Globally stabilizing control of fed-batch processes with Haldane kinetics using growth rate estimation feedback

The regulation of the biomass specific growth rate is an important goal in many biotechnological applications. To achieve this goal in fed-batch processes, several control strategies have been developed employing a closed loop version of the exponential feeding law, an estimation of the controlled variable and some error feedback term. In the case of non-monotonic kinetics, the specified growth rate can be achieved at two different substrate concentration values. Because of the inherent unstable properties of the system in the decreasing portion of the kinetics function, stabilization becomes a crucial problem in this high-substrate operating region. In this context, the dynamic behavior of fed-batch processes with Haldane kinetics is further investigated. In particular, some conditions for global stability and performance improvement are derived. Then, a stabilizing control law based on a partial state feedback with gain dependent on the output error feedback and gain saturation is proposed. Although particular emphasis is put on the critical case of high-substrate operation, low-substrate regulation is also treated.     

An extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain growth rate

In this paper, we present an extremum-seeking scheme based on an approach to variable structure control for fed-batch bioreactors. The proposed scheme deals with uncertainty on the specific growth rate without assuming an explicit mathematical expression. The control approach exploits the inhibitory effect of the substrate concentration on the growth rate, in such a manner that the closed-loop system reaches the sliding regime on an optimal switching manifold, which is defined by maximizing biomass production. The control scheme comprises an estimation scheme consisting of a high-gain observer and a discrete gradient estimator which computes the unknown terms. The practical stabilizability for the closed-loop system around an unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.     

高带宽无线局域网中PI速率控制算法

针对传统传输控制协议（TCP）在高带宽、无线网络中性能表现不佳的问题, 建立了一个端到端的虚拟路由器模型, 提出了一个端到端的发送端比例积分（PI）速率控制算法。根据RTT的变化, 利用PI控制器计算发送端的发送速率, 使瓶颈节点的队长稳定在一个目标位置, 减少拥塞丢包, 避免无线链路错误丢包引起的对拥塞窗口的错误调整。仿真结果表明, 与传统拥塞控制协议相比, 新机制能较好地控制路由器队长、提高网络负载的稳定性和网络吞吐率。     

Nonlinear PI control for variable pitch wind turbine

Wind turbine uses a pitch angle controller to reduce the power captured above the rated wind speed and release the mechanical stress of the drive train. This paper investigates a nonlinear PI (N-PI) based pitch angle controller, by designing an extended-order state and perturbation observer to estimate and compensate unknown time-varying nonlinearities and disturbances. The proposed N-PI does not require the accurate model and uses only one set of PI parameters to provide a global optimal performance under wind speed changes. Simulation verification is based on a simplified two-mass wind turbine model and a detailed aero-elastic wind turbine simulator (FAST), respectively. Simulation results show that the N-PI controller can provide better dynamic performances of power regulation, load stress reduction and actuator usage, comparing with the conventional PI and gain-scheduled PI controller, and better robustness against of model uncertainties than feedback linearization control.     

On-line PI control of stable processes

A relay based on-line automatic tuning method for PI controllers for stable processes is presented. In the proposed method, prior to controller re-tuning a relay in tandem with the controller and plant induces limit cycle oscillations. Based on the limit cycle measurements, a first order plus dead time (FOPDT) model of the process dynamics is obtained. Simple tuning rules based on ISTE performance criterion and the first order model are developed. The controller settings may be re-tuned non-iteratively to achieve enhanced performance without disrupting closed loop control. A number of simulation examples are given to illustrate the potential advantages of the proposed on-line tuning method.     

Integrated condition monitoring and control of fed-batch fermentation processes

This paper investigates the benefits that the partial least squares (PLS) modelling approach offers engineers involved in the operation of fed-batch fermentation processes. It is shown that models developed using PLS can be used to provide accurate inference of quality variables that are difficult to measure on-line, such as biomass concentration. It is further shown that this model can be used to provide fault detection and isolation capabilities and that it can be integrated within a standard model predictive control framework to regulate the growth of biomass within the fermenter. This model predictive controller is shown to provide its own monitoring capabilities that can be used to identify faults within the process and also within the controller itself. Finally it is demonstrated that the performance of the controller can be maintained in the presence of fault conditions within the process.     

Nonlinear model-state feedback control for nonminimum-phase processes

A general nonlinear controller design methodology for continuous-time nonminimum-phase systems is presented, which utilizes synthetic outputs that are statically equivalent to the original process outputs and make the system minimum-phase. A systematic procedure is proposed for the construction of statically equivalent outputs with prescribed transmission zeros. The calculated outputs are used to construct a model-state feedback controller. The proposed method is applied to a nonminimum-phase chemical reactor control problem where a series/parallel reaction is taking place.     

PI control of discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. In this paper, we exploit their unique physical structure to show how two term, i.e. proportional plus integral (or PI) action, can be used to control these processes to produce desired behavior (as opposed to just stability).     

Batch-to-batch control of fed-batch processes using control-affine feedforward neural network

A control strategy for fed-batch processes is proposed based on control affine feed-forward neural network (CAFNN). Many fed-batch processes can be considered as a class of control affine nonlinear systems. CAFNN is constructed by a special structure to fit the control affine system. It is similar to a multi-layer feed-forward neural network, but it has its own particular feature to model the fed-batch process. CAFNN can be trained by a modified Levenberg–Marquardt (LM) algorithm. However, due to model-plant mismatches and unknown disturbances, the optimal control policy calculated based on the CAFNN model may not be optimal when applied to the fed-batch process. In terms of the repetitive nature of fed-batch processes, iterative learning control (ILC) can be used to improve the process performance from batch to batch. Due to the special structure of CAFNN, the gradient information of CAFNN can be computed analytically and applied to the batch-to-batch ILC. Under the ILC strategy from batch to batch, endpoint product qualities of fed-batch processes can be improved gradually. The proposed control scheme is illustrated on a simulated fed-batch ethanol fermentation process.     

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.     

Fuzzy predictive PI control for processes with large time delays

This paper presents the design, tuning and performance analysis of a new predictive fuzzy controller structure for higher order plants with large time delays. The designed controller consists of a fuzzy proportional-integral (PI) part and a fuzzy predictor. The fuzzy predictive PI controller combines the advantages of fuzzy control while maintaining the simplicity and robustness of a conventional PI controller. The dynamics of the prediction term are adaptive to the system's time delay. The prediction term has two parts: a fuzzy predictor that uses the system time delay as an input for calculating the prediction horizon and an exponential term that uses the prediction horizon as its positive power. The prediction term also introduces phase lead into the system which compensates for the phase lag due to the time delay in the plant, thereby stabilizing the closed-loop configuration. The performance of the proposed controller is compared with the responses of the conventional predictive PI controller, showing many advantages of the new design over its conventional counterpart.     

一类非自衡加纯滞后系统的双预测PI控制

提出了一类基于非自衡加大纯滞后过程的双预测PI控制器的结构形式,这种控制器结构筒单,可调参数少,参数的调节方便、直观,仿真结果表明：在干扰和模型失配的情况下,此类控制器仍具有良好的控制性能和鲁棒稳定性,是一种值得在实际工程中推广应用的新型控制器。     

PI output feedback control of differential linear repetitive processes

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations which increase in amplitude in the pass-to-pass direction and cannot be controlled by standard control laws. Here we give new results on the design of physically based control laws. These are for the sub-class of so-called differential linear repetitive processes which arise in applications areas such as iterative learning control. They show how a form of proportional-integral (PI) control based only on process outputs can be designed to give stability plus performance and disturbance rejection.     

Nonlinear model predictive control of fed-batch fermentations using dynamic flux balance models

Fed-batch fermentation is an important production technology in the biochemical industry. Using fed-batch Saccharomyces cerevisiae fermentation as a prototypical example, we developed a general methodology for nonlinear model predictive control of fed-batch bioreactors described by dynamic flux balance models. The control objective was to maximize ethanol production at a fixed final batch time by adjusting the glucose feeding rate and the aerobic–anaerobic switching time. Effectiveness of the closed-loop implementation was evaluated by comparing the relative performance of NMPC and the open-loop optimal controller. NMPC was able to compensate for structural errors in the intracellular model and parametric errors in the substrate uptake kinetics and cellular energetics by increasing ethanol production between 8.0% and 14.7% compared with the open-loop operating policy. Minimal degradation in NMPC performance was observed when the biomass, glucose, and ethanol concentration and liquid volume measurements were corrupted with Gaussian white noise. NMPC based on the dynamic flux balance model was shown to improve ethanol production compared to the same NMPC formulation based on a simpler unstructured model. To our knowledge, this study represents the first attempt to utilize a dynamic flux balance model within a nonlinear model-based control scheme.     

Nonlinear feedback control of multivariable non-minimum-phase processes

A new method of controlling nonlinear processes with a non-minimum-phase delay-free part is presented. Two control laws are derived for stable, multiple-input multiple-output processes. They are obtained by requesting an approximately linear, input–output response and exploiting the connections between model-predictive control and input–output linearization. Conditions under which the closed-loop system is asymptotically stable are given. The application and performance of the control laws are illustrated using numerical simulation of two chemical reactor examples that exhibit non-minimum-phase behavior.     

高阶时滞对象的预测PI(D)控制

利用频率域模型降阶理论,提出了高阶时滞对象的预测PI(D)控制器两种设计方法.一种方法是直接将高阶滞后对象在频率域内降阶为低阶滞后对象,针对低阶滞后对象设计预测PI(D)控制器;另一种方法是按照规定的性能指标设计控制器,并将该控制器在频率域内降阶为具有预测PI(D)控制器的结构形式.这两种方法设计的控制器均具有结构简单、可调参数少、参数调节方便的特点.仿真表明:在模型失配的情况下,此两类预测PI(D)控制器仍然具有良好的控制性能和鲁棒稳定性能.     

Closed-loop growth-rate regulation in fed-batch dual-substrate processes with additive kinetics based on biomass concentration measurement

This paper deals with the design of feeding rates for dual-substrate fed-batch processes where the main control objective is the regulation of the microbial growth rate. To this end, feedback of the growth rate error is incorporated to a biomass proportional dual feeding law. A second-order sliding mode observer is used to estimate the growth rate, so that no additional sensors are required. Stability conditions are derived and robustness against several disturbances such as yield uncertainty, measurement errors and kinetic model mismatch is analytically and numerically evaluated. The advantages of the proposal include: minimal measurement requirements, regulation with fast convergence to the desired growth rate and reduced regulation error in the presence of disturbances.     

Nonlinear PI control of uncertain systems: an alternative to parameter adaptation

A novel approach to stabilization and trajectory tracking for nonlinear systems with unknown parameters and uncertain disturbances is developed. We take a drastic departure from the classical adaptive control approach consisting of a parameterized feedback law and an identifier, which tries to minimize a tracking (or prediction) error. Instead, we propose a simple nonlinear PI structure that generates a stable error equation with a perturbation function that exhibits at least one root. Trajectories are forced to converge to this root by suitably adjusting the nonlinear PI gains. We consider the two basic problems of: (i) matched uncertainties, when the uncertain terms are in the image of the input matrix, and (ii) unknown control directions, when the control signal is multiplied by a gain of unknown sign. We show that, without knowing the system parameters, and with only basic information on the uncertainties we can achieve global asymptotic stability and global tracking, without injecting high gains into the loop. Interestingly, we prove that we can take as our nonlinear PI structure an activation function reminiscent of that used in neural networks. Although most of the results are derived assuming full state measurement, we also present an observer-based solution for a chain of integrators with unknown control direction. The procedure is shown to provide simple solutions to the classical problems of neural network function approximation, as well as eccentricity control and friction compensation of mechanical systems.     

大滞后过程的PI控制器整定

提出一种简单而有效的大滞后过程PI控制器整定方法．基于继电反馈试验,辨识出一阶加纯滞后模型,其Nyquist曲线在一个大的频率范围内接近于大滞后过程．根据有效模型并基于一种新的鲁棒性能指标,设计出PI控制器．仿真结果表明了PI控制器的有效性。