Yaman Arkun

A nonlinear DMC algorithm and its application to a semibatch polymerization reactor

Abstract In this paper a new nonlinear model-predictive control method is developed and applied to a semibatch polymerization reactor. The proposed control algorithm uses an explicit nonlinear process model and the basic elements of the classical dynamic matrix control (DMC). update of the DMC model by a disturbance vector which accounts for the effect of nonlinearities in the prediction horizon is the key feature of the method.

Study of the control-relevant properties of backpropagation neural network models of nonlinear dynamical systems

Abstract Neural networks have been used for important applications in chemical engineering. Such applications include: fault detection in process control systems, modeling of nonlinear dynamics, control of nonlinear systems, solution of nonlinear programming problems and others. Most of the articles published on the subject consider neural networks to be “black boxes” and concentrate on the applications. After introducing the basic principles of neural networks, we will concentrate on studying control-relevant properties of neural network models of nonlinear systems. In particular, we study the stability of these models as well as the stability of the models inverse. This provides a background with which to study the neural network-based control algorithms proposed in the literature.

Nonlinear identification and control of a high-purity distillation column: a case study

Abstract Identification and control of ill-conditioned, interactive and highly nonlinear processes pose a challenging problem to the process industry. In the absence of a reasonably accurate model, these processes are fairly difficult to control. Using a high-purity distillation column as an example, model identification and control issues are addressed in this paper. The structure of the identified models is that of the polynomial type nonlinear autoregressive models with exogenous inputs (NARX). While most of the work in this area has concentrated on linear models (one-time scale and two-time scale models), this work is aimed at identifying the inherent nonlinearities. Comparisons are drawn between the identified models based on statistical criteria (AIC etc.) and other validation tests. Simulation results are provided to demonstrate the closed-loop performance of the nonlinear ARX models in the control of the distillation column. The controller employed is based on a nonlinear model predictive scheme with state and parameter estimation.

A methodology for sequential design of robust decentralized control systems

A general analysis theory is presented which can incorporate robust performance defined in ¿ framework for sequential design purposes. As a result, a systematic methodology for sequential design of robust decentralized controllers is proposed. To do so, new formulations of linear fractional transformation of complementary sensitivity function and sensitivity function are given. They are used to derive robustness constraints on individual decentralized controllers. When these robustness constraints are satisfied, the closed-loop system is guranteed to possess robust performance if and only if the whole system is nominally stable as well.

Control configuration design applied to the Tennessee Eastman plant-wide control problem

Abstract When a plant-wide control structure is being designed, there are often more measurements and manipulations than are required. Therefore the designer must judiciously select a subset of them that will be used for feedback control. If the control structure is to be decentralized, a set of pairings between the selected measurements and manipulations must also be established. This subset of process variables and their feedback interconnections has been termed the control configuration, and must be decided prior to the design of the controller. However the number of possible control configurations is usually very high, and the complexity of the controller depends upon the control configuration chosen. This paper presents a systematic way to design the control configuration so as to reduce controller complexity, and yet meet control objectives in the presence of uncertainty This method, called control configuration design, is then applied to a plant-wide control problem posed by Tennessee Eastman

A general method to calculate input-output gains and the relative gain array for integrating processes

Abstract A general method based on singular value decomposition and state-space models is presented to calculate a set of gains between inputs and outputs of processes with integrators. The practical importance of these gains for determining input- output sensitivities and asymptotic properties is illustrated along with the calculation of the relative gain array for integrating systems. The new results are particularly applicable to large chemical processes and can be easily incorporated into flowsheet simulators.

A global solution to the nonlinear model predictive control algorithms using polynomial ARX models

In nonlinear model predictive control algorithms, a nonlinear objective function is minimized on-line at every sampling time. Finding a global optimum is not very easy as the objective function is generally nonlinear and nonconvex. In this paper we show that the structure of the polynomial ARX models lends model predictive algorithms some useful properties that are helpful in determining the global optimum solution. The approach used is based on transformation and change of variables to recast the problem into a convex objective function with convex constraints. A method is then proposed that guarantees a global solution to the optimization problem.

A multiobjective approach to design chemical plants with robust dynamic operability characteristics

Abstract In chemical plants, operability problems arise mainly due to poor process designs, inaccurate models and/or the control system designs that are unable to cope with process uncertainties. In this paper, a process design methodology is presented that addresses the issue of improving dynamic operability in the present of process uncertainty through appropriate design modifications. The multiobjective nature of the design problem is carefully exploited in the subsequent formulations and a nonlinear programming approach is taken for the simultaneous treatment of both steady-state and dynamic constraints. Scope—Today, a chemical engineer faces the challenge of designing chemical plants that can operate safely, smoothly and profitably within a dynamic process environment. For a typical chemical plant, major contributions to such an environment originate from external disturbances such as variations in the feedstock quality, different product specifications and/or internal disturbances like catalyst poisoning and heat-exchanger fouling. To guarantee a flexible operation despite such upsets, traditionally, the procedure was either to oversize the equipment or to place large storage tanks between the processing units. Proposed design methods attempted to find optimal operating regimes for chemical plants while compensating for process uncertainty through empirical overdesign factors. Studies concerned with the interplay between the process design and operation aspects have appeared recently [1, 2] and focused on achieving better controllability upon modifying the plant design, without explicitly considering process uncertainty. Nevertheless, maintaining satisfactory dynamic operability in an environment of uncertainty remained as a pressing issue and the need was raised quite frequently for a rigorous treatment of the topic [3]. The development of new analytical tools [4, 5] made it possible to consider dynamic operability at the process design stage and modify the plant design accordingly. In this paper, a methodology is presented, that systematically guides the designer towards process designs with better dynamic operability and economics, The problem is formulated within a multiobjective optimization framework and makes extensive use of singular-value decomposition and nonlinear semi-infinite programming techniques. Conclusions and Significance—A multiobjective optimization problem is proposed for designing chemical processes with better dynamic operability characteristics. Robustness indices are used as the indicators of dynamic operability and placed as constraints within the optimization scheme. A semi-infinite nonlinear programming problem results due to the frequency-dependent nature of such constraints. A discretization procedure is suggested to handle the infinite number of constraints and an ellipsoid algorithm allows an interactive solution of the process design problem. A process consisting of three CSTRs is treated as an example, illustrating the potential of the methodology in solving design-related operability problems.

Nonlinear Predictive Control of a Semi Batch Polymerization Reactor by an Extended DMC

In this paper a new nonlinear model predictive control law is applied to a semi-batch polymerization reactor. The particular model used in this study is the free radical polymerization of polymethylmethacrylate. The principal nonlinearities are due to the reaction rates and the gel effect. Two cases are considered: jacket temperature controlling the reaction temperature, and a MIMO structure where both the reaction temperature and the molecular weight are controlled by the jacket temperature and the initiator feed. The proposed control algorithm uses an explicit nonlinear process model and some of the elements of the classical DMC to solve the nonlinear input-output operator equation without computing the derivatives of the states and output equations. Constraints are not included in the present method.

Model predictive control of plant transitions using a new identification technique for interpolating nonlinear models

Abstract This paper presents a model based controller design approach for plants that operate in several distinct operating regimes and make transitions between them. Often it is difficult to identify a single global model that describes plant behavior in all the regimes. In the present work we propose an identification method that builds linear models for the individual regimes, and then interpolates nonlinear models in between these local models to match plant dynamics during transitions. The identification technique is shown to work well with transition data which lack excitation. A model predictive controller based on the local and the transition models is then presented and applied to a reactor.