Nonlinear control of bioreactors with input multiplicities in dilution rate

Control problems of continuous bioreactors having two input multiplicities in dilution rate on the productivity are analyzed. The nonlinear system is represented by a unity gain linear subsystem cascaded with a nonlinear gain subsystem. A conventional PI controller designed for the linear subsystem followed by the solution of the nonlinear gain equation gives a nonlinear controller. The performance of the nonlinear controller is compared with that of the conventional PI controller and also of the nonlinear controller [1] designed based on the output equation. The present nonlinear PI controller gives a superior performance. A single set of controller settings can be used for both the operating points. Whereas the linear PI controller and the nonlinear controller proposed by Henson and Seborg [1] destabilize the system.     

Nonlinear control of bioreactors with input multiplicities—an experimental work

The phrase input multiplicities means that an input variable with more than one value produces the same output value as if there were a single input–single output process. With input multiplicities, the value of the process gain changes as the manipulated variable changes, and beyond a certain input value, the sign of the gain also changes. A conventional PI controller for processes with input multiplicities may give unstable, less economical, or oscillatory responses. In the present work, control problems of a continuous bioreactor exhibiting two input multiplicities in the dilution rate on productivity were experimentally analyzed. A regulatory problem for the evaluation of controllers was taken up, i.e. a step change was made in the feed substrate concentration from 20 to 25 g/l at steady state conduction at lower (0.09386 h⁻¹) and higher (0.2278 h⁻¹) dilution rates for the same productivity of 2.9 g/l h. The nonlinear PI controller gave a more stable and fast response at both input dilution rates. The linear PI controller designed for a lower input dilution rate was stable, with some oscillations at the lower dilution rate, but the response was unstable at a higher dilution rate due to the input multiplicity behaviour of the process. Thus, nonlinear PI controller performance was found to be superior to that of the linear controller, and earlier reported theoretical results have been validated by the present experimental work.     

Nonlinear feedforward control of bioreactors with input multiplicities

A steady-state nonlinear feedforward controller (FFC) for measurable disturbances is designed for a continuous bioreactor, which is represented by Hammerstein type nonlinear model wherein the nonlinearity is a polynomial with input multiplicities. The manipulated variable is the feed substrate concentration (S_f) and the disturbance variable is the dilution rate (D). The productivity (Q=DP) is considered as the controlled variable. The desired value of Q=3.73 gives two values of feed substrate concentration. The nonlinearity in the gain is considered for relating output to the manipulated variable and separately for the relation between output to disturbance variable. The FFC is also designed for the overall linearized system. The performance of the FFC is evaluated on the nonlinear differential equation model. The FFC is also designed for the model based on a single nonlinear steady-state equation containing both D and S_f. This nonlinear FFC gives the best performance. The nonlinear FFC is also designed by using only linear gain for the disturbance and nonlinear gain for the manipulated variable. Similarly, nonlinear FFC is also designed by using linear gain for the manipulated variable and the nonlinear gain for the disturbance variable. The performances of these FFC schemes are compared.     

Anti-control of periodic firing in HR model in the aspects of position,amplitude and frequency

This paper proposes a novel controller to control position, amplitude and frequency of periodic firing activity in Hindmarsh–Rose model based on Hopf bifurcation theory which is composed of linear control gain and nonlinear control gain. First, we select the activation of the fast ion channel as control parameter. Based on explicit criterion of Hopf bifurcation, a series of conditions are obtained to derive the linear gains of controller responsible for control of the location where the periodic firing activity occurs. Then, based on the control parameter, a series of conditions are obtained to derive the nonlinear gains of controller responsible for controlling the amplitude and frequency of periodic firing activity by using center manifold and normal form. Finally, the numerical experiments show that our controller can make the periodic firing activity occur at designed value and control the amplitude and frequency of periodic firing activity by adjusting nonlinear control gain of controller.     

An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models

A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.     

Identification of Hammerstein model for bioreactors with input multiplicities

A closed loop identification method of Hammerstein model for continuous bioreactor with input multiplicity is proposed. Hammerstein model consists of nonlinear steady-state gain followed by a unity gain linear system. The method consists of first getting local first order plus time delay (FOPTD) models around the two input multiplicity values of the substrate feed concentration. The model parameters of the FOPTD is identified by a least square optimization method. The initial guess for the model parameters are obtained from the settling time, the initial delay in the closed loop servo response and using a simple proportional controller formula. From the local process gain values obtained for the several step changes around the two operating conditions, the nonlinear gain portion of the Hammerstein is then obtained. The actual nonlinear gain and the identified nonlinear gain is compared.     

Closed loop identification of transfer function model for unstable bioreactors for tuning PID controllers

Closed loop identification of transfer function model for an unstable bioreactor is proposed based on an optimization method using either a step or a pulse response of PI/PID controlled bioreactor. A simple method is proposed for the initial guesses of the parameters of the first order plus time delay (FOPTD) transfer function model. A PID controller is designed for the identified model. Simulation study on the nonlinear model equations of an unstable bioreactor exhibiting multiple steady-states shows that the PID controller designed on the identified FOPTD model gives a good closed loop response similar to the one designed based on the linearized model from the nonlinear model equations.     

Maintaining synchronization by decentralized feedback control in time delay neural networks with parameter uncertainties

A decentralized feedback control scheme is proposed to synchronize linearly coupled identical neural networks with time-varying delay and parameter uncertainties. Sufficient condition for synchronization is developed by carefully investigating the uncertain nonlinear synchronization error dynamics in this article. A procedure for designing a decentralized synchronization controller is proposed using linear matrix inequality (LMI) technique. The designed controller can drive the synchronization error to zero and overcome disruption caused by system uncertainty and external disturbance.     

Comparative evaluation of various control schemes for fed-batch fermentation

The crucial problem associated with control of fed-batch fermentation process is its time-varying characteristics. A successful controller should be able to deal with this feature in addition to the inherent nonlinear characteristics of the process. In this work, various schemes for controlling the glucose feed rate of fed-batch baker's yeast fermentation were evaluated. The controllers evaluated are fixed-gain proportional-integral (PI), scheduled-gain PI, adaptive neural network and hybrid neural network PI. The difference between the specific carbon dioxide evolution rate and oxygen uptake rate (Q_c-Q_o) was used as the controller variable. The evaluation was carried out by observing the performance of the controllers in dealing with setpoint tracking and disturbance rejection. The results confirm the unsatisfactory performance of the conventional controller where significant oscillation and offsets exist. Among the controllers considered, the hybrid neural network PI controller shows good performance.     

Control of bioreactors using a neural network model

Control of a continuous bioreactor based on a artificial neural network (ANN) model is carried out theoretically. The ANN model is identified, from input-output data of a bioreactor, using a three-layer feedforward network trained by a back propagation algorithm. The performance of the controller designed on the ANN model is compared with that of a conventional PI controller.     

Cybernetic model predictive control of a continuous bioreactor with cell recycle

The control of poly-beta-hydroxybutyrate (PHB) productivity in a continuous bioreactor with cell recycle is studied by simulation. A cybernetic model of PHB synthesis in Alcaligenes eutrophus is developed. Model parameters are identified using experimental data, and simulation results are presented. The model is interfaced to a multirate model predictive control (MPC) algorithm. PHB productivity and concentration are controlled by manipulating dilution rate and recycle ratio. Unmeasured time varying disturbances are imposed to study regulatory control performance, including unreachable setpoints. With proper controller tuning, the nonlinear MPC algorithm can track productivity and concentration setpoints despite a change in the sign of PHB productivity gain with respect to dilution rate. It is shown that the nonlinear MPC algorithm is able to track the maximum achievable productivity for unreachable setpoints under significant process/model mismatch. The impact of model uncertainty upon controller performance is explored. The multirate MPC algorithm is tested using three controllers employing models that vary in complexity of regulation. It is shown that controller performance deteriorates as a function of decreasing biological complexity.     

Control of unstable bioreactor using fuzzy tuned PI controller

A fuzzy tuning scheme for conventional PI controller is developed for controlling an unstable continuous bioreactor. The performance is compared with that of a fixed setting conventional PI controller. The performance of the tuning scheme is studied by simulating the non-linear model equations of the bioreactor. The robustness of the controller is also studied for uncertainties in the process parameters such as yield factor and measurement delay. Simulation results show that the fuzzy tuning improves the overall performance and particularly it is more robust to parameter uncertainties.     

EEG-based communication and control: speed-accuracy relationships

People can learn to control mu (8–12 Hz) or beta (18–25 Hz) rhythm amplitude in the EEG recorded over sensorimotor cortex and use it to move a cursor to a target on a video screen. In our current EEG-based brain–computer interface (BCI) system, cursor movement is a linear function of mu or beta rhythm amplitude. In order to maximize the participant's control over the direction of cursor movement, the intercept in this equation is kept equal to the mean amplitude of recent performance. Selection of the optimal slope, or gain, which determines the magnitude of the individual cursor movements, is a more difficult problem. This study examined the relationship between gain and accuracy in a 1-dimensional EEG-based cursor movement task in which individuals select among 2 or more choices by holding the cursor at the desired choice for a fixed period of time (i.e., the dwell time). With 4 targets arranged in a vertical column on the screen, large gains favored the end targets whereas smaller gains favored the central targets. In addition, manipulating gain and dwell time within participants produces results that are in agreement with simulations based on a simple theoretical model of performance. Optimal performance occurs when correct selection of targets is uniform across position. Thus, it is desirable to remove any trend in the function relating accuracy to target position. We evaluated a controller that is designed to minimize the linear and quadratic trends in the accuracy with which participants hit the 4 targets. These results indicate that gain should be adjusted to the individual participants, and suggest that continual online gain adaptation could increase the speed and accuracy of EEG-based cursor control.     

血压自适应控制系统研究

本文设计一个自适应血压自动控制系统,首先,通过动物实验,获得了受控对象的参数变化范围的信息.在此基础上,我们应用参考模型和自校正调节器两种算法设计自适应控制系统.计算机仿真证明这两类算法均可成功地应用于血压的自适应控制,尽管受控对象存在未知时变延时,时间常数和增益的变化.最后,将设计的系统在动物(狗)中作了检验.在18条狗上作升压或降压试验证明,两种算法均有良好的过渡过程特性,这一系统将可应用于临床,以改进药物注射系统的性能.     

An intelligent control method based on fuzzy logic for a robotic testing system for the human spine

In previous biomechanical studies of the human spine, we implemented a hybrid controller to investigate load-displacement characteristics. We found that measurement errors in both position and force caused the controller to be less accurate than predicted. As an alternative to hybrid control, a fuzzy logic controller (FLC) has been developed and implemented in a robotic testing system for the human spine. An FLC is a real-time expert system that can emulate part of a human operator's knowledge by using a set of action rules. The FLC provides simple but robust solutions that cover a wide range of system parameters and can cope with significant disturbances. It can be viewed as a heuristic and modular way of defining a nonlinear, table-based control system. In this study, an FLC is developed which uses the force difference and the change in force difference as the input parameters, and the displacement as the output parameter. A rule-table based on these parameters is designed for the controller Experiments on a physical model composed of springs demonstrate the improved performance of the proposed method.     

Design of methanol Feed control in Pichia pastoris fermentations based upon a growth model

The methylotrophic yeast Pichia pastoris is an effective system for recombinant protein productions that utilizes methanol as an inducer, and also as carbon and energy source for a Mut(+) (methanol utilization plus) strain. Pichia fermentation is conducted in a fed-batch mode to obtain a high cell density for a high productivity. An accurate methanol control is required in the methanol fed-batch phase (induction phase) in the fermentation. A simple "on-off" control strategy is inadequate for precise control of methanol concentrations in the fermentor. In this paper we employed a PID (proportional, integral and derivative) control system for the methanol concentration control and designed the PID controller settings on the basis of a Pichia growth model. The closed-loop system was built with four components: PID controller, methanol feed pump, fermentation process, and methanol sensor. First, modeling and transfer functions for all components were derived, followed by frequency response analysis, a powerful method for calculating the optimal PID parameters K(c) (controller gain), tau(I) (controller integral time constant), and tau(D) (controller derivative time constant). Bode stability criteria were used to develop the stability diagram for evaluating the designed settings during the entire methanol fed-batch phase. Fermentations were conducted using four Pichia strains, each expressing a different protein, to verify the control performance with optimal PID settings. The results showed that the methanol concentration matched the set point very well with only small overshoot when the set point was switched, which indicated that a very good control performance was achieved. The method developed in this paper is robust and can serve as a framework for the design of other PID feedback control systems in biological processes.     

Bioreactor controlled by PI algorithm and operated with a perfusion chamber to support endothelial cell survival and proliferation

This paper reports the optimization of a perfusion bioreactor system previously reported by us (Chouinard et al., 2009). The implementation of a proportional-integral (PI) controller algorithm to control oxygen concentration and pH is presented and discussed. P and I values used by the controller were first estimated using a First-Order-Plus-Dead-Time (FOPDT, Matlab Simulink) and then tuned manually. A new gas exchanger design compatible with the PI controller was introduced and validated to decrease interaction between the injected gases and overall inertia of the system. The gas exchanger was used to adjust both pH and dissolved oxygen (DO) concentration. This new bioreactor system allowed real-time PI control over pH and DO concentration at different flow rates (from 2 to 70 mL min(-1)). Cell viability and proliferation were investigated to validate the updated bioreactor design and performance.     

Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

On-line gas analysis in animal cell cultivation: I. Control of dissolved oxygen and pH

To monitor gas reaction rates in animal cell culture at constant dissolved oxygen concentration (DO) and constant pH it was necessary to develop improved control methods. Decoupling of both controllrs was obtained by manipulation of molar fractions of oxygen and carbon dioxide in the gas phase. Two pairs of DO and pH controllers were designed and tested both in simulation and exprimental runs. The first controller pair was developed for headspace aeration only, whereas the second controller pair was designed for bubble aeration using a microsparger and flushing the headspace with helium. pH was controlled by a conventional discrete PID controller in its velocity form. For DO control two linear state space feedback controllers with parameter adaptation were established. In these controllers the oxygen uptake rate (OUR) was considered as a disturbance and was not included in the mathematical model. The feedback gain adaptation was based on the difference between the actual molar fraction of oxygen at time step n and the initial molar fraction. This difference is related to OUR and was used to increase or decrease the state feedback controller gain (k and k(1), respectively) in a slow manner. With these controllers it was possible to get an excellent online estimate of OUR. In the case of bubble aeration a simple gas phase mass balance was sufficient, whereas during the headspace aeration a liquid phase balance was required. It has been shown that determination of OUR using gas balance requires a significantly better controller performance compared to just keeping DO and pH within reasonable limits. (c) 1995 John Wiley & Sons, Inc.