Balas Valentina Emilia - Innovations in Intelligent Machines-5 Computational Intelligence in Control Systems Engineering

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Valentina Emilia Balas , Petia Koprinkova-Hristova and Lakhmi C. Jain (eds.) Studies in Computational Intelligence Innovations in Intelligent Machines-5 2014 Computational Intelligence in Control Systems Engineering 10.1007/978-3-662-43370-6_1

Springer-Verlag Berlin Heidelberg 2014

1. Decentralized Fuzzy-Neural Identification and I-Term Adaptive Control of Distributed Parameter Bioprocess Plant

Ieroham Baruch 1

(1)

Department of Automatic Control, CINVESTAV-IPN, Ave. IPN No 2508, A.P. 14-470, 07360 Mexico, D.F., Mexico

Ieroham Baruch (Corresponding author)

Email:

Eloy Echeverria Saldierna

Email:

Abstract

The chapter proposed to use of a Recurrent Neural Network Model (RNNM) incorporated in a fuzzy-neural multi model for decentralized identification of an aerobic digestion process, carried out in a fixed bed and a recirculation tank anaerobic wastewater treatment system. The analytical model of the digestion bioprocess represented a distributed parameter system, which is reduced to a lumped system using the orthogonal collocation method, applied in four collocation points. The proposed decentralized RNNM consists of five independently working Recurrent Neural Networks (RNN), so to approximate the process dynamics in four different measurement points plus the recirculation tank. The RNN learning algorithm is the second order Levenberg-Marquardt one. The comparative graphical simulation results of the digestion wastewater treatment system approximation, obtained via decentralized RNN learning, exhibited a good convergence, and precise plant variables tracking. The identification results are used for I-term direct and indirect (sliding mode) control obtaining good results.

1.1 Introduction

In the last decade, the Computational Intelligence tools (CI), like Artificial Neural Networks (ANN), Fuzzy Systems (FS), and its hybrid neuro-fuzzy and fuzzy-neural systems, became universal means for many applications in identification, prediction and control. Because of their approximation and learning capabilities, the ANNs have been widely employed to dynamic process modeling and control, including biotechnological plants, []. For sake of clarity all abbreviations used in this chapter are summarized in a Table A.1 and given in Appendix 2.

1.2 Description of the RTNN Topology and Learning

This part described the RTNN topology and both the backpropagation first order learning and the Levenberg-Marquardt second order learning of this RTNN.

1.2.1 Description of the RTNN Topology and Its Real-Time BP Learning

Block-diagrams of the RTNN topology and its adjoint, are given on Figs..

Fig. 1.1

Block diagram of the RTNN model

Fig. 1.2

Block diagram of the adjoint RTNN model

Following Figs. ]. The RTNN topology and learning are described in vector-matrix form as:

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

(1.6)

(1.7)

(1.8)

(1.9)

(1.10)

(1.11)

(1.12)

(1.13)

where: X, Y, U are state, augmented output, and input vectors with dimensions N, (L + 1), (M + 1), respectively, where Z1 and U1 are the (N 1) output and (M 1) input of the hidden layer; the constant scalar threshold entries are Z2 = 1, U2 = 1, respectively; V is a (L 1) pre-synaptic activity of the output layer; T is the (L 1) plant output vector, considered as a RNN reference; A is (N N) block-diagonal weight matrix; B and C are [N (M + 1)] and [L (N + 1)]augmented weight matrices; B0 and C0 are (N 1) and (L 1) threshold weights of the hidden and output layers; F[], G[] are vector-valued tanh()-activation functions with corresponding dimensions; F[], G[] are the derivatives of these tanh() functions; W is a general weight, denoting each weight matrix (C, A, B) in the RTNN model, to be updated; W (C, A, B), is the weight correction of W; , are learning rate parameters; C is an weight correction of the learned matrix C; B is an weight correction of the learned matrix B; A is an weight correction of the learned matrix A; the diagonal of the matrix A is denoted by Vec() and Eq. ( ], is given.

Theorem of Stability of the RTNN

Let the RTNN with Jordan Canonical Structure is given by Eqs. () and the nonlinear plant model, is as follows :

where : {Yd (), Xd (), U()} are output, state and input variables with dimensions l, nd, m, respectively ; F(), G() are vector valued nonlinear functions with respective dimensions . Under the assumption of RTNN identifiability made, the application of the BP learning algorithm for A(), B(), C(), in general matricial form, described by Eqs. (), and the learning rates (k), (k) ( here they are considered as time-dependent and normalized with respect to the error ) are derived using the following Lyapunov function :

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