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.

Computer-assisted production scheduling, planning and control in foundries

The present study describes a pragmatic approach to the implementation of production planning and scheduling techniques in foundries of all types and looks at the use of `state-of-the-art' management control and information systems. Following a review of systems for the classification of manufacturing companies, a definitive statement is made which highlights the important differences between foundries (i.e. `component makers') and other manufacturing companies (i.e. `component buyers'). An investigation of the manual procedures which are used to plan and control the manufacture of components reveals the inherent problems facing foundry production management staff, which suggests the unsuitability of many manufacturing techniques which have been applied to general engineering companies. From the literature it was discovered that computer-assisted systems are required which are primarily `information-based' rather than `decision based', whilst the availability of low-cost computers and `packaged-software' has enabled foundries to `get their feet wet' without the financial penalties which characterized many of the early attempts at computer-assistance (i.e. pre-1980). Moreover, no evidence of a single methodology for foundry scheduling emerged from the review. A philosophy for the development of a CAPM system is presented, which details the essential information requirements and puts forward proposals for the subsequent interactions between types of information and the sub-system of CAPM which they support. The work developed was oriented specifically at the functions of production planning and scheduling and introduces the concept of `manual interaction' for effective scheduling. The techniques developed were designed to use the information which is readily available in foundries and were found to be practically successful following the implementation of the techniques into a wide variety of foundries. The limitations of the techniques developed are subsequently discussed within the wider issues which form a CAPM system, prior to a presentation of the conclusions which can be drawn from the study.

Deep hole drilling with twist drills: aspects of the CNC process and its real time monitoring and adaptive control

Deep hole drilling is one of the most complicated metal cutting processes and one of the most difficult to perform on CNC machine-tools or machining centres under conditions of limited manpower or unmanned operation. This research work investigates aspects of the deep hole drilling process with small diameter twist drills and presents a prototype system for real time process monitoring and adaptive control; two main research objectives are fulfilled in particular : First objective is the experimental investigation of the mechanics of the deep hole drilling process, using twist drills without internal coolant supply, in the range of diarneters Ø 2.4 to Ø4.5 mm and working length up to 40 diameters. The definition of the problems associated with the low strength of these tools and the study of mechanisms of catastrophic failure which manifest themselves well before and along with the classic mechanism of tool wear. The relationships between drilling thrust and torque with the depth of penetration and the various machining conditions are also investigated and the experimental evidence suggests that the process is inherently unstable at depths beyond a few diameters. Second objective is the design and implementation of a system for intelligent CNC deep hole drilling, the main task of which is to ensure integrity of the process and the safety of the tool and the workpiece. This task is achieved by means of interfacing the CNC system of the machine tool to an external computer which performs the following functions: On-line monitoring of the drilling thrust and torque, adaptive control of feed rate, spindle speed and tool penetration (Z-axis), indirect monitoring of tool wear by pattern recognition of variations of the drilling thrust with cumulative cutting time and drilled depth, operation as a data base for tools and workpieces and finally issuing of alarms and diagnostic messages.

Exploiting uncertainty in nonlinear stochastic control problem

This work introduces a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. Convergence of the output error for the proposed control method is verified by using a Lyapunov function. Several simulation examples are provided to demonstrate the efficiency of the developed control method. The manner in which such a method is extended to nonlinear multi-variable systems with different delays between the input-output pairs is considered and demonstrated through simulation examples.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Construction project control in the UK:current practice, existing problems and recommendations for future improvement

The aim of this study is to address the main deficiencies with the prevailing project cost and time control practices for construction projects in the UK. A questionnaire survey was carried out with 250 top companies followed by in-depth interviews with 15 experienced practitioners from these companies in order to gain further insights of the identified problems, and their experience of good practice on how these problems can be tackled. On the basis of these interviews and syntheses with literature, a list of 65 good practice recommendations have been developed for the key project control tasks: planning, monitoring, reporting and analysing. The Delphi method was then used, with the participation of a panel of 8 practitioner experts, to evaluate these improvement recommendations and to establish their degree of relevance. After two rounds of Delphi, these recommendations are put forward as "critical", "important", or "helpful" measures for improving project control practice.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

Bounds on end-to-end performance of networks employing erasure control coding

Erasure control coding has been exploited in communication networks with an aim to improve the end-to-end performance of data delivery across the network. To address the concerns over the strengths and constraints of erasure coding schemes in this application, we examine the performance limits of two erasure control coding strategies, forward erasure recovery and adaptive erasure recovery. Our investigation shows that the throughput of a network using an (n, k) forward erasure control code is capped by r =k/n when the packet loss rate p ≤ (te/n) and by k(l-p)/(n-te) when p > (t e/n), where te is the erasure control capability of the code. It also shows that the lower bound of the residual loss rate of such a network is (np-te)/(n-te) for (te/n) < p ≤ 1. Especially, if the code used is maximum distance separable, the Shannon capacity of the erasure channel, i.e. 1-p, can be achieved and the residual loss rate is lower bounded by (p+r-1)/r, for (1-r) < p ≤ 1. To address the requirements in real-time applications, we also investigate the service completion time of different schemes. It is revealed that the latency of the forward erasure recovery scheme is fractionally higher than that of the scheme without erasure control coding or retransmission mechanisms (using UDP), but much lower than that of the adaptive erasure scheme when the packet loss rate is high. Results on comparisons between the two erasure control schemes exhibit their advantages as well as disadvantages in the role of delivering end-to-end services. To show the impact of the bounds derived on the end-to-end performance of a TCP/IP network, a case study is provided to demonstrate how erasure control coding could be used to maximize the performance of practical systems. © 2010 IEEE.