Nonlinear control of bioreactors with input multiplicities

Control of bioreactors exhibiting two input multiplicities, i.e., steady-state gains having opposite sign, is theoretically analyzed. The nonlinear system is represented by a unity gain linear system cascaded with a nonlinear gain. A conventional PI controller designed for the linear portion of the system 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 linear PI controller designed for the overall linear system. The nonlinear PI controller performance is superior to that of the linear PI controller.     

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.     

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.     

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.     

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.     

Internal model control for structured rank deficient system based on full rank decomposition

In this paper, an internal model control method is first proposed for structured rank deficient systems based on full rank decomposition. The system is first converted into a column full rank system by designing a pre-compensator. Then a feedback-compensator is designed to improve the dynamic characteristics of the full rank system and decrease the controller design difficulties. Rather than performing complex designing calculations, the pre- and feedback- compensators are designed by the full rank decomposition method. Furthermore, the non-square relative gain subsystem selection criterion is used to choose the square subsystem and to realize loop pairing. Consequently, the selected square subsystem is used as an internal model to design the internal model controller. Finally, a simple process is taken as the simulation object to demonstrate the validity and feasibility of the new method. Simulations results illustrate that the proposed strategy is not only simple and easy to implement but also has a good performance even the system model is mismatched.     

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.     

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.     

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.     

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.     

Stability of the human respiratory control system II. Analysis of a three-dimensional delay state-space model

A number of mathematical models of the human respiratory control system have been developed since 1940 to study a wide range of features of this complex system. Among them, periodic breathing (including Cheyne-Stokes respiration and apneustic breathing) is a collection of regular but involuntary breathing patterns that have important medical implications. The hypothesis that periodic breathing is the result of delay in the feedback signals to the respiratory control system has been studied since the work of Grodins et al. in the early 1950's [1]. The purpose of this paper is to study the stability characteristics of a feedback control system of five differential equations with delays in both the state and control variables presented by Khoo et al. [4] in 1991 for modeling human respiration. The paper is divided in two parts. Part I studies a simplified mathematical model of two nonlinear state equations modeling arterial partial pressures of O2 and CO2 and a peripheral controller. Analysis was done on this model to illuminate the effect of delay on the stability. It shows that delay dependent stability is affected by the controller gain, compartmental volumes and the manner in which changes in the ventilation rate is produced (i.e., by deeper breathing or faster breathing). In addition, numerical simulations were performed to validate analytical results. Part II extends the model in Part I to include both peripheral and central controllers. This, however, necessitates the introduction of a third state equation modeling CO2 levels in the brain. In addition to analytical studies on delay dependent stability, it shows that the decreased cardiac output (and hence increased delay) resulting from the congestive heart condition can induce instability at certain control gain levels. These analytical results were also confirmed by numerical simulations.     

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.     

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.     

Improvement of nitrogen removal and reduction of operating costs in an activated sludge process with feedforward–cascade control strategy

In this paper, a feedforward–cascade controller for dissolved oxygen concentration in an activated sludge process is designed in order to meet stricter effluent quality standards at a minimum cost. Conventional proportional and integral (PI) constant dissolved oxygen set-point control and feedforward–cascade dissolved oxygen set-point control are evaluated using the reduced model of activated sludge model no. 1 and reduced IWA simulation benchmark. The feedforward–cascade control has been based on a hierarchical structure where a high level or cascade control selects the set-point of the low level or conventional controller and low level directly control dissolved oxygen concentration. And feedforward control is introduced in the control system for preventing the influent loading from influencing the system. Simulation results show that feedforward–cascade control of the activated sludge process is more successful than conventional PI control in meeting the effluent standards and reducing operational costs. This control strategy can be expected to be accepted by the operating personnel in wastewater treatment plants.     

An expert system for fault management assistance on a space sleep experiment

The expert system, Principal Investigator-in-a-box, or [PI], was designed to assist astronauts or other operators in performing experiments outside their expertise. Currently, the software helps astronauts calibrate instruments for a Sleep and Respiration Experiment without contact with the investigator on the ground. It flew on the Space Shuttle missions STS-90 and STS-95. [PI] displays electrophysiological signals in real time, alerts astronauts via the indicator lights when a poor signal quality is detected, and advises astronauts how to restore good signal quality. Thirty subjects received training on the sleep instrumentation and the [PI] interface. A beneficial effects of [PI] and training reduced troubleshooting time. [PI] benefited subjects on the most difficult scenarios, even though its lights were not 100% accurate. Further, questionnaires showed that most subjects preferred monitoring waveforms with [PI] assistance rather than monitoring waveforms alone. This study addresses problems of complex troubleshooting and the extended time between training and execution that is common to many human operator situations on earth such as in power plant operation, and marine exploration.     

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.     

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.     

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.     

Calibration of vector navigation in desert ants.

Desert ants (Cataglyphis sp.) monitor their position relative to the nest using a form of dead reckoning [1] [2] [3] known as path integration (PI) [4]. They do this with a sun compass and an odometer to update an accumulator that records their current position [1]. Ants can use PI to return to the nest [2] [3]. Here, we report that desert ants, like honeybees [5] and hamsters [6], can also use PI to approach a previously visited food source. To navigate to a goal using only PI information, a forager must recall a previous state of the accumulator specifying the goal, and compare it with the accumulator's current state [4]. The comparison - essentially vector subtraction - gives the direction to the goal. This whole process, which we call vector navigation, was found to be calibrated at recognised sites, such as the nest and a familiar feeder, throughout the life of a forager. If a forager was trained around a one-way circuit in which the result of PI on the return route did not match the result on the outward route, calibration caused the ant's trajectories to be misdirected. We propose a model of vector navigation to suggest how calibration could produce such trajectories.