# Process control

## Fuzzy model based control

For the effective application of Takagi-Sugeno fuzzy models in model based control a control-related framework have been worked out. This framework is based on the following generating elements: Identification, Adaptation, Inversion, and Linearization. By means of these building blocks, inverse model based and model predictive (MPC) controllers were generated. Because of the learning capacity of the fuzzy model, the adaptive version of these solutions has been also worked out.

J. Abonyi, R. Babuska, F. Szeifert, Fuzzy modeling with multidimensional membership functions: constrained identification and control design, IEEE Systems, Man and Cybernetics, Part B, Oct, 2001

J. Abonyi, L. Nagy, F. Szeifert, Fuzzy model-based predictive control by instanteneous linearisation, Fuzzy Sets and Systems ,120(1), 109-122, 2001

J. Abonyi and R. Babuska, M. Ayala Botto, F. Szeifert, L. Nagy, Identification and control of nonlinear systems using fuzzy Hammerstein models, Industrial and Engineering Chemistry Research, 39, 4302-4314, 2000

J. Abonyi, A. Bódizs, L. Nagy, F. Szeifert, Hybrid fuzzy convolution model and its application in model predictive control, Chemical Engineering Research and Design, 78(A), 597-604, 2000

J. Abonyi, T. Chován, L. Nagy, F. Szeifert, Hybrid convolution model and its application in predictive pH control, Computers and Chemical Engineering, S221-S224, 1999

J. Abonyi, L. Nagy, F. Szeifert, Adaptive fuzzy inference system and its application in modelling and model based control, Chemical Engineering Research and Design, 77, A, 281-290, 1999

J. Abonyi, Á. Bódizs, L. Nagy, F. Szeifert, Predictor corrector controller using Wiener fuzzy convolution model, Hungarian Journal of Industrial Chemistry, 27(3), 227-233, 1999

J. Abonyi, H. C. Andersen, L. Nagy, F. Szeifert, Inverse fuzzy process model based direct adaptive control, Mathematics and Computers in Simulation, 51 (1-2), 119-132, 1999

## Tendency model-based improvement of the slave loop in cascade temperature control of batch process units

In the fine chemical industry, the batch or fed-batch reactor functions as the heart of the transformation process. Due to the complexity of chemical synthesis, the control of these reactors remains a problem of temperature control commonly performed indirectly via the jacket of the reactor. This results in a cascade control scheme based on the control a secondary, more responsive process that influences the main process. This control loop is often referred to as the slave loop of the process. This paper highlights that the slave process of batch process units, i.e. the jacket of the reactor, can have more complex dynamics than the master loop has; and very often this could be the reason for the non-satisfying control performance. Since the slave process is determined by the mechanical construction of the unit, the above mentioned problem can be effectively handled by a model-based controller designed using an appropriate nonlinear tendency model. The presented analysis shows that the complex dynamics of the slave process can be decomposed into static nonlinear and dynamic linear parts. This decomposition is beneficial since it allows the effective incorporation of the resulted tendency model into nonlinear model-based control algorithms. Real-time control results show that the proposed methodology gives superior control performance over the widely applied cascade PID-PID control scheme.

J. Madár, F. Szeifert, L. Nagy, T. Chován, J. Abonyi, Tendency model-based improvement of the slave loop in cascade temperature control of batch process units, Computers and Chemical Engineering 28 737–744, 2004

## Direct and indirect adaptive control

## (Controller Output Error Method)

This research studies inverse fuzzy-model-based controllers to compensate non-linear terms that affect the system dynamics. The controller is based on an inverse semi-linguistic fuzzy process model, identified and adapted via input-matching technique. This entails generating two control signals; the first control signal is applied to the plant and the second is inferred from the plant’s response to the first control signal. The controller output error is the difference between these two control signals and is used by the algorithm to adapt the controller.

For the adaptation of the fuzzy model a general learning rule has been developed employing gradient-descent algorithm. The on-line learning ability of the fuzzy model allows the controller to be used in applications, where the knowledge to control the process does not exist or the process is subject to changes in its dynamic characteristics.

J. Abonyi, H. C. Andersen, L. Nagy, F. Szeifert, Inverse fuzzy process model based direct adaptive control, Mathematics and Computers in Simulation, 51 (1-2), 119-132, 1999, IF 0.281

J. Abonyi, L. Nagy, F. Szeifert, Adaptive fuzzy inference system and its application in modelling and model based control, Chemical Engineering Research and Design, 77, A, 281-290, 1999, IF 0.686

## Model predictive control of a continuous vacuum crystalliser in an industrial environment: A feasibility study

Crystallisers are essentially multivariable systems with high interaction amongst the process variables. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to their coordinated approach.

In the absence of a real continuous crystalliser, a detailed momentum-model was applied using the process simulator in Simulink.

This process has been controlled by a model predictive controller widely used in industry. A new framework has been worked out for the incorporation of the Honeywell Profit. Suite controller to the simulator of the crystalliser. The engineering model and the controller were connected via OPC (OLE-Object Linking and Embedding for Process Control standard). Models were developed in Profit. Suite using the new fully-automated identification method. The feasibility study illustrated that the applied identification tool gave an accurate and robust model, and that the non-linear crystalliser may be controlled and optimised very well with the Honeywell Profit. Suite package. The developed system is proven to be useful in research and development.

N. Moldoványi, J. Abonyi, Model predictive control of a continuous vacuum crystalliser in an industrial environment: A feasibility study, Chem. Biochem. Eng. Q. 23 (2) 195-205 (2009)

## Fuzzy supervisory control

In industrial applications of adaptive controllers, standard algorithms have to be combined with heuristically derived safety nets. These safety nets are often realised in expert systems. The aim of this research is to develop an intelligent supervision system, where the heuristic knowledge is represented by fuzzy rules. The aim of the application of fuzzy techniques on the supervisory level is to design an easily interpretable and transparent algorithm that allows the incorporation of control specifications and a priori knowledge of the operators by using linguistic terms.

J. Abonyi, R. Babuska, F. Szeifert, Fuzzy expert system for supervision in adaptive control, IFAC Proceedings of Artificial Intelligence in Real-Time Control, PERGAMON Press, 2001

## Effective optimization for fuzzy model predictive control

This work addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, time-consuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For long-range predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a high-purity distillation column.

S. Mollov, R. Babuska, J. Abonyi, Henk B. Verbruggen, Effective optimization for fuzzy model predictive control, IEEE Transactions on fuzzy systems 12: pp. 661-675. (2004)

## Feedback linearizing control using hybrid neural networks identified by sensitivity approach

Globally linearizing control (GLC) is a control algorithm capable of using nonlinear process model directly. In GLC, mostly, first-principle models derived from dynamic mass, energy and momentum balances are used. When the process is not perfectly known, the unknown parts of the first principles model should be represented by black-box models, e.g. by neural networks. This paper is devoted to the identification and application of such hybrid models for GLC. It is shown that the first principles part of the model determines the dominant structure of the controller, while the black-box elements of the hybrid model are used as state and/or disturbance estimators. For the identification of the neural network elements of the hybrid model a sensitivity approach based algorithm has been developed. The underlying framework is illustrated by the temperature control of a continuous stirred tank reactor where a neural network is used to model the heat released by an exothermic chemical reaction.

J. Madar, J. Abonyi., F. Szeifert, Feedback linearizing control using hybrid neural networks identified by sensitivity approach, Engineering applications of artificial intelligence 18:(3) pp. 343-351. (2005)