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.

Stability indicators, a tool for organizational planning and control

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The implications of cost behaviour for profit planning and control

The work described in the following pages was carried out at various sites in the Rod Division of the Delta Metal Company. Extensive variation in the level of activity in the industry during the years 1974 to I975 had led to certain inadequacies being observed 1n the traditional cost control procedure. In an attempt to remedy this situation it was suggested that a method be found of constructing a system to improve the flexibility of cost control procedures. The work involved an assimilation of the industrial and financial environment via pilot studies which would later prove invaluable to home in on the really interesting and important areas. Weaknesses in the current systems which came to light made the methodology of data collection and the improvement of cost control and profit planning procedures easier to adopt. Because of the requirements of the project to investigate the implications of Cost behaviour for profit planning and control, the next stage of the research work was to utilise the on-site experience to examine at a detailed level the nature of cost behaviour. The analysis of factory costs then showed that certain costs, which were the most significant exhibited a stable relationship with respect to some known variable, usually a specific measure of Output. These costs were then formulated in a cost model, to establish accurate standards in a complex industrial setting in order to provide a meaningful comparison against which to judge actual performance. The necessity of a cost model was •reinforced by the fact that the cost behaviour found to exist was, in the main, a step function, and this complex cost behaviour, the traditional cost and profit planning procedures could not possibly incorporate. Already implemented from this work is the establishment of the post of information officer to co-ordinate data collection and information provision.

The stability and formulation of topical analgesics

High-performance liquid chromatographic methods are developed for the simultaneous determination of various salicylates, their p-hydroxy isomers and nicotinic acid esters. The method is sensitive enough to detect trace amounts (~µM/L)of the product generated from cross reactivity between the drugs and the vehicle. The developed method also allows analysis of various topical products containing salicylate and nicotinate esters in their formulations. Applying this method, the degradation profiles of salicylates, nicotinates, p-hydroxy benzoate, o-methoxy benzoate and aspirin prodrugs in alkaline media are determined. The profile for alkyl salicylate degradation is found to be first order (A---? B) When the alcoholic radical is similar to that of the ester. In alcohol having a radical different from that of the ester function, the degradation is found to proceed through competitive transesterification and hydrolysis. The intermediates are identified following synthesis and isolation. The rate and extent of transesterification depends on the proportion of alcohol present in the system. Equations are presented to model the time profiles of reactant and product concentration. The reactions are base catalysed and the predominant pathway involves a concerted solvent attack upon the salicylate anion. Competitive hydrolysis of both ester components also follows this mechanism at moderate pH values but rates increase under strongly alkaline conditions as direct hydroxide attack becomes significant. In contrast, transesterification is independent of base concentration once full ionization is accomplished. The competitive hydrolysis is modelled using equations involving the dielectric constant of the medium. A range of other esters are also shown to undergo base-catalysed transesterification. In non-alcoholic solution phenyl salicylate undergoes a concentration-dependent oligomerisation which yields salsalate among the products. Competitive transesterification and hydrolysis also occur in products for topical use which have vehicles based upon alcohol, glycol or glycol polymers. Such reactions may compromise stability assessments, pharmaceutical integrity and delivery profiles.

The effects of the environment on the stability and expression of genetically engineered plasmids

The lac promoter is widely used in plasmid expression systems, even though it is prone to catabolite repression. As a consequence glycerol is often used as an alternative carbon source. Three plasmids containing various sizes of the staphylococcal protein A (SPA) gene, which are under the control of the lac promoter were investigated in continuous culture, to evaluate the effects of nutrient limitations on their stability and expression. The fears of catabolite repression were dispelled as a low expression plasmid (pPA16) produced a greater amount of truncated SPA under glucose limiting conditions (11 ug mg-1 cell protein) when compared to that using glycerol (8 ug mg-1 cell protein). Segregational instability was also observed under glycerol limiting conditions at all the dilution rates investigated. Whereas pPA16 was relatively stable under glucose limiting conditions, with SPA production being continuous. Experiments using excess glycerol with limited ammonium increased the stability of pPA16, (when compared to limited glycerol) with expression of SPA being continuous but reduced (6 ug mg-1 cell protein). With excess glucose and limited ammonium the copy numbers remained high but expression of SPA paralled that produced under glucose limiting conditions. This might indicate that the higher levels of glucose are reducing expression (catabolite repression) or that the low level of ammonium is affecting protein production. A high expression plasmid (pPA31) produced nearly 100 ug full length SPA mg-1 cell protein, while another high expression plasmid (pPA34) producing truncated SPA proved to be very unstable. An ELISA was developed to detect the SPA produced by these experiments, which could be adapted for western blotting or immunogold probing using electron microscopy. SPA was localised in electron lucent areas present in the periplasmic space of the E. coli host harbouring pPA16. While in the same host containing pPA31, SPA was localised not only in electron lucent areas but also around the whole of the outer-membrane.

The dynamics and control of a remotely piloted plan-symmetric helicopter

Prior to the development of a production standard control system for ML Aviation's plan-symmetric remotely piloted helicopter system, SPRITE, optimum solutions to technical requirements had yet to be found for some aspects of the work. This thesis describes an industrial project where solutions to real problems have been provided within strict timescale constraints. Use has been made of published material wherever appropriate, new solutions have been contributed where none existed previously. A lack of clearly defined user requirements from potential Remotely Piloted Air Vehicle (RPAV) system users is identified, A simulation package is defined to enable the RPAV designer to progress with air vehicle and control system design, development and evaluation studies and to assist the user to investigate his applications. The theoretical basis of this simulation package is developed including Co-axial Contra-rotating Twin Rotor (CCTR), six degrees of freedom motion, fuselage aerodynamics and sensor and control system models. A compatible system of equations is derived for modelling a miniature plan-symmetric helicopter. Rigorous searches revealed a lack of CCTR models, based on closed form expressions to obviate integration along the rotor blade, for stabilisation and navigation studies through simulation. An economic CCTR simulation model is developed and validated by comparison with published work and practical tests. Confusion in published work between attitude and Euler angles is clarified. The implementation of package is discussed. dynamic adjustment of assessment. the theory into a high integrity software Use is made of a novel technique basing the integration time step size on error Simulation output for control system stability verification, cross coupling of motion between control channels and air vehicle response to demands and horizontal wind gusts studies are presented. Contra-Rotating Twin Rotor Flight Control System Remotely Piloted Plan-Symmetric Helicopter Simulation Six Degrees of Freedom Motion ( i i)