Brian Roffel

Internal Model Control

Internal model control is also a linear multivariable control technique that makes use of a process model in order to compute the input moves that have to be made. Although the technique is not as popular as model predictive control, such as DMC, it is nevertheless useful for a short explanation. Also some difference with model predictive control will be pointed out.

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.

A structured modeling approach for dynamic hybrid fuzzy-first principles models

Hybrid fuzzy-first principles models can be attractive if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented with fuzzy submodels describing additional equations, such as mass transformation and transfer rates. In this paper, a structured approach for designing this type of model is presented. The modeling problem is reduced to several simpler problems, which are solved independently: hybrid model structure and subprocess determination, subprocess behavior estimation, identification and integration of the submodels to form the hybrid model. The hybrid model is interpretable and transparent. The approach is illustrated using data from a (simulated) fed-batch bioreactor.

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.

Combining prior knowledge with data driven modeling of a batch distillation column including start-up

This paper presents the development of a simple model which describes the product quality and production over time of an experimental batch distillation column, including start-up. The model structure is based on a simple physical framework, which is augmented with fuzzy logic. This provides a way to use prior knowledge about the dynamics, which have a general validity, while additional information about the specific column behavior is derived from measured process data. The model framework is applicable for a wide range of columns operating under a certain control policy. The model framework for the particular column under study makes a priori assumptions about the specific behavior superfluous. In addition, a detailed description of the internal dynamics is not required, which reduces modeling effort. Three different hybrid model structures are compared; the model that uses the available sources of information most effectively can be used to simulate production including part of the start-up by applying constant quality control.

A new identification method for fuzzy linear models of nonlinear dynamic systems

The most promising methods for identifying a fuzzy model are data clustering, cluster merging and subsequent projection of the clusters on the input variable space. This article proposes to modify this procedure by adding a cluster rotation step, and a method for the direct calculation of the consequence parameters of the fuzzy linear model. These two additional steps make the model identification procedure more accurate and limits the loss of information during the identification procedure. The proposed method has been tested on a nonlinear first order model and a nonlinear model of a bioreactor and results are very promising.

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.

Fuzzy clustering, genetic algorithms and neuro-fuzzy methods compared for hybrid fuzzy-first principles modeling

Hybrid fuzzy-first principles models can be a good alternative if a complete physical model is difficult to derive. These hybrid models consist of a framework of dynamic mass and energy balances, supplemented by fuzzy submodels describing additional equations, such as mass transformation and transfer rates. Identification of these fuzzy submodels is one of the main issues in constructing hybrid models. In this paper, a new approach to constructing hybrid fuzzy-first principles models is presented, which uses a Kalman filter for parameter estimation. In addition, a comparison between three classes of identification techniques for fuzzy submodels is presented: fuzzy clustering, genetic algorithms and neuro-fuzzy methods. The comparison is illustrated for a penicillin fed batch-reactor test case. Fuzzy clustering proved to be the most suitable technique, with genetic algorithms being a good alternative.