fermentation process is complex due to the use of microorganisms, which cannot be accurately captured using a first-principles model, we utilize a previously developed hybrid model in the proposed MPC formulation. The MPC uses a GAMS-MATLAB framework to determine the optimal input profiles while considering practical process constraints. It is shown using multiple datasets, that the MPC can increase productivity while also decreasing the plant operating cost.