A generic plant-wide control structure is proposed for the optimal operation of a grinding mill circuit. An economic objective function is defined for the grinding mill circuit with reference to the economic objective of the larger mineral processing plant. A mineral processing plant in this study consists of a comminution and a separation circuit and excludes the extractive metallurgy at a metal refinery. The comminution circuit's operational performance primarily depends on the mill's performance. Since grindcurves define the operational performance range of a mill, the grindcurves are used to define the setpoints for the economic controlled variables for optimal steady-state operation. For a given metal price, processing cost, and transportation cost, the proposed structure can be used to define the optimal operating region of a grinding mill circuit for the best economic return of the mineral processing plant. The plant-wide control structure identifies the controlled and manipulated variables to ensure the grinding mill circuit can be maintained at the desired operating condition. The plant-wide control framework specifies regulatory and supervisory control aims which can be achieved by means of non-linear model-based control. An impediment to implementing model-based control is the computational expense to solve the non-linear optimisation function. To resolve this issue, the reference-command tracking version of model predictive static programming (MPSP) is applied to a grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of Model Predictive Control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, is compared to the performance of a standard non-linear MPC (NMPC) technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and NMPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices, and using a closed form expression to update the control. The MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for on-line applications of the NMPC philosophy to real-world industrial process plants. The MPSP and NMPC simulation studies above assume full-state feedback. However, this is not always possible for industrial grinding mill circuits. Therefore, a non-linear observer model of a grinding mill is developed which distinguishes between the volumetric hold-up of water, solids, and the grinding media in the mill. Solids refer to all ore small enough to discharge through the end-discharge grate, and grinding media refers to the rocks and steel balls. The rocks are all ore too large to discharge from the mill. The observer model uses the accumulation rate of solids and the discharge rate as parameters. It is shown that with mill discharge flow-rate, discharge density, and volumetric hold-up measurements, the model states and parameters are linearly observable. Although instrumentation at the mill discharge is not yet included in industrial circuits because of space restrictions, this study motivates the benefits to be gained from including such instrumentation. An Extended Kalman Filter (EKF) is applied in simulation to estimate the model states and parameters from data generated by a grinding mill simulation model from literature. Results indicate that if sufficiently accurate measurements are available, especially at the discharge of the mill, it is possible to reliably estimate grinding media, solids and water hold-ups within the mill. Such an observer can be used as part of an advanced process control strategy. / 'n Generiese aanlegwye beheerstruktuur vir die optimale beheer van 'n maalmeulkring word voorgehou. 'n Ekonomiese doelwitfunksie is gedefinieer vir die maalmeulkringbaan met verwysing tot die ekonomiese doelwit van die groter mineraalverwerkingsaanleg. 'n Mineraalverwerkingsaanleg bestaan in hierdie studie slegs uit die vergruisings- en skeidingskringbane. Die ekstraktiewe metallurgie by die metaal raffinadery word uitgesluit. Die vergruisingskringbaan se operasionele werksverrigting is hoofsaaklik van die maalmeul se werksverrigting afhanklik. Aangesien maalkurwes die bereik van die maalmeul se werksverrigting beskryf, kan die maalkurwes gebruik word om die stelpunte van die ekonomiese beheerveranderlikes te definieer vir werking by optimale gestadigde toestand. Gegewe 'n bepaalde metaalprys, bedryfskoste, en vervoerkoste, kan die voorgestelde struktuur gebruik word om die optimale werksgebied vir die maalmeulkring te definieer vir die beste ekonomiese gewin van die algehele mineraalverwerkingsaanleg. Die aanlegwye beheerstruktuur omskryf die beheerveranderlikes en manipuleerbare veranderlikes wat benodig word om die maalmeulkring by die gewenste werksgebied te handhaaf. Die aanlegwye beheerstruktuur spesifiseer regulatoriese en toesighoudende beheer doelwitte. Hierdie doelwitte kan bereik word deur gebruik te maak van nie-lineêre model gebaseerde beheer. Die probleem is dat die bewerkingskoste om nie-lineëre optimeringsfunksies op te los 'n struikelblok is om model gebaseerde beheer op industriële aanlegte toe te pas. Ter oplossing hiervan, word die stelpunt-volg weergawe van model gebaseerde voorspellende statiese programmering (MVSP) toegepas op 'n maalmeulkringbaan. MVSP is 'n innoverende optimale beheertegniek, en bestaan uit 'n kombinasie van die filosofieë van model gebaseerder voorspellende beheer (MVB) en aanpassende dinamiese programmering. Die verrigting van die voorgestelde MVSP beheertegniek word vergelyk met die verrigting van 'n standaard nie-lineëre MVB (NMVB) tegniek deur beide beheertegnieke op dieselfde aanleg vir dieselfde toestande toe te pas. Resultate dui aan dat die MVSP beheertegniek in staat is om die gekose stelpunt te midde van model-aanleg wanaanpassing, steurnisse, en metingsgeraas te volg. Die verrigting van MVSP en NMVB vergelyk goed, maar MVSP bied duidelike voordele. Die bewerkingspoed vir MVSP word vinniger gemaak deur die dinamiese optimeringsprobleem in 'n laeorde statiese optimeringsprobleem te omskep, die sensitiwiteitsmatrikse rekursief uit te werk, en deur 'n geslote uitdrukking ter opdatering van die beheeraksie te gebruik. Die MVSP beheertegniek benodig normaalweg slegs 'n paar iterasies om tot 'n oplossing te konvergeer, selfs indien beperkings op die insette toegepas word. Om die rede word MVSP as 'n potensiële kandidaat beskou vir aanlyntoepasings van die NMVB filosofie op industriële aanlegte. Die MVSP en NMVB simulasie studies hierbo neem aan dat volle toestandterugvoer moontlik is. Hierdie is nie altyd moontlik vir industriële maalmeulkringbane nie. Om die rede is 'n nie-lineêre waarnemingsmodel van 'n maalmeul ontwikkel. Die model onderskei tussen die volumetriese hoeveelheid water, vaste stowwe, en maalmedia in die meul. Vaste stowwe verwys na alle erts wat klein genoeg is om deur die uitskeidingsif aan die ontslagpunt van die meul te vloei. Maalmedia verwys na rotse en staalballe in die meul, met rotse wat te groot is om deur die uitskeidingsif te vloei. Die waarnemingsmodel maak gebruik van die ontslaantempo en die opeenhopingstempo van vaste stowwe as parameters. Indien die meul se ontslagvloeitempo, ontslagdigtheid, en totale volumetriese aanhouding gemeet word, is alle toestande en parameters van die waarnemingsmodel lineêr waarneembaar. Alhoewel instrumentasie by die meul se ontslagpunt as gevolg van ruimte beperkings nog nie op industriële aanlegte ingesluit word nie, dui hierdie studie die voordele aan wat verkrygbaar is deur sulke instrumentasie in te sluit. 'n Verlengde Kalman Filter (VKF) word in simulasie gebruik om die model se toestande en parameters af te skat. 'n Bestaande maalmeul simulasie model vanuit die literatuur word gebruik om die nodige data vir die VKF te genereer. Resultate dui aan dat indien die metings akkuraat genoeg is, veral by die ontslagpunt van die meul, betroubare afskattings van die volumetriese hoeveelheid maalmedia, vaste stowwe, en water in die meul gemaak kan word. So 'n afskatter kan vorentoe gebruik word as deel van 'n gevorderde prosesbeheer strategie. / Thesis (PhD)--University of Pretoria, 2016. / Electrical, Electronic and Computer Engineering / PhD / Unrestricted

The motivation of this research is to propose innovative nonlinear and optimal control design algorithms, which can be used in real life. The algorithms need to be computationally efficient, should deal with control constraints and should operate under state feedback. To show the efficacy of algorithms, automatic therapy for different cancer problems is chosen to be the field of application. In this thesis, first an advanced control design technique called ’optimal dynamic in-version’ has been successfully experimented with control constraints. The proposed approach has subsequently been shown to be quite effective in proposing automatic drug delivery schemes with simultaneous application of chemo and immunotherapy drugs for complete elimination of cancer cells in melanoma (a skin cancer) as well as glioma (a brain cancer). As per the current practice, the amount of drug dosages are generally given based on some apriori statistical study with a very small sample size, which in reality may either also lead to drug toxicity (due to excessive drug) or may become ineffective (due to insufficient drug) for a particular patient. Subject to the fidelity of the mathematical model (which has been taken from published literature), it has been shown in this thesis that nonlinear control theory can be used for computation of drug dosages, which can then be used in a feedback strategy, thereby customizing the drug for the patient’s condition, to cure the disease successfully. Next, attention has been shifted to impulsive control of systems. Such impulsive con-trol systems appear in many other applications such as control of swings, control of spacecrafts and rockets using reaction control system, radiotherapy in cancer treatment and so on. Two impulsive control design philosophies are proposed in this thesis. In one approach, recently proposed model predictive static programming (MPSP) has been extended for impulsive control systems and has been named as impulsive-MPSP (I-MPSP). In other approach, another recent development, namely the Pseudospectral method has been utilized to consider both the magnitude of the control impulses as well as the time instants at which they are applied as the decision variables. It can be noted, that to the best of the knowledge of the author, the time instants of control application, being considered as decision variables is being proposed for the first time in the nonlinear and optimal control framework. Both I-MPSP and Pseudospectral methods are computationally quite efficient and hence can be used for feedback control (I-MPSP happens to be computationally more efficient than the Pseudospectral method). Applicability of the proposed extensions have been shown by solving various benchmark problems such as (i) a scalar linear problem, (ii) Van der Pol’s oscillator problem and (iii) an inverted pendulum problem. Finally the applicability of the proposed I-MPSP strategy has been shown by solving challenging problems such as radiotherapy treatment of head and neck and adenocarcimona cancers. Radio-therapy model is considered with oxygen effect, in which radiosensitivity parameters are considered in different forms. Head and neck cancer is considered with constant radiosensitivity parameters and adenocarcinoma is considered with constant, linear, quadratic and saturation model of radiosensitivity parameters. Note that toxicity constraints on normal tissue, which are nonlinear control constraints, are also successfully incorporated in this control design.

A new suboptimal guidance law design approach for aerospace vehicles is proposed in this thesis, followed by an advanced control design for supersonic air-breathing engines. The guidance law is designed using the newly developed Generalized Model Predictive Static Programming (G-MPSP), which is based on the continuous time nonlinear optimal control framework. The key feature of this technique is one-time backward propagation of a small-dimensional weighting matrix dynamics, which is used to update the entire control history. This key feature, as well as the fact that it leads to a static optimization problem, lead to its computational efficiency. It has also been shown that the existing model predictive static programming (MPSP), which is based on the discrete time framework, is a special case of G-MPSP. The G-MPSP technique is further extended to incorporate ‘input inequality constraints’ in a limited sense using the penalty function philosophy. Next, this technique has been developed also further in a ‘flexible final time’ framework to converge rapidly to meet very stringent final conditions with limited number of iterations. Using the G-MPSP technique in a flexible final time and input inequality constrained formulation, a suboptimal guidance law for a solid motor propelled carrier launch vehicle is successfully designed for a hypersonic mission. This guidance law assures very stringent final conditions at the injection point at the end of the guidance phase for successful beginning of the hypersonic vehicle operation. It also ensures that the angle of attack and structural load bounds are not violated throughout the trajectory. A second-order autopilot has been incorporated in the simulation studies to mimic the effect of the inner-loops on the guidance performance. Simulation studies with perturbations in the thrust-time behaviour, drag coefficient and mass demonstrate that the proposed guidance can meet the stringent requirements of the hypersonic mission. The G-MPSP technique in a fixed final time and input inequality constrained formulation has also been used for optimal guidance of an aerospace vehicle propelled by supersonic air-breathing engine, where the resulting thrust can be manipulated by managing the fuel flow and nozzle area (which is not possible in solid motors). However, operation of supersonic air-breathing engines is quite complex as the thrust produced by the engine is a result of very complex nonlinear combustion dynamics inside the engine. Hence, to generate the desired thrust, accounting for a fairly detailed engine model, a dynamic inversion based nonlinear state feedback control design has been carried out. The objective of this controller is to ensure that the engine dynamically produces the thrust that tracks the commanded value of thrust generated from the guidance loop as closely as possible by regulating the fuel flow rate. Simultaneously, by manipulating throat area of the nozzle, it also manages the shock wave location in the intake for maximum pressure recovery with sufficient margin for robustness. To filter out the sensor and process noises and to estimate the states for making the control design operate based on output feedback, an extended Kalman filter (EKF) based state estimation design has also been carried out and the controller has been made to operate based on estimated states. Moreover, independent control designs have also been carried out for the actuators so that their response can be faster. In addition, this control design becomes more challenging to satisfy the imposed practical constraints like fuel-air ratio and peak combustion temperature limits. Simulation results clearly indicate that the proposed design is quite successful in assuring the desired performance of the air-breathing engine throughout the flight trajectory, i.e., both during the climb and cruise phases, while assuring adequate pressure margin for shock wave management.