Gorazd Karer

Hybrid fuzzy model-based predictive control of temperature in a batch reactor

Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model was made. We established that the latter approach clearly outperforms the approach where a linear model is used.

Feedforward control of a class of hybrid systems using an inverse model

Abstract: In this paper we describe the design of a control algorithm for MISO systems, which can be modelled as hybrid fuzzy models. Hybrid fuzzy models present a convenient approach to modelling nonlinear hybrid systems. We discuss the formulation of a hybrid fuzzy model, its structure and the identification procedure. This is followed by a derivation of the inverse model and its implementation in the control algorithm. The control scheme we are discussing splits the control algorithm in two parts: the feedforward part and the feedback part. In the paper, we deal with the feedforward part of the control algorithm, which is based on an inverse of a hybrid fuzzy model. Next, a batch-reactor process is introduced. The modelling of the batch reactor is tackled and the results of the simulation experiments using the proposed control algorithm are presented. The experiments involved controlling the temperature of a batch reactor using two on/off input valves and a continuous mixing valve. The main advantage of the proposed approach is that the feedforward part of the control algorithm can bring the system close to the desired adjusted feasible trajectory, which avoids the need for a very complex feedback part of the algorithm. Therefore, the control algorithm presents a low computational burden, particularly comparing to the standard model predictive control algorithms. These usually require a considerable computational effort, which often thwarts their implementation on real industrial systems. Nevertheless, we show that using the proposed control approach the hybrid fuzzy model framework presents a convenient option for modelling complex systems for control purposes in practice.

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.

Predictive Approaches to Control of Complex Systems

A predictive control algorithm uses a model of the controlled system to predict the system behavior for various input scenarios and determines the most appropriate inputs accordingly. Predictive controllers are suitable for a wide range of systems; therefore, their advantages are especially evident when dealing with relatively complex systems, such as nonlinear, constrained, hybrid, multivariate systems etc. However, designing a predictive control strategy for a complex system is generally a difficult task, because all relevant dynamical phenomena have to be considered. Establishing a suitable model of the system is an essential part of predictive control design. Classic modeling and identification approaches based on linear-systems theory are generally inappropriate for complex systems; hence, models that are able to appropriately consider complex dynamical properties have to be employed in a predictive control algorithm. This book first introduces some modeling frameworks, which can encompass the most frequently encountered complex dynamical phenomena and are practically applicable in the proposed predictive control approaches. Furthermore, unsupervised learning methods that can be used for complex-system identification are treated. Finally, several useful predictive control algorithms for complex systems are proposed and their particular advantages and drawbacks are discussed. The presented modeling, identification and control approaches are complemented by illustrative examples. The book is aimed towards researches and postgraduate students interested in modeling, identification and control, as well as towards control engineers needing practically usable advanced control methods for complex systems.

Theoretical and fuzzy modelling of a pharmaceutical batch reactor

This paper deals with the development of a batch-reactor model with a theoretical and a locally affine fuzzy model. The batch reactor is used in the pharmaceutical industry for the production of drugs, where a rapid and precise temperature control is necessary. The model has to be built to include all the main features necessary for the purposes of modelling. The development of the model for the reactor is designed for further control development and simulation purposes, without doing any further experiments on the real process. In our case we use the model for simulating the reactors jacket temperature and the reactors core temperature. The theoretical model describes all the nonlinearities of the process of heating and cooling the content of the batch reactor. The main contribution of the theoretical model is in the modelling of the heat transfer between the reactors jacket and the reactors core, mainly caused by the change in the overall heat transfer, which also covers the main nonlinearity. Because of the complexity of the theoretical model a locally affine fuzzy model is also developed.

Predictive Control of Temperature in a Batch Reactor with Discrete Inputs

The paper deals with model predictive control (MPC) of systems with discrete inputs based on reachability analysis. The basic algorithm is - due to its MPC nature - suitable for controlling a wide spectrum of systems, provided that they have discrete inputs only, therefore its advantages are especially evident when dealing with relatively complex systems. The tree of evolution used by the algorithm is tackled, cost function selection is discussed and a universal cost function form is proposed. Computational complexity of the control method is treated thoroughly and an approach for reducing it by holding the inputs through a number of time steps is presented. Usability of the algorithm is verified on a batch reactor simulation example. The basic approach and the approach with holding the inputs through a number of time steps are compared. The results suggest that the latter can significantly improve control, especially when dealing with stiff systems such as the batch reactor

Fuzzy model xml formulation for production dynamics analysis and control

Abstract The paper introduces an XML schema complying with PMML standard suitable for a general fuzzy model formulation. It also presents a graphical user interface that is a part of a tool for analysis and control of production dynamics, which was developed at the Competence Center for Advanced Control Technologies. The interface is used for eFuMo model identification, validation and simple conversion from an eFuMo model to a standardized XML message and vice versa. The conversion can be carried out via a DOM object, which enables manipulation of XML structure in Matlab, or directly. The XML files that comply with the PMML standard provide a way for applications to describe and exchange models produced by data-mining and machine-learning algorithms. The goal of the presented work is to provide a platform for including fuzzy models into the PMML framework and thus stimulate interoperability of various applications that take advantage of fuzzy models, e.g. in production dynamics analysis and control, as well as in other implementations.

Piecewise Affine and Equivalent Models

There are several model formulations suitable for predictive control of hybrid systems to be found in the literature. However, most of the development in this field has been based on piecewise affine - PWA [18] and equivalent models.

Introduction to Predictive Control of Complex Systems

One of the advanced control approaches that has been relatively well established in industrial practice is predictive control [8, 22]. Initially, predictive control has mainly been used in petrochemical industry. However, it has recently been gaining ground in other industrial sectors as well.

Self-adaptive Predictive Control with an Online Local-Linear-Model Identification

In this chapter we describe a self-adaptive predictive control method for systems with time-varying dynamical characteristics, which is based on an online identification of the model of the system we want to control [8, 1, 13, 14].