Optimal state changeover control of a multivariable system using a minicomputer

A study of the application of the calculation and implementation of an open loop optimal changeover policy for a multivariable system on a minicomputer has been made. If the required changeover time and control time interval have been specified, a switching policy for the controls may be calculated using standard linear programming techniques. The multivariable system was an analog computer simulation of a liquid-liquid extraction column. By repeated use of the procedure with different overall changeover times, a “best” changeover policy could be determined. The criterion for this policy was a minimum changeover time with the restriction that the sum of squared errors between the required and actual final states was less than a specified small value. Practical as opposed to theoretical small values of this error criterion were used.     

Optimal operating policies for closed-loop recycling HPLC processes

In this paper, optimal operating policies for HPLC separation processes based on a closed-loop recycling strategy are presented. Successful application of closed-loop recycling HPLC processes had been reported, mainly in the pharmaceutical industry, but there is still limited knowledge about the dynamic behaviour of this process and little work on optimal operation of closed-loop recycling systems has been presented in the open literature. This paper investigates different operating policies for a closed-loop recycling HPLC system using an equilibrium-dispersive model coupled with a dynamic optimisation technique. The operating policies include: conventional recycling, recycling with peak shaving and recycling with peak shaving and multiple feed injection. The determination of optimal operating policies is aimed to maximise the amount of purified product(s) and thereby achieve better column performance whilst keeping the matrix cost constant. The practical implementation of these operating policies will also be considered.     

Integrated process design and control of divided-wall distillation columns using molecular tracking

This work explores the dynamic and control behavior of dividing wall distillation columns from two different steady-state design approaches (molecular tracking and optimization method) for three different mixtures. The controllability of the six design cases was evaluated using singular value decomposition and the closed-loop performance was evaluated using integral absolute error in Aspen Dynamics. The results demonstrate that the side-draw location obtained by molecular tracking (MT) provides optimal controllability. As a result, there is a slight advantage in control properties while obtaining designs by reducing the time to find the optimal solution through the MT method.     

Machine-learning-based construction of barrier functions and models for safe model predictive control

In this paper, we propose a control Lyapunov-barrier function-based model predictive control method utilizing a feed-forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed-forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed-loop stability while preventing the closed-loop states from entering unsafe regions in state-space under sample-and-hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state-space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.     

Optimization of compression ratio in closed-loop CO<Subscript>2</Subscript> liquefaction process

We suggest a systematic method for obtaining the optimal compression ratio in the multi-stage closed-loop compression process of carbon dioxide. Instead of adopting the compression ratio of 3 to 4 by convention, we propose a novel approach based on mathematical analysis and simulation. The mathematical analysis prescribes that the geometric mean is a better initial value than the existing empirical value in identifying the optimal compression ratio. In addition, the optimization problem considers the initial installation cost as well as the energy required for the operation. We find that it is best to use the fifth stage in the general closed-loop type carbon dioxide multi-stage compression process.     

Control strategies for complex chemical processes. Applications in polymerization processes

The proper implementation of advanced control schemes for complex chemical processes heavily rely on the availability of appropriate mathematical models. The main objective of this paper is to show through examples how process models can be inserted into advanced controllers to allow the successful control of the process when the controlled variables are not measured or are measured infrequently. The control strategies are illustrated with actual data obtained for two typical polymerization processes. In the first example, a control algorithm is designed and implemented experimentally for the simultaneous closed-loop control of composition and average molecular weight of a copolymer latex. In the second case, a control scheme is designed for the simultaneous control of polymer production, polymer composition and melting index (MI) in a solution ethylene Ziegler-Natta polymerization process.     

Constraint handling optimal PI control of open-loop unstable process: Analytical approach

This paper proposes the closed-form analytical design of proportional-integral (PI) controller parameters for the optimal control of an open-loop unstable first order process subject to operational constraints. The main idea of the design process is not only to minimize the control performance index, but also to cope with the constraints in the process variable, controller output, and its rate of change. To derive an analytical design formula, the constrained optimal control problem in the time domain was transformed to an unconstrained optimization in a parameter space associated with closed-loop dynamics. By taking advantage of the proposed analytical approach, a convenient shortcut algorithm was also provided for finding the optimal PI parameters quickly, based on the graphical analysis for the optimal solution of the corresponding optimization problem in the parameter space. The resulting optimal PI controller guarantees the globally optimal closed-loop response and handles the operational constraints precisely.     

Closed-loop step response identification of integrating and unstable processes

Motivated by the fact that integrating and unstable processes are usually operated in a closed-loop manner for safety and economic reasons, this paper proposes a systematic closed-loop identification method based on step response test to facilitate closed-loop system operation and on-line optimization. To avoid jeopardizing the closed-loop system stability of such a process, guidelines are given for proper implementation of a closed-loop step test for model identification. By introducing a damping factor to the closed-loop step response for realization of the Laplace transform in frequency domain, a frequency response estimation algorithm is developed in terms of the closed-loop control structure used for identification. Accordingly, three model identification algorithms are derived analytically in frequency domain to obtain the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT). To enhance fitting accuracy for a higher order process, in particular for a specified frequency range interested to control design and on-line tuning, a weighted least-squares fitting algorithm is also given based on the estimated process frequency response points. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms.     

Holographic recording in a photo-cross-linkable liquid crystalline copolymer using a 325-nm laser with various polarizations

Surface relief (SR) gratings with a molecularly oriented structure and pure polarization hologram were fabricated on a photo-cross-linkable liquid crystalline copolymer using a 325-nm laser with various two-beam polarization modes. For intensity holography, the polarization information from the two beams simultaneously provided the molecular motion and molecular reorientation; the SR height reached up to 186 nm and the concave area revealed a molecular reorientation when the exposing beams were linearly polarized. In contrast, SR formation was negligible for polarization holography when molecular reorientation due to the polarization modulation was observed. The resulting polarization gratings changed the polarization properties of the diffraction beams, and their diffraction efficiency was reached 24%, which agreed with theoretical expectations.     

Application of MHE to large-scale nonlinear processes with delayed lab measurements

The paper addresses nonlinear estimation problems on nonlinear processes containing several lab measurements sampled slowly and with long delay, which is the usual case in industrial polymerization applications. A moving horizon estimation algorithm is developed to compute the theoretical optimal solution given the multi-rate measurements. In this algorithm, the MHE window is recalculated as the new lab measurement becomes available. Simulation studies on a polymerization process with plant model mismatch are performed. Observability analysis and estimation results of MHE with and without lab measurements show that lab measurements help identify the disturbances and can improve the performance of both estimation and closed-loop control.     

Use of microelectronics to upgrade process control into production control

Process control in oil extraction and processing is traditionally done by independent control loops and logic (sequence) controls. In the best case, all controls are located in one central control room. The operator’s task is to draw the right conclusions from the process conditions signalled to him, to coordinate, to plan and to keep logsheets. On the basis of this information, he can coordinate between control loops and optimize unit operations. With the application of modern microelectronic-based control systems (integrated control systems), it is possible to present the operator’s information on a higher level (e.g., yield figures and energy consumptions computed from basic data), to do computerized planning operations and updatings, and to retrieve data which are used as an input for accounting systems and management information systems. Underlying principles, means for implementation, as well as benefits (both proven and potential) are described. The available hardware and software packages hardly form any limitations; on the contrary, we must often limit ourselves to optimal use of the available tools and not fall into the trap of “maximal automation.” Our aim is not to automate and control as much as possible, but to use automation as one of the means to process oilseeds and edible oils with the highest possible efficiency.     

Closed-loop optimal operation of batch distillation columns

Often, the main source of disturbance for a batch distillation system is an upset in the feed to the process. If the operation of a batch column is carried out on the basis of the nominal value of the feed composition, a high degree of uncertainty in the initial conditions to the batch may lead to run the column suboptimally, with a possibly large economic penalty. In this paper, a three-step strategy is proposed for the closed-loop implementation of optimal operating policies for batch rectifiers. First, the optimal reflux rate is calculated off-line for several feed compositions. Then, a correlation is developed off-line between the optimal reflux rate and the composition profile in the column at the end of the startup phase. Finally, the detection of the composition profile is performed on-line during the startup phase, so that the optimal reflux rate can be calculated and implemented in a closed-loop fashion. This allows operating the column optimally even though the actual feed composition is not known. Since the calculations to be performed on-line are straightforward, the computational demand is kept to a minimum. Results for binary and ternary systems indicate that, by using the proposed procedure, the column performance can be improved by as much as 30% with respect to a conventional open-loop optimal strategy.     

Decoupling internal model control for multivariable systems with multiple time delays

In this paper, the decoupling internal model control (IMC) with stability is investigated for multivariable stable processes with multiple time delays. All the stabilizing IMC controllers which solve this decoupling problem and the resulting closed-loop systems are characterized in terms of the open-loop system's time delays and non-minimum phase zeros. It shows that the inclusion of some time delays and non-minimum phase zeros might be necessary to make a decoupling solution realizable and stabilizing. Based on this characterization, a control design method for best achievable performance is presented. However, owing to the high complexity of the theoretical controller, a practical controller design procedure is developed with the help of the proposed model reduction algorithm. Examples are given to illustrate our analysis and design. Significant performance improvement over the existing multivariable Smith predictor control has been achieved with the proposed approach.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

To satisfy the diverse product quality specifications required by the broad range of polyolefin applications, polymerization plants are forced to operate under frequent grade transition policies. Commonly, the optimal solution to this problem is based on the minimization of a suitable objective function defined in terms of the changeover time, product quality specifications, process safety constraints and the amount of off-spec polymer, using dynamic optimization methods. However, considering the great impact that a given control structure configuration can have on the process operability and product quality optimization, the time optimal grade transition problem needs to be solved in parallel with the optimal selection of the closed-loop control pairings between the controlled and manipulated variables. In the present study, a mixed integer dynamic optimization approach is applied to a catalytic gas-phase ethylene-1-butene copolymerization fluidized bed reactor (FBR) to calculate both the “best” closed-loop control configuration and the time optimal grade transition policies. The gPROMS/gOPT computational tools for modelling and dynamic optimization, and the GAMS/CPLEX MILP solver are employed for the solution of the combined optimization problem. Simulation results are presented showing the significant quality and economic benefits that can be achieved through the application of the proposed integrated approach to the optimal grade transition problem for a gas-phase polyolefin FBR.     

ENHANCED IMC-PID CONTROLLER DESIGN WITH LEAD-LAG FILTER FOR UNSTABLE AND INTEGRATING PROCESSES WITH TIME DELAY

In this article, a design method for a PID controller is proposed based on IMC principles for control of open loop integrating and unstable first-order processes with time delay. The design is based on H₂ optimal closed-loop transfer function for set point changes and step input disturbances. The method has one tuning parameter, and systematic guidelines are provided for the selection of this tuning parameter based on peak value of the sensitivity function. The performance of the designed controller is verified on various integrating and unstable processes, and it is observed that nominal and robust control performance is achieved with the proposed design method. Improved closed-loop performance was obtained when compared to other methods recently reported in the literature. Further, the proposed method provides good closed-loop performance even when there are large uncertainties in the process parameters.     

Fractionation of a coal tar pitch by ultra-filtration, and characterization by size exclusion chromatography, UV-fluorescence and laser desorption-mass spectroscopy

Ultra-filtration (UF) provides a new way of generating narrow bands of sample in the fractionation of coal and petroleum-derived liquids. It allows larger quantities of high-mass fractions to be recovered, making more detailed investigations possible, through the use of techniques requiring larger amounts of sample. In this work, UF-separated fractions have been used to study molecular mass distributions of a coal tar pitch, used as laboratory standard. The pitch was fractionated by solvent solubility into three fractions. These were further fractionated by ultra-filtration, using membranes specific to protein molecular sizes classed as “1 kDa”, “5 kDa”, “10 kDa” and “100 kDa”. Planar chromatography was used as a tertiary fractionation method, to sub-divide the UF-fractions. The various fractions were examined by size exclusion chromatography (SEC), UV-fluorescence spectroscopy and laser desorption-mass spectrometry (LD-MS). There was good agreement between mass estimates based on SEC and LD-MS of the smaller UF-fractions, with evidence for the presence of material with molecular masses ranging between 800 and 10,000 u. Examining the largest UF fractions of the pitch-pyridine-insoluble sample also gave clear evidence for material with molecular masses above 10,000 u. Taken together, however, the LD-MS data showed progressively diminishing differences, as the sizes of the UF membranes, and the likely molecular masses of the sample fractions, increased. One likely explanation is incomplete sampling during the laser desorption procedure. The evidence suggests that the upper mass limit detectable for these and similar samples by LD-MS has been reached. Despite these reservations, LD-MS appears as the best method to date, for investigating the mass ranges of samples derived from coal tar pitch and heavy petroleum fractions.     

Control of pH processes based on the genetic algorithm

In this work, we propose a PID control strategy based on the genetic algorithm coupled with cubic spline interpolation method for the control of pH processes. The control scheme proposed in the present work consists of closed-loop identification based on the genetic algorithm and cubic spline method. First, we compute the parameters (K_C, Τ_I, Τ_D) of the PID controller using relay feedback and apply these parameters to control the pH Process. Then approximate linear models corresponding to each pH range are obtained by the closed-loop identification based on closed-loop operation data. The optimal parameters of the PID controller at each pH region are then computed by using the genetic algorithm. From numerical simulations and control experiments we could achieve better control performance compared to the conventional fixed gain PID control method. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

TDLAS检测系统的激光器驱动电路

针对温度变化对半导体激光器(LD)的输出激光波长及其工作稳定性的影响,提出运用热电制冷器TEC构成二级制冷系统,分别对激光器的外部和内部温度进行精准控制。采用闭环PID电路产生控制信号控制TEC的驱动电流和方向,从而达到制冷和加热的目的;为进一步实现对驱动信号的滤波,提出采用级联方式的LTC1064构成四阶滤波系统。测试结果表明:TEC温控系统取得了很好的温控效果,响应速度快,精度达到±0.01℃,滤波系统有效滤除了正弦波中的直流分量和高次谐波的干扰,满足激光器对温度和驱动信号的要求。