Mathematical modelling and control of agitated extraction columns

Liquid-liquid extraction has long been known as a unit operation that plays an important role in industry. This process is well known for its complexity and sensitivity to operation conditions. This thesis presents an attempt to explore the dynamics and control of this process using a systematic approach and state of the art control system design techniques. The process was studied first experimentally under carefully selected. operation conditions, which resembles the ranges employed practically under stable and efficient conditions. Data were collected at steady state conditions using adequate sampling techniques for the dispersed and continuous phases as well as during the transients of the column with the aid of a computer-based online data logging system and online concentration analysis. A stagewise single stage backflow model was improved to mimic the dynamic operation of the column. The developed model accounts for the variation in hydrodynamics, mass transfer, and physical properties throughout the length of the column. End effects were treated by addition of stages at the column entrances. Two parameters were incorporated in the model namely; mass transfer weight factor to correct for the assumption of no mass transfer in the. settling zones at each stage and the backmixing coefficients to handle the axial dispersion phenomena encountered in the course of column operation. The parameters were estimated by minimizing the differences between the experimental and the model predicted concentration profiles at steady state conditions using non-linear optimisation technique. The estimated values were then correlated as functions of operating parameters and were incorporated in·the model equations. The model equations comprise a stiff differential~algebraic system. This system was solved using the GEAR ODE solver. The calculated concentration profiles were compared to those experimentally measured. A very good agreement of the two profiles was achieved within a percent relative error of ±2.S%. The developed rigorous dynamic model of the extraction column was used to derive linear time-invariant reduced-order models that relate the input variables (agitator speed, solvent feed flowrate and concentration, feed concentration and flowrate) to the output variables (raffinate concentration and extract concentration) using the asymptotic method of system identification. The reduced-order models were shown to be accurate in capturing the dynamic behaviour of the process with a maximum modelling prediction error of I %. The simplicity and accuracy of the derived reduced-order models allow for control system design and analysis of such complicated processes. The extraction column is a typical multivariable process with agitator speed and solvent feed flowrate considered as manipulative variables; raffinate concentration and extract concentration as controlled variables and the feeds concentration and feed flowrate as disturbance variables. The control system design of the extraction process was tackled as multi-loop decentralised SISO (Single Input Single Output) as well as centralised MIMO (Multi-Input Multi-Output) system using both conventional and model-based control techniques such as IMC (Internal Model Control) and MPC (Model Predictive Control). Control performance of each control scheme was. studied in terms of stability, speed of response, sensitivity to modelling errors (robustness), setpoint tracking capabilities and load rejection. For decentralised control, multiple loops were assigned to pair.each manipulated variable with each controlled variable according to the interaction analysis and other pairing criteria such as relative gain array (RGA), singular value analysis (SVD). Loops namely Rotor speed-Raffinate concentration and Solvent flowrate Extract concentration showed weak interaction. Multivariable MPC has shown more effective performance compared to other conventional techniques since it accounts for loops interaction, time delays, and input-output variables constraints.

Design, development and control of a new generation high performance linear actuator for parallel robots and other applications

The main focus of this research is to design and develop a high performance linear actuator based on a four bar mechanism. The present work includes the detailed analysis (kinematics and dynamics), design, implementation and experimental validation of the newly designed actuator. High performance is characterized by the acceleration of the actuator end effector. The principle of the newly designed actuator is to network the four bar rhombus configuration (where some bars are extended to form an X shape) to attain high acceleration. Firstly, a detailed kinematic analysis of the actuator is presented and kinematic performance is evaluated through MATLAB simulations. A dynamic equation of the actuator is achieved by using the Lagrangian dynamic formulation. A SIMULINK control model of the actuator is developed using the dynamic equation. In addition, Bond Graph methodology is presented for the dynamic simulation. The Bond Graph model comprises individual component modeling of the actuator along with control. Required torque was simulated using the Bond Graph model. Results indicate that, high acceleration (around 20g) can be achieved with modest (3 N-m or less) torque input. A practical prototype of the actuator is designed using SOLIDWORKS and then produced to verify the proof of concept. The design goal was to achieve the peak acceleration of more than 10g at the middle point of the travel length, when the end effector travels the stroke length (around 1 m). The actuator is primarily designed to operate in standalone condition and later to use it in the 3RPR parallel robot. A DC motor is used to operate the actuator. A quadrature encoder is attached with the DC motor to control the end effector. The associated control scheme of the actuator is analyzed and integrated with the physical prototype. From standalone experimentation of the actuator, around 17g acceleration was achieved by the end effector (stroke length was 0.2m to 0.78m). Results indicate that the developed dynamic model results are in good agreement. Finally, a Design of Experiment (DOE) based statistical approach is also introduced to identify the parametric combination that yields the greatest performance. Data are collected by using the Bond Graph model. This approach is helpful in designing the actuator without much complexity.

Control of pattern formation by time-delay feedback with global and local contributions

We consider the suppression of spatiotemporal chaos in the complex GinzburgLandau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations. © 2010 Elsevier B.V. All rights reserved.

AN ENERGY BASED MINIMUM-TIME OPTIMAL CONTROL OF DC-DC CONVERTERS

Time-optimal response is an important and sometimes necessary characteristic of dynamic systems for specific applications. Power converters are widely used in different electrical systems and their dynamic response will affect the whole system. In many electrical systems like microgrids or voltage regulators which supplies sensitive loads fast dynamic response is a must. Minimum time is the fastest converter to compensate the step output reference or load change. Boost converters as one of the wildly used power converters in the electrical systems are aimed to be controlled in optimal time in this study. Linear controllers are not able to provide the optimal response for a boost converter however they are still useful and functional for other applications like reference tracking or stabilization. To obtain the fastest possible response from boost converters, a nonlinear control approach based on the total energy of the system is studied in this research. Total energy of the system considers as the basis for developing the presented method, since it is easy and accurate to measure besides that the total energy of the system represents the actual operating condition of the boost converter. The detailed model of a boost converter is simulated in MATLAB/Simulink to achieve the time optimal response of the boost converter by applying the developed method. The simulation results confirmed the ability of the presented method to secure the time optimal response of the boost converter under four different scenarios.

Modelling and control of a floating oscillating water column

A novel numerical model of a Bent Backwards Duct Buoy (BBDB) Oscillating Water Column (OWC) Wave Energy Converter was created based on existing isolated numerical models of the different energy conversion systems utilised by an OWC. The novel aspect of this numerical model is that it incorporates the interdependencies of the different power conversion systems rather than modelling each system individually. This was achieved by accounting for the dynamic aerodynamic damping caused by the changing turbine rotational velocity by recalculating the turbine damping for each simulation sample and applying it via a feedback loop. The accuracy of the model was validated using experimental data collected during the Components for Ocean Renewable Energy Systems (CORES) EU FP-7 project that was tested in Galway Bay, Ireland. During the verification process, it was discovered that the model could also be applied as a valuable tool when troubleshooting device performance. A new turbine was developed and added to a full scale model after being investigated using Computational Fluid Dynamics. The energy storage capacity of the impulse turbine was investigated by modelling the turbine with both high and low inertia and applying three turbine control theories to the turbine using the full scale model. A single Maximum Power Point Tracking algorithm was applied to the low-inertia turbine, while both a fixed and dynamic control algorithm was applied to the high-inertia turbine. These results suggest that the highinertia turbine could be used as a flywheel energy storage device that could help minimize output power variation despite the low operating speed of the impulse turbine. This research identified the importance of applying dynamic turbine damping to a BBDB OWC numerical model, revealed additional value of the model as a device troubleshooting tool, and found that an impulse turbine could be applied as an energy storage system.

Distributed non-cooperative robust economic predictive control for dynamically coupled linear systems.

In this thesis, a tube-based Distributed Economic Predictive Control (DEPC) scheme is presented for a group of dynamically coupled linear subsystems. These subsystems are components of a large scale system and control inputs are computed based on optimizing a local economic objective. Each subsystem is interacting with its neighbors by sending its future reference trajectory, at each sampling time. It solves a local optimization problem in parallel, based on the received future reference trajectories of the other subsystems. To ensure recursive feasibility and a performance bound, each subsystem is constrained to not deviate too much from its communicated reference trajectory. This difference between the plan trajectory and the communicated one is interpreted as a disturbance on the local level. Then, to ensure the satisfaction of both state and input constraints, they are tightened by considering explicitly the effect of these local disturbances. The proposed approach averages over all possible disturbances, handles tightened state and input constraints, while satisfies the compatibility constraints to guarantee that the actual trajectory lies within a certain bound in the neighborhood of the reference one. Each subsystem is optimizing a local arbitrary economic objective function in parallel while considering a local terminal constraint to guarantee recursive feasibility. In this framework, economic performance guarantees for a tube-based distributed predictive control (DPC) scheme are developed rigorously. It is presented that the closed-loop nominal subsystem has a robust average performance bound locally which is no worse than that of a local robust steady state. Since a robust algorithm is applying on the states of the real (with disturbances) subsystems, this bound can be interpreted as an average performance result for the real closed-loop system. To this end, we present our outcomes on local and global performance, illustrated by a numerical example.

Active Dendrites Enhance Neuronal Dynamic Range

Since the first experimental evidences of active conductances in dendrites, most neurons have been shown to exhibit dendritic excitability through the expression of a variety of voltage-gated ion channels. However, despite experimental and theoretical efforts undertaken in the past decades, the role of this excitability for some kind of dendritic computation has remained elusive. Here we show that, owing to very general properties of excitable media, the average output of a model of an active dendritic tree is a highly non-linear function of its afferent rate, attaining extremely large dynamic ranges (above 50 dB). Moreover, the model yields double-sigmoid response functions as experimentally observed in retinal ganglion cells. We claim that enhancement of dynamic range is the primary functional role of active dendritic conductances. We predict that neurons with larger dendritic trees should have larger dynamic range and that blocking of active conductances should lead to a decrease in dynamic range.

A Dynamic Analysis of Tuberculosis Dissemination to Improve Control and Surveillance

Background: Detailed analysis of the dynamic interactions among biological, environmental, social, and economic factors that favour the spread of certain diseases is extremely useful for designing effective control strategies. Diseases like tuberculosis that kills somebody every 15 seconds in the world, require methods that take into account the disease dynamics to design truly efficient control and surveillance strategies. The usual and well established statistical approaches provide insights into the cause-effect relationships that favour disease transmission but they only estimate risk areas, spatial or temporal trends. Here we introduce a novel approach that allows figuring out the dynamical behaviour of the disease spreading. This information can subsequently be used to validate mathematical models of the dissemination process from which the underlying mechanisms that are responsible for this spreading could be inferred. Methodology/Principal Findings: The method presented here is based on the analysis of the spread of tuberculosis in a Brazilian endemic city during five consecutive years. The detailed analysis of the spatio-temporal correlation of the yearly geo-referenced data, using different characteristic times of the disease evolution, allowed us to trace the temporal path of the aetiological agent, to locate the sources of infection, and to characterize the dynamics of disease spreading. Consequently, the method also allowed for the identification of socio-economic factors that influence the process. Conclusions/Significance: The information obtained can contribute to more effective budget allocation, drug distribution and recruitment of human skilled resources, as well as guiding the design of vaccination programs. We propose that this novel strategy can also be applied to the evaluation of other diseases as well as other social processes.

Robust STATCOM control for the stabilisation of fixed-speed wind turbines during low voltages

This paper presents a robust voltage control scheme for fixed-speed wind generators using a static synchronous compensator (STATCOM) controller. To enable a linear and robust control framework with structured uncertainty, the overall system is represented by a linear part plus a nonlinear part that covers an operating range of interest required to ensure stability during severe low voltages. The proposed methodology is flexible and readily applicable to larger wind farms of different configurations. The performance of the control strategy is demonstrated on a two area test system. Large disturbance simulations demonstrate that the proposed controller enhances voltage stability as well as transient stability of induction generators during low voltage ride through (LVRT) transients and thus enhances the LVRT capability. (C) 2011 Elsevier Ltd. All rights reserved.

An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (C) 2008 Elsevier B.V. All rights reserved.

Dynamic Design of Piezoelectric Laminated Sensors and Actuators using Topology Optimization

Sensors and actuators based on piezoelectric plates have shown increasing demand in the field of smart structures, including the development of actuators for cooling and fluid-pumping applications and transducers for novel energy-harvesting devices. This project involves the development of a topology optimization formulation for dynamic design of piezoelectric laminated plates aiming at piezoelectric sensors, actuators and energy-harvesting applications. It distributes piezoelectric material over a metallic plate in order to achieve a desired dynamic behavior with specified resonance frequencies, modes, and enhanced electromechanical coupling factor (EMCC). The finite element employs a piezoelectric plate based on the MITC formulation, which is reliable, efficient and avoids the shear locking problem. The topology optimization formulation is based on the PEMAP-P model combined with the RAMP model, where the design variables are the pseudo-densities that describe the amount of piezoelectric material at each finite element and its polarization sign. The design problem formulated aims at designing simultaneously an eigenshape, i.e., maximizing and minimizing vibration amplitudes at certain points of the structure in a given eigenmode, while tuning the eigenvalue to a desired value and also maximizing its EMCC, so that the energy conversion is maximized for that mode. The optimization problem is solved by using sequential linear programming. Through this formulation, a design with enhancing energy conversion in the low-frequency spectrum is obtained, by minimizing a set of first eigenvalues, enhancing their corresponding eigenshapes while maximizing their EMCCs, which can be considered an approach to the design of energy-harvesting devices. The implementation of the topology optimization algorithm and some results are presented to illustrate the method.

Robust model predictive control with zone control

Model predictive control (MPC) is usually implemented as a control strategy where the system outputs are controlled within specified zones, instead of fixed set points. One strategy to implement the zone control is by means of the selection of different weights for the output error in the control cost function. A disadvantage of this approach is that closed-loop stability cannot be guaranteed, as a different linear controller may be activated at each time step. A way to implement a stable zone control is by means of the use of an infinite horizon cost in which the set point is an additional variable of the control problem. In this case, the set point is restricted to remain inside the output zone and an appropriate output slack variable is included in the optimisation problem to assure the recursive feasibility of the control optimisation problem. Following this approach, a robust MPC is developed for the case of multi-model uncertainty of open-loop stable systems. The controller is devoted to maintain the outputs within their corresponding feasible zone, while reaching the desired optimal input target. Simulation of a process of the oil re. ning industry illustrates the performance of the proposed strategy.

A stable MPC with zone control

Several MPC applications implement a control strategy in which some of the system outputs are controlled within specified ranges or zones, rather than at fixed set points [J.M. Maciejowski, Predictive Control with Constraints, Prentice Hall, New Jersey, 2002]. This means that these outputs will be treated as controlled variables only when the predicted future values lie outside the boundary of their corresponding zones. The zone control is usually implemented by selecting an appropriate weighting matrix for the output error in the control cost function. When an output prediction is inside its zone, the corresponding weight is zeroed, so that the controller ignores this output. When the output prediction lies outside the zone, the error weight is made equal to a specified value and the distance between the output prediction and the boundary of the zone is minimized. The main problem of this approach, as long as stability of the closed loop is concerned, is that each time an output is switched from the status of non-controlled to the status of controlled, or vice versa, a different linear controller is activated. Thus, throughout the continuous operation of the process, the control system keeps switching from one controller to another. Even if a stabilizing control law is developed for each of the control configurations, switching among stable controllers not necessarily produces a stable closed loop system. Here, a stable M PC is developed for the zone control of open-loop stable systems. Focusing on the practical application of the proposed controller, it is assumed that in the control structure of the process system there is an upper optimization layer that defines optimal targets to the system inputs. The performance of the proposed strategy is illustrated by simulation of a subsystem of an industrial FCC system. (C) 2008 Elsevier Ltd. All rights reserved.

Dynamic positioning systems: An experimental analysis of sliding mode control

Vessel dynamic positioning (DP) systems are based on conventional PID-type controllers and an extended Kalman filter. However, they present a difficult tuning procedure, and the closed-loop performance varies with environmental or loading conditions since the dynamics of the vessel are eminently nonlinear. Gain scheduling is normally used to address the nonlinearity of the system. To overcome these problems, a sliding mode control was evaluated. This controller is robust to variations in environmental and loading conditions, it maintains performance and stability for a large range of conditions, and presents an easy tuning methodology. The performance of the controller was evaluated numerically and experimentally in order to address its effectiveness. The results are compared with those obtained from conventional PID controller. (c) 2010 Elsevier Ltd. All rights reserved.

An unexpected role for visual feedback in vehicle steering control

Some motor tasks can be completed, quite literally, with our eyes shut. Most people can touch their nose without looking or reach for an object after only a brief glance at its location. This distinction leads to one of the defining questions of movement control: is information gleaned prior to starting the movement sufficient to complete the task (open loop), or is feedback about the progress of the movement required (closed loop)? One task that has commanded considerable interest in the literature over the years is that of steering a vehicle, in particular lane-correction and lane-changing tasks. Recent work has suggested that this type of task can proceed in a fundamentally open loop manner [1 and 2], with feedback mainly serving to correct minor, accumulating errors. This paper reevaluates the conclusions of these studies by conducting a new set of experiments in a driving simulator. We demonstrate that, in fact, drivers rely on regular visual feedback, even during the well-practiced steering task of lane changing. Without feedback, drivers fail to initiate the return phase of the maneuver, resulting in systematic errors in final heading. The results provide new insight into the control of vehicle heading, suggesting that drivers employ a simple policy of “turn and see,” with only limited understanding of the relationship between steering angle and vehicle heading.