Coleman Brosilow

Nonlinear model predictive control of styrene polymerization at unstable operating points

Abstract Model predictive control and coordinated control strategies are combined to accomplish the control of a simulated, nonlinear, open-loop unstable process. The process is the free radical solution polymerization of styrene in a continuous-stirred tank reactor (CSTR). The controls are the flowrate of cooling water supplied to the CSTR jacket and the flowrate of styrene monomer to the reactor. A model predictive control algorithm uses a process model to estimate unmeasured disturbances and to compute the control effort(s) required to suppress disturbances and force the process to follow a desired response trajectory toward the set point. A coordinated controller uses multiple controls to force the controlled process variable to follow the desired trajectory. In the case of the styrene reactor, the cooling water flow is selected as the primary control effort while the monomer flow is the secondary control effort. If the cooling water can maintain the desired process variable trajectory, the monomer flow remains at its nominal level (which is normally set by the operator). Otherwise, the monomer flow changes in order to assist the cooling water in maintaining the desired reactor temperature trajectory. In this way secure control is maintained even for large disturbances to the reactor. The extension of the model predictive control algorithm to incorporate a coordinated control strategy is straighforward. Further, the ap algorithm to a fourth-order, nonlinear, unstable process presents no special difficulties. The control effects are computed using a single-step algorithm with a time horizon of either one or two sampling time(s). This algorithm chooses the control so that the model output exactly tracks the desired model output at the next time horizon. Time horizons greater than one sampling time have been used previously to stabilize the algorithm when it is applied to high-order, stable, linear process models. A time horizon of two is necessary to stabilize the cooling water flow for the unstable, fourth-order styrene reactor. A time horizon of one sampling time yields a stable controller for the monomer flow. The control effort calculations use a Newtons algorithm to solve separately for each control effort (first cooling water and then monomer flow). The performance of the model predictive, coordinated control algorithm applied to the styrene reactor is illustrated for both perfect and imperfect models. Model prediction errors that actually arise from modeling errors are assumed to be due to changes in the unmeasured initiator level in the reactor. By adjusting the initiator level, stable control and exact tracking of the set point at steady state are accomplished in spite of significant modeling errors.

Paper: Inferential control applications

In high-order, long-dead-time processes, inferential control systems will generally outperform conventional feedback control systems. To implement inferential control the user must know how to •-tune the inferential controller on line, •-avoid control degradation due to saturation of the control effort, •-smooth manual-automatic switching, •-design a cascade control system. In addition, the user should be able to determine whether the benefits of inferential control justify its selection over a PID control system. This report presents ways to meet these requirements and applies the methods to an industrial autoclave plant and to a laboratory heat exchange system.

Internal model predictive control (IMPC)

A computationally simple model predictive control algorithm incorporates the attractive features of the internal model control (IMC) law. The algorithm first computes the IMC control effort via a model state feedback implementation that automatically compensates for past control effort saturation. Before applying the calculated control, the algorithm checks to see if this control effort, when applied over a single sampling interval and followed by a control effort at the opposite limit (relative to its steady-state level), will cause the model output to exceed its desired trajectory. If not, the calculated control is applied. Otherwise the control is reduced appropriately. Application of the new algorithm to a variety of linear single-input single-output systems shows a smooth, rapid response, without significant overshoot. Comparisons with a QDMC algorithm, tuned to give the same unconstrained behavior as the IMC system and the best possible constrained performance, favor the IMPC system. Application of the new algorithm to a simple multivariable problem drawn from web control in film manufacturing demonstrates the flexibility of the algorithm in dealing with control effort saturation in multivariable systems.

Nonlinear Model-Based Control of Nonminimum-Phase Processes

This paper reviews the properties of model-state feedback and input/output linearizing state feedback for the synthesis of nonlinear controllers. These concepts are extended to nonminimum-phase systems, where a synthetic output, which is statically equivalent to the actual process output, is used to design the model-state feedback controller. Systematic procedures are outlined for the construction of the synthetic output and the assignment of local zeros. The proposed controller is illustrated with a nonminimum-phase van de Vusse reactor through simulations.

Simulation of large scale dynamic systems—I. Modular integration methods

Abstract Modular simulation of dynamic systems offers the possibility of computational speed through parallel processing of individual subsystems and through the use of the best integration algorithms for each subsystem. Such simulation needs coordination algorithms to keep the various subsystems in time synchronization and to compute the interconnections between the subsystems. A mathematical description of the coordination problem leads to the development of several new algorithms. These new algorithms are shown to have desirable convergence and stability properties. In particular a new Newton type algorithm is A-stable in a sense similar to that defined for ordinary integration algorithms. Numerical tests with several small example problems and with the simulation of the dynamics of an atmospheric crude unit consisting of 5 interacting columns are used to evaluate the various coordination algorithms. The crude unit simulation was carried out using a prototype modular simulator for distillation systems. The simulator description and the results of applying it to a crude unit are given in Part II. Scope —A formal mathematical definition of the problem of simulating the dynamics of large integrated systems using independent simulations of its subsystems (the coordination problem) yields a framework in which to analyse the behavior of modular integration methods. Analysis shows that most common existing technique, constant extrapolation, has several practical and theoretical defects which are overcome with new Newton type methods. Several examples illustrate and amplify theoretical results. Significance —The modular integration methods presented in this work provide viable alternatives to simulating large systems by integrating a single huge set of equations. They offer the possibility of simulating the dynamics of very large scale process systems using parallel (micro) processors.

Multivariable Model State Feedback

Abstract A Model State Feedback (MSF) implementation of IMC controllers for multivariable processes is developed. Model State Feedback uses a linear combination of past and present process model states to form the IMC control efforts. Implementing the IMC control in model state feedback form compensates for past control effort saturation, which can lead to significant performance degradation in lead -lag IMC control implementations. Another potential source of performance degradation is the distortion of the control vector which occurs when components of the control vector are truncated due to control effort saturation. Saturation induced directionality problems are avoided by temporarily increasing filter time constants to bring the control vector into the constraint set. The required computations are straight forward because control efforts are available as explicit functions of filter constants. A defect of MSF implementations is that they can exhibit limit cycles, or large overshoots, for very small filter constants. A simple method for estimating the minimum filter time constants which do not lead to poor performance for SISO systems is presented. The method is an extension of that developed by Campo and Morari(1990).

Incorporating process uncertainty and analytic design of PID controllers into undergraduate process control

Unique features of the undergraduate process control course described in this article are that 1 an internal model control framework is used to develop PID controller design methodologies for very general processes, 2 process uncertainty is incorporated into the design methodology using MATLAB-based software that we call IMCTUNE, and 3 all exams are open book, open notes, and open computer.

Simulation of large scale dynamic systems—II. A modulator simulator for the dynamics of distillation systems

Abstract A modular dynamic simulator has been developed to simulate the dynamics of interacting distillation columns. The dynamic simulator consists of a Fortran software package with dynamic modules to simulate distillation columns, reboilers, condensers and control systems. The modules can be modified to simulate special reboilers, condensers and control systems. User input to the simulator consists of the system description, constants, physical property data and an optional initial state. Two example problems have been used to test the simulator: (1) A 5 component, 29 stage distillation column with controllers, and (2) An atmospheric crude unit with 4 side strippers. Each of the side strippers and the main column are simulated independently. Steady-state conditions for the crude unit are computed by following a policy which approximates crude unit start-up procedures. We illustrate the type of results obtainable from the simulator by presenting several dynamic responses of the crude unit to step disturbances. Scope —We describe a modular simulator for distillation systems built around the coordinator concept described and analyzed in Part I. Simulation of 2 substantial problems, a 29 stage distillation column, and crude unit, demonstrate the methodology. Significance —The simulator and worked examples demonstrate the validity of reducing a complex simulation to an interconnection of independent simulations tied together by a coordinator. The advent of parallel processing should enable simulation of the dynamics of extremely large, and heretofore intractable, systems using the modular approach.

Knowledge verification in expert systems combining declarative and procedural representations

Abstract We present an algorithm to verify the consistency and completeness of an object-oriented structured knowledge base of an expert system which combines procedures with a declarative representation using if-then rules. The algorithm has three stages. The first stage of the algorithm converts the procedures into rules which are added to the existing rules to produce the equivalent rule set . The second stage of the algorithm partitions the equivalent rule set into decision subtables by regrouping rules with similar conditions in their if part or similar actions in their then part. In the third stage, each subtable is checked for consistency by looking for redundant rules and potentially or strictly conflicting rules. Completeness is verified by looking for unreferenced attribute values and missing rules. The algorithm is designed to automatically check any modification to the knowledge base as the system is being developed or updated. We demonstrate the algorithm on examples from process control.

A new algorithm for dynamic simulation

Abstract Chemical engineering systems such as separation columns and reactors are described by mixed differential (e.g., mass and energy balances) and algebraic (e.g., thermodynamic relationships) equations. Existing solution methods solve such equations by sequentially satisfying first the differential equations and then the algebraic equations. Such methods have been shown to lack robustness when solving large complex problems like the dynamics of crude units. This paper describes a Newton-like Runge Kutta algorithm for simultaneous solution of mixed differential-algebraic equations such that original form of the algebraic constraints are well satisfied. The proposed algorithm is applied to a single stage flash unit for distillation. Simulation experiments demonstrate the robustness and effectiveness of the algorithm.