Daniel R. Lewin

A generalized method for HEN synthesis using stochastic optimization — II.: The synthesis of cost-optimal networks

Abstract This paper presents a generalized method for the synthesis of heat-exchanger networks (HENs) based on genetic algorithms (GAs). This approach is a modification of the algorithm presented in the first part of this paper, which was limited to MILP formulations. Since the aim of this study is to obtain a family of cost-optimum HENs in which stream splitting is supported, both the objective function and the constraints are non-linear. An automated procedure is used to formulate a constrained non-linear optimization model, whose solution provides a measure of the fitness of each candidate HEN generated by the GA. A novel algorithm is proposed for the solution of the NLP, which exploits the observation that optimal designs usually involve relatively few stream splits, and that the NLP constraints are linear in the heat duties. The NLP is solved using a cascaded algorithm involving an upper-level non-linear optimization of the stream split flows, and a lower-level pseudo-linear optimization of the heat exchanger duties. The performance of the proposed approach is demonstrated using several medium-scale case studies, and the obtained solutions are compared with those available in literature.

A generalized method for HEN synthesis using stochastic optimization – I. General framework and MER optimal synthesis

Abstract This paper presents a novel approach for the synthesis of heat-exchanger networks (HENs) based on genetic algorithms (GAs). The use of the algorithm is demonstrated on the solution of relatively simple HEN synthesis problems in which maximum energy recovery (MER) is desired and which can be resolved without resorting to stream splitting. As a result, the parametric optimization problem is an LP. The problem is solved in two parts: (a) the structure of the HEN is determined by GAs, and (b) the heat loads of units are fixed by the Simplex algorithm to meet MER which is used by the GAs to rate fitness. A physically meaningful HEN structure representation is proposed which can be both effectively manipulated by genetic operators and is also appropriate for parametric optimization by the Simplex algorithm. The approach is demonstrated on several case studies, and the obtained solutions are compared with those which have appeared in the literature. The second part of this paper uses essentially the same framework to tackle the general HEN synthesis problem in which an arbitrarily non-linear objective function can be optimized, and in which the constraints can also be non-linear.

Brief Identification and control of open-loop unstable processes by relay methods

This paper describes a reliable automatic PID tuning method for open-loop unstable processes. Identification with low order models is performed by means of two relay tests, one with an additional delay, which does not require a priori knowledge about the process, with the only necessary condition being that the process be gain stabilisable. This paper provides an overview of the method, states conditions that need to be satisfied for its successful implementation, and demonstrates its application on a number of examples.

Automated Nonlinear Model Predictive Control using Genetic Programming

Abstract This paper describes the use of genetic programming (GP) to generate an empirical dynamic model of a process, and its use in a nonlinear, model predictive control (NMPC) strategy. GP derives both a model structure and its parameter values in such a way that the process trajectory is predicted accurately. Consequently, the performance of the NMPC strategy is expected to improve on the performance obtained using linear models. The GP approach and the nonlinear MPC strategy are described, and demonstrated by simulation on two multivariable process: a mixing tank, which involves only moderate nonlinearities, and the more complex Karr liquid–liquid extraction column.

Modeling, simulation and control of liquid-liquid extraction columns

A model describing the hydrodynamics and mass transfer of countercurrent liquid-liquid extraction columns is developed and solved. The hydrodynamic model assumes that the dispersed-phase drops behave as spheres of uniform diameter. The model has been found to be qualitatively in agreement with experimental results published in the literature. It is shown that conventional dispersion interface level control using the continuous-phase effluent flow rate as the manipulated variable causes unavoidable overshoots and oscillations in the mean holdup and outlet concentrations, while an alternative scheme using the continuous-phase feed flow rate leads to a significant improvement in the dynamic response. A model-based decentralized MIMO control scheme is designed and tested by simulation, and is shown to provide excellent servo and regulatory performance.

Modeling and temperature control of rapid thermal processing

In the past few years, rapid thermal processing (RTP) has gained acceptance as mainstream technology for semiconductor manufacturing. This single wafer approach allows for faster wafer processing and better control of process parameters on the wafer. However, as feature sizes become smaller, and wafer uniformity demands become more stringent, there is an increased demand from rapid thermal (RT) equipment manufacturers to improve control, uniformity and repeatability of processes on wafers. In RT processes, the main control problem is that of temperature regulation, which is complicated due to the high non-linearity of the heating process, process parameters that often change significantly during and between the processing of each wafer, and difficulties in measuring temperature and edge effects. This paper summarizes work carried out in cooperation with Steag CVD Systems, in which algorithms for steady state and dynamic temperature uniformity were developed. The steady-state algorithm involves the reverse engineering of the required power distribution, given a history of past distributions and the resulting temperature profile. The algorithm for dynamic temperature uniformity involves the development of a first-principles model of the RTP chamber and wafer, its calibration using experimental data, and the use of the model to develop a controller.

Control of an Unstable Batch Chemical Reactor

Abstract As often experienced in industrial practice, a fixed-parameter PID can do a good job, even for potentially challenging problems such as open-loop unstable processes. However in such cases, considerable a priori process knowledge may be required in order to adequately tune the controller and make the control performance robust to changes in operating conditions. Adaptive schemes, on the other hand, require less prior plant information but they should not be regarded as magic solutions to control problems. In this study, alternative adaptive control schemes are presented for the temperature control of an open-loop unstable batch chemical reactor in which the sequential exothermic reactions A→B→C are carried out. The performance of such control systems are compared with that of a PID controller, designed using IMC-based rules, and detuned to ensure robustness to process parameter changes along the temperature trajectory. Since the required detuning results in poor disturbance rejection, one would expect that the adoption of adaptive strategies should improve performance. However, the fact that a fixed-parameter PID controller can be designed to perform reasonably well does not imply that a self-tuning version will do at least as well. A self-tuning scheme combined with a parametric control approach can successfully deal with the reactor start-up and the regulatory problem, provided that the adaptive schemes process model order is adequately selected. Thus, a self-tuning PID controller, which is based on a second-order model, is liable to failure if the true process is effectively of higher order.

A simple tool for disturbance resiliency diagnosis and feedforward control design

The ease with which a vector of two or more disturbances can be rejected by a control system can be quantified using the Disturbance Cost (DC), which is simply the amount of feedback action required in order to completely eliminate the effect of disturbance on the process outputs. A graphical representation of this measure, limited to vectors of two disturbances, can be expressed as contours of DC values as a function of frequency and disturbance direction. A useful property of the DC is its independence from specific controller tuning, and as such it is an appropriate screening tool for use at the preliminary process design stage. It is a useful tool for such applications as the investigation of control strucure resilience to disturbances, for selecting from alternative feedback control structures, and to facilitate the design of feedforward control systems.

New product design via analysis of historical databases

Abstract A methodology is presented to define a set of operating conditions to produce a desired product, given a database of historical operating conditions and the product quality that they produced. This approach relies on the generation of a reliable model that can be used to predict the quality variables (the Y block) from the decision variables (the X block). Genetic programming (GP) is used to automatically generate accurate nonlinear models relating latent vectors for the X and Y blocks. The GP has the capability to carry out simultaneous optimization of model relationship structures and parameters, as well as to identify the most important basis functions. Once an adequate model is generated, it is used to predict the required process conditions to meet the new quality target by reverse mapping.

DYNAMIC CONTROLLABILITY AND RESILIENCY DIAGNOSIS USING STEADY STATE PROCESS FLOWSHEET DATA

A simple procedure for assessing the controllability and resiliency of a process flowsheet is presented. The approach relies on a simplified modeling strategy, whereby an approximate linear dynamic model of the process is derived from steady-state flowsheet information. The resulting linear approximation can then be tested using the wealth of available linear controllability and resiliency measures available. In this paper, the procedure is used to screen the disturbance resiliency of alternative heat-integrated distillation column schemes reported in the literature. The results confirm the conclusions obtained by others largely relying on closed-loop simulations using rigorous dynamic models. The overall approach appears to be very promising as a short-cut diagnostic and screening tool, which in theory could be integrated into commercial flowsheeting software.