A novel LSSVM-L Hammerstein model structure for system identification and nonlinear model predictive control of CSTR servo and regulatory control

A continuous stirred tank reactor (CSTR) servo and the regulatory control problem are challenging because of their highly non-linear nature, frequent changes in operating points, and frequent disturbances. System identification is one of the important steps in the CSTR model-based control design. In earlier work, a non-linear system model comprises a linear subsystem followed by static nonlinearities and represented with Laguerre filters followed by the LSSVM (least squares support vector machines). This model structure solves linear dynamics first and then associated nonlinearities. Unlike earlier works, the proposed LSSVM-L (least squares support vector machines and Laguerre filters) Hammerstein model structure solves the nonlinearities associated with the non-linear system first and then linear dynamics. Thus, the proposed Hammerstein’s model structure deals with the nonlinearities before affecting the entire system, decreasing the model complexity and providing a simple model structure. This new Hammerstein model is stable, precise, and simple to implement and provides the CSTR model with a good model fit%. Simulation studies illustrate the benefit and effectiveness of the proposed LSSVM-L Hammerstein model and its efficacy as a non-linear model predictive controller for the servo and regulatory control problem.

Block-oriented identification of non-linear systems with input time delay in presence of measurement noise: a Laguerre–neural network approach

This paper proposes an approach for identification of non-linear dynamic systems with input time delay into the block-oriented Wiener model in the presence of measurement noise. The model comprised a linear dynamic subsystem (LDS) at the input side that is cascaded with a non-linear static subsystem (NSS). The LDS comprised Laguerre filters, whereas the NSS is constructed using committee neural networks (CNNs). The Laguerre filter compensates for the input time delay, whereas the CNN finds an appropriate non-linear mapping between its input and output with the useful property of the measurement noise attenuation. The parameters of the Laguerre filters as well as those of the CNN are determined using offline training algorithms. In order to find the optimal values of the weights of the CNN, a noise analysis is conducted. The proposed method is applied to a simulated continuous-stirred tank reactor (CSTR) with input time delay and measurement noise. The results indicate substantial benefits of the proposed method compared with the similar methods proposed in the literature for system identification.

Reduced model of linear systems via Laguerre filters

In this paper, we propose a technique to reduce the complexity of an existing (initial) model via the Laguerre filters. We present an analytical method for the parameter identification of the Fourier coefficients of the Laguerre model. This technique is based on the bilinear discrete transformation and in which the Fourier coefficients are expressed in recurrent form in terms of the Laguerre pole. This latter is estimated by an iterative technique, based on the Newton algorithm. This identification technique is after extended to the case of the ARX-Laguerre model and the MISO-ARX-Laguerre model and its performances are illustrated by numerical simulations.

Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO) systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.