scholarly journals Dual-Input Slope Seeking Control of Continuous Micro-Algae Cultures with Experimental Validation

2021 ◽  
Vol 11 (16) ◽  
pp. 7451
Author(s):  
Christian Feudjio Letchindjio ◽  
Jesús Zamudio Lara ◽  
Laurent Dewasme ◽  
Héctor Hernández Escoto ◽  
Alain Vande Wouwer

This paper investigates the application of adaptive slope-seeking strategies to dual-input single output dynamic processes. While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal). Moreover, the consideration of more than one input signal allows minimizing the input energy thanks to the degrees of freedom offered by the additional inputs. The actual process is assumed to be locally approachable by a Hammerstein model, combining a nonlinear static map with a linear dynamic model. The proposed strategy is based on the interplay of three components: (i) a recursive estimation algorithm providing the model parameters and the performance index gradient, (ii) a slope generator using the static map parameter estimates to convert the performance index setpoint into slope setpoints, and (iii) an adaptive controller driving the process to the desired setpoint. The performance of the slope strategy is assessed in simulation in an application example related to lipid productivity optimization in continuous cultures of micro-algae by acting on both the incident light intensity and the dilution rate. It is also validated in experimental studies where biomass production in a continuous photo-bioreactor is targeted.

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Y. H. Tsoi ◽  
S. Q. Xie

The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1519
Author(s):  
Mikulas Huba ◽  
Pavol Bistak ◽  
Damir Vrancic ◽  
Katarina Zakova

The article reviews the results of a number of recent papers dealing with the revision of the simplest approaches to the control of first-order time-delayed systems. The concise introductory review is extended by an analysis of two discrete-time approaches to dead-time compensation control of stable, integrating, and unstable first-order dead-time processes including simple diagnostics of the model used and focusing on the possibility of simplified but reliable plant modelling. The first approach, based on the first historically known dead-time compensator (DTC) with possible dead-beat performance, is based on the reconstruction of the actual process variables and the compensation of input disturbances by an extended state observer (ESO). Such solutions play an important role both in a disturbance observer (DOB) based control and in an active disturbance rejection control (ADRC). The second approach considered comes from the Smith predictor with two degrees of freedom, which combines feedforward control with output disturbance reconstruction and compensation by the parallel plant model. It is shown that these two approaches offer advantageous properties in the case of actuator limitations, in contrast to the commonly used PID controllers. However, when applied to integrating and unstable first-order systems, the unconstrained and possibly unobservable output disturbance signal of the second solution must be eliminated from the control loop, due to the hidden structural instability of the Smith predictor-like solutions. The modified solutions, usually referred to as filtered Smith predictor (FSP), then no longer provide a disturbance signal and thus no longer fully fit into the concept of Industry 4.0, which is focused on further optimization, predictive maintenance in dynamic systems, diagnosis, fault detection and fault identification of dynamic processes and forms the basis for the digitalization of smart production. Nevertheless, the detailed analysis of the elimination of the unstable disturbance response mode is also worth mentioning in terms of other possible solutions. The application of both approaches to the control of a thermal process shows almost equivalent quality, but with different dependencies on the tuning parameters used. It is confirmed that a more detailed identification of the controlled process and the resulting higher complexity of the control algorithms does not necessarily lead to an increase in the resulting quality of the transients, which underlines the importance of the simplified plant modelling for practice.


1990 ◽  
Vol 259 (2) ◽  
pp. H626-H634
Author(s):  
C. F. Starmer ◽  
V. V. Nesterenko ◽  
F. R. Gilliam ◽  
A. O. Grant

Models of ion channel blockade are frequently validated with observations of ionic currents resulting from electrical or chemical stimulation. Model parameters for some models (modulated receptor hypothesis) cannot be uniquely determined from ionic currents. The time course of ionic currents reflects the activation (fraction of available channels that conduct in the presence of excitation) and availability of channels (the ability of the protein to make a transition to a conducting conformation and where this conformation is not complexed with a drug). In the presence of a channel blocking agent, the voltage dependence of availability appears modified and has been interpreted as evidence that drug-complexed channels exhibit modified transition rates between channel protein conformations. Because blockade and availability both modify ionic currents, their individual contributions to macroscopic conductance cannot be resolved from ionic currents except when constant affinity binding to a bindable site is assumed. Experimental studies of nimodipine block of calcium channels and lidocaine block of sodium channels illustrate these concepts.


When the oscillating electric spark is examined in a rapidly rotating mirror, the successive oscillations render themselves evident in the image as a series of lumnious curved streamers which emanate from the poles and extend towards the centre of the spark gap. These streamers were first observed by Feddersen in 1862, but the work of Schuster and Hemsalech in 1900 may be said to have opened up a new era in the subject. These workers threw the image of the spark on the slit of a spectroscope, and photographed the resulting spectrum on a film which was maintained in rapid rotation in a direction at right angles to that of the incident light. In their photographs they found that the air lines extended straight across from pole to pole, but that the metal lines were represented by curved bands drawn out in the centre of the spark gap. There is a close relation between these bands and the streamers seen in the unanalysed inductive spark. Schuster and Hemsalech carried out their experiments with the smallest possible inductance in series with the spark, and thus made the period of the oscillations so small that the drawing out on the film was insufficient to separate the individual oscillations from each other. Thus their curved lines represent a composite structure, consisting of all the streamers due to the successive oscillations superposed on each other. It follows from their results that the light of the streamers in the spark is entirely produced by the glowing of the metallic vapour of the electrodes, and that, while the luminosity of the air is practically instantaneous in its occurrence, that due to the metal vapour occurs in the centre of the spark gap an appreciable time later than near the poles. The actual process which goes on in the spark and gives rise to this delay in the arrival of the metallic vapour at the centre of the gap is not yet thoroughly understood. Schuster and Hemsalech make the natural supposition that it is due to the fact that the metal of the electrode is vaporised and rendered incandescent by the heat of the spark, and that the vapour takes an appreciable time to diffuse from the electrodes to the centre of the gap. The exception which has been taken to this view has arisen in part from the difficulty of observing the Doppler effect on the metallic lines which should be a concomitant of the diffusion of the vapour from the poles, and in part from the extraordinary results which the authors themselves obtained in some metals for the velocity of the diffusion corresponding to the different lines. In the case of bismuth and, in a less degree, of cadmium the different metallic lines could be divided into groups of different curvatures which indicated different velocities of diffusion towards the centre of the gap. As regards the former matter, there does not seem to be involved any real difficulty to the explanation, as Dr. Schuster has himself recently shown. The curious effect of the different curvatures of the lines of the same element has, however, always remained more or less of a difficulty in the way of a complete acceptance of their view. Schuster and Hemsalech themselves refer to the possibility in the case of bismuth that the metal may be a compound, and that the two kinds of molecules give rise to the differently curved lines. Other explanations have been made by different writers, but it cannot be said that any explanation adequately supported by experiment has been forthcoming. In view of this incompleteness in our knowledge of the constitution of the streamers it seemed to me that further observations with a rotating mirror would possibly be of value, and the investigations recorded below succeed, I think, in throwing a clearer light on the nature of the streamers, and on certain other phenomena which are characteristic of the spark.


2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.


1991 ◽  
Vol 18 (2) ◽  
pp. 320-327 ◽  
Author(s):  
Murray A. Fitch ◽  
Edward A. McBean

A model is developed for the prediction of river flows resulting from combined snowmelt and precipitation. The model employs a Kalman filter to reflect uncertainty both in the measured data and in the system model parameters. The forecasting algorithm is used to develop multi-day forecasts for the Sturgeon River, Ontario. The algorithm is shown to develop good 1-day and 2-day ahead forecasts, but the linear prediction model is found inadequate for longer-term forecasts. Good initial parameter estimates are shown to be essential for optimal forecasting performance. Key words: Kalman filter, streamflow forecast, multi-day, streamflow, Sturgeon River, MISP algorithm.


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