Bernardus H.L. Betlem

First principles dynamic modeling and multivariable control of a cryogenic distillation process

In order to investigate the feasibility of constrained multivariable control of a heat-integrated cryogenic distillation process, a rigorous first principles dynamic model was developed and tested against a limited number of experiments. It was found that the process variables showed a large amount of interaction, which is responsible for the difficulties with the presently used, PID-based, control scheme, especially in load-following situations, which are common in air separation plants such as for instance integrated coal gasification combined cycle plants. Contrary to what is suggested in the literature, it was found that vapor hold-up in low-temperature, high-pressure columns does not play a significant role in the process dynamics. Despite large throughput changes and non-linear process behavior, multivariable model predictive control using a linearized model for average operating conditions, could work well provided all process flows have sufficient range. Due to the strong interactive nature of the process variables, process changes have to be made slowly, since otherwise manipulated variables easily saturate and process output targets cannot be maintained.

Advanced practical process control

1 Introduction to Advanced Process Control Concepts.- 1.1 Process Time Constant.- 1.2 Domain Transformations.- 1.3 Laplace Transformation.- 1.4 Discrete Approximations.- 1.5 z-Transforms.- 1.6 Advanced and Modified z-Transforms.- 1.7 Common Elements in Control.- 1.8 The Smith Predictor.- 1.9 Feed-forward Control.- 1.10 Feed-forward Control in a Smith Predictor.- 1.11 Dahlins Control Algorithm.- References.- 2 Process Simulation.- 2.1 Simulation using Matlab Simulink.- 2.2 Simulation of Feed-forward Control.- 2.3 Control Simulation of a 2x2 System.- 2.4 Simulation of Dahlins Control Algorithm.- 3 Process Modeling and Identification.- 3.1 Model Applications.- 3.2 Types of Models.- 3.2.1 White Box and Black Box Models.- 3.2.2 Linear and Non-linear Models.- 3.2.3 Static and Dynamic Models.- 3.2.4 Distributed and Lumped Parameter Models.- 3.2.5 Continuous and Discrete Models.- 3.3 Empirical (linear) Dynamic Models.- 3.4 Model Structure Considerations.- 3.4.1 Parametric Models.- 3.4.2 Non-parametric Models.- 3.5 Model Identification.- 3.5.1 Introduction.- 3.5.2 Identification of Parametric Models.- 3.5.3 Identification of Non-parametric Models.- References.- 4 Identification Examples.- 4.1 SISO Furnace Parametric Model Identification.- 4.2 MISO Parametric Model Identification.- 4.3 MISO Non-parametric Identification of a Non-integrating Process.- 4.4 MIMO Identification of an Integrating and Non-integrating Process.- 4.5 Design of Plant Experiments.- 4.5.1 Nature of Input Sequence.- 4.5.2 PRBS Type Input.- 4.5.3 Step Type Input.- 4.5.4 Type of Experiment.- 4.6 Data File Layout.- 4.7 Conversion of Model Structures.- 4.8 Example and Comparison of Open and Closed Loop Identification.- References.- 5 Linear Multivariable Control.- 5.1 Interaction in Multivariable Systems.- 5.1.1 The Relative Gain Array.- 5.1.2 Properties of the Relative Gain Array.- 5.1.3 Some Examples.- 5.1.4 The Dynamic Relative Gain Array.- 5.2 Dynamic Matrix Control.- 5.2.1 Introduction.- 5.2.2 Basic DMC Formulation.- 5.2.3 One Step DMC.- 5.2.4 Prediction Equation and Unmeasurable Disturbance Estimation.- 5.2.5 Restriction of Excessive Moves.- 5.2.6 Expansion of DMC to Multivariable Problems.- 5.2.7 Equal Concern Errors.- 5.2.8 Constraint Handling.- 5.2.9 Constraint Formulation.- 5.3 Properties of Commercial MPC Packages.- References.- 6 Multivariable Optimal Constraint Control Algorithm.- 6.1 General Overview.- 6.2 Model Formulation for Systems with Dead Time.- 6.3 Model Formulation for Multivariable Processes.- 6.4 Model Formulation for Multivariable Processes with Time Delays.- 6.5 Model Formulation in Case of a Limited Control Horizon.- 6.6 Mocca Control Formulation.- 6.7 Non-linear Transformations.- 6.8 Practical Implementation Guidelines.- 6.9 Case Study.- 6.10 Control of a Fluidized Catalytic Cracker.- 6.11 Examples of Case Studies in MATLAB.- 6.12 Control of Integrating Processes.- 6.13 Lab Exercises.- 6.14 Use of MCPC for Constrained Multivariable Control.- References.- 7 Internal Model Control.- 7.1 Introduction.- 7.2 Factorization of Multiple Delays.- 7.3 Filter Design.- 7.4 Feed-forward IMC.- 7.5 Example of Controller Design.- 7.6 LQ Optimal Inverse Design.- References.- 8 Nonlinear Multivariable Control.- 8.1 Non-linear Model Predictive Control.- 8.2 Non-linear Quadratic DMC.- 8.3 Generic Model Control.- 8.3.1 Basic Algorithm.- 8.3.2 Examples of the GMC Algorithm.- 8.3.3 The Differential Geometry Concept.- 8.4 Problem Description.- 8.4.1 Model Representation.- 8.4.2 Process Constraints.- 8.4.3 Control Objectives.- 8.5 GMC Application to the CSTR System.- 8.5.1 Relative Degree of the CSTR System.- 8.5 2 Cascade Control Algorithm.- 8.6 Discussion of the GMC Algorithm.- 8.7 Simulation of Reactor Control.- 8.8 One Step Reference Trajectory Control.- 8.9 Predictive Horizon Reference Trajectory Control.- References.- 9 Optimization of Process Operation.- 9.1 Introduction to Real-time Optimization.- 9.1.1 Optimization and its Benefits.- 9.1.2 Hierarchy of Optimization.- 9.1.3 Issues to be Addressed in Optimization.- 9.1.4 Degrees of Freedom Selection for Optimization.- 9.1.5 Procedure for Solving Optimization Problems.- 9.1.6 Problems in Optimization.- 9.2 Model Building.- 9.2.1 Phases in Model Development.- 9.2.2 Fitting Functions to Empirical Data.- 9.2.3 The Least Squares Method.- 9.3 The Objective Function.- 9.3.1 Function Extrema.- 9.3.2 Conditions for an Extremum.- 9.4 Unconstrained Functions: one Dimensional Problems.- 9.4.1 Newtons Method.- 9.4.2 Quasi-Newton Method.- 9.4.3 Polynomial Approximation.- 9.5 Unconstrained Multivariable Optimization.- 9.5.1 Introduction.- 9.5.2 Newtons Method.- 9.6 Linear Programming.- 9.6.1 Example.- 9.6.2 Degeneracies.- 9.6.3 The Simplex Method.- 9.6.4 The Revised Simplex Method.- 9.6.5 Sensitivity Analysis.- 9.7 Non-linear Programming.- 9.7.1 The Lagrange Multiplier Method.- 9.7.2 Other Techniques.- 9.7.3 Hints for Increasing the Effectiveness of NLP Solutions.- References.- 10 Optimization Examples.- 10.1 AMPL: a Multi-purpose Optimizer.- 10.1.1 Example of an Optimization Problem.- 10.1.2 AMPL Formulation of the Problem.- 10.1.3 General Structure of an AMPL Model.- 10.1.4 General AMPL Rules.- 10.1.5 Detailed Review of the Transportation Example.- 10.2 Optimization Examples.- 10.2.1 Optimization of a Separation Train.- 10.2.2 A Simple Blending Problem.- 10.2.3 A Simple Alkylation Reactor Optimization.- 10.2.4 Gasoline Blending.- 10.2.5 Optimization of a Thermal Cracker.- 10.2.6 Steam Net Optimization.- 10.2.7 Turbogenerator Optimization.- 10.2.8 Alkylation Plant Optimization.- References.- 11 Integration of Control and Optimization.- 11.1 Introduction.- 11.2 Description of the Desalination Plant.- 11.3 Production Maximization of Desalination Plant.- 11.4 Linear Model Predictive Control of Desalination Plant.- 11.5 Reactor problem definition.- 11.6 Multivariable Non-linear Control of the Reactor.- References.- Appendix I. MCPC software guide.- I.1 Installation.- I.2 Model identification.- I.2.1 General process information.- I.2.2 Identification data.- I.2.3 Output details.- I.3 Controller design.- I.4 Control simulation.- I.5 Dealing with constraints.- I.6 Saving a project.- Appendix II. Comparison of control strategies for a hollow shaft reactor.- II.1 Introduction.- II.2 Model Equations.- II.3 Proportional Integral Control.- II.4 Linear Multivariable Control.- II.5 Non-linear Multivariable Control.- References.

Optimal batch distillation control based on specific measures

Two independent measures characterise a single batch distillation run: the degree of separation difficulty, which indicates the difficulty at the start and the degree of exhaustion, which indicates bottom exhaustion at the end of the run. If one of both measures remains within bounds, then constant quality control appears to be the best control policy. It has been proven in the literature that the application of slop recycling increases the production rate. One of the goals of this study is to derive simple scheduling models based on specific measures for the optimal operation of batch distillation with slop recycling. Simulation studies for a cyclic pseudo-steady state operation over a broad range of degrees of difficulty for binary and ternary distillations are performed. Also the influence of the tray hold-up has been studied. All simulations show that at maximum production rate the degree of separation difficulty balances the degree of exhaustion (dependent variable in the optimum). The slop recycling strategy keeps the degree of exhaustion during the production phase and the degree of difficulty during the slop phase within bounds. As a result, the improvement of slop recycling at constant quality control compared to constant reflux control is 15–20% for difficult separation and can amount to more than 35% for relatively easy separations. The resulting production time appears to have a linear relation with the average separation difficulty. This relation has been experimentally verified.

Optimal mode of operation for biomass production

The rate of biomass production is optimised for a predefined feed exhaustion using the residue ratio as a degree of freedom. Three modes of operation are considered: continuous, repeated batch, and repeated fed-batch operation. By means of the Production Curve, the transition points of the optimal modes of operation are derived. The analytical expressions of these transitions for variable bioreaction kinetic parameters are determined. The key measures “degree of difficulty of conversion” and “degree of exhaustion” are introduced to define the optimal modes in more general terms. The “degree of difficulty” describes the effect of the kinetic parameters and the feed substrate concentration on the conversion; the “degree of exhaustion” describes the desired final condition. In fed-batch operation, the proposed constant feed policy approximates the optimal feed policy closely.

Multiple nonlinear parameter estimation using PI feedback control

Green ceramic formulations comprising a polyisobutylene binder are suitable for tape casting and can be effectively removed during thermal processing in reducing atmospheres. The binder may be removed in substantially dry reducing atmosphere. The tapes may be used for forming ceramic substrates and metallized ceramics such as those used in electronic packaging.

A comparison of the performance of profile position and composition estimators for quality control in binary distillation

In this study a number of control strategies have been developed for control of the overhead composition of a binary distillation column. The nonlinear wave model as presented in the literature, has been substantially modified in order to express it in variables that can easily be measured and make it more robust to feed flow and feed composition changes. The new model consists essentially of the equation for wave propagation and a static mass and energy balance across the top section of the column. Taylor series developments are used to relate the temperature on the measurement tray to the temperature and concentration on the tray where the inflection point of the concentration profile is located. The model has been incorporated in control of the overhead quality of a toluene/o-xylene benchmark column. In addition, a number of partial least squares (PLS) estimators have been developed: a nonlinear estimator for inferring the overhead composition from temperature measurements and a linear and nonlinear estimator for inferring the inflection point of the concentration profile in the column. These estimators are also used in a cascade control strategy and compared with use of the wave propagation model. Finally a control strategy consisting of a simple temperature controller and a composition controller were implemented on the simulated column. The study shows that the inferential control using PLS estimators performs equally well than control using the nonlinear wave model. In all cases the advantage of using inferential controllers is substantial compared with using single tray temperature control or composition control.

Influence of tray hydraulics on tray column dynamics

To column control, in contrast to column design, tray hold-up and dependencies of tray hold-up on the operating conditions play an important role. The essence of this article is the development of an improved model of tray hydraulics over a broad operating range and its experimental validation by means of batch distillation. First, the column dynamics are related to tray column design parameters and operating conditions. The model parameters are fitted by column residence time measurements. Two tray load regimes are distinguished: an aeration regime and an obstruction regime. At low column load a vapour increase will decrease the tray mass since the liquid is driven out by larger aeration. At high load the opposite is the case, since the liquid is driven up by stowage. The resulting dynamic behaviour is studied by linearising the rigorous tray model in an operating point. Especially the influence of the vapour flow on the column dynamics is investigated. For the influence of the tray composition change on the molar mass, a new composition-shift parameter κ is defined. The influence appeared to be small.

Batch distillation column low-order models for quality program control

For batch distillation, the dynamic composition behaviour can be described by the dominant time constant and the bottom exhaustion. Its magnitude is determined by the change of the composition distribution and is maximal when the inflection point of the molar fraction profile is located in the middle of the column. Then, the tray interactions are minimal. The distribution change during the batch run strongly depends on the applied control strategy. Under constant quality control, the dominant time constant proved to be nearly constant whereas under constant reflux control the dominant time constant can vary by more than a factor of four. To calculate the dominant time constant from static design calculations, two different methods are discussed: the retention time and the “change of inventory” time method. These methods are experimentally verified.

Optimal operation of rapid pressure swing adsorption with slop recycling

Rapid pressure swing adsorption (RPSA) is a cyclic process operating, basically, in three phases: a pressurization, a delay, and a depressurization phase. A new, modified operation is suggested by the addition of either a raffinate recycle phase or an extract recycle phase, during which raffinate respectively extract is returned to the feed tank. This feasibility study focuses on design based on the optimal process operation. The degree of difficulty of separation is used as an independent variable to indicate under what condition slop recycle is useful. Slop recycle proves to increase the recovery and in some case the productivity. The addition of a raffinate recycle phase is only profitable for difficult separations, when the composition profile is inclined towards a concave shape. The addition of an extract recycle is nearly always profitable as during the depressurization phase over some period the product fraction in the exhaust exceeds the fraction in the feed. For high degrees of difficulty the improvement in the recovery is over 100%, and for easy separations this is still about 40%. All simulations are carried out for a hypothetical binary mixture, a product purity of 90%, a cyclic stationary state, and optimized switching times.

Estimation of the Polymerization Rate of Liquid Propylene Using Adiabatic Reaction Calorimetry and Reaction Dilatometry

The use of pressure-drop and constant-pressure dilatometry for obtaining rate data for liquid propylene polymerization in filled batch reactors was examined. The first method uses reaction temperature and pressure as well as the compressibility of the reactor contents to calculate the polymerization rate; in the second, the polymerization rate is calculated from the monomer feed rate to the reactor. Estimated polymerization rates compare well to those obtained using the well-developed isoperibolic calorimetry technique, besides pressure-drop dilatometry provides more kinetic information during the initial stages of the polymerization than the other methods.