**Intelligent Proportional Differential Neural Network Control for**

** Unknown Nonlinear System**

**Haoping WANG ^{1}, Shanzhi LI^{1}, Yang TIAN^{1,*}, Abdel AITOUCHE^{2}**

^{1 }Automation School,

Sino-French International Joint Laboratory of Automatic Control and Signal Processing (LaFCAS),

Nanjing University of Science& Technology (NUST),

Nanjing 210094, China

^{* }*Corresponding author*

^{2 }CRIStAL UMR CNRS 9189,

Hautes etudes d’ingenieur HEI-Lille,

Lille,59046, France

tianyang@njust.edu.cn

**Abstract: **This paper presents an intelligent proportion-differential neural network (iPDNN) controller for unknown nonlinear systems. This controller is based on the intelligent proportion integration differentiation (iPID) controller. In an iPID controller system, a unknown nonlinear SISO system is regarded as an ultra-local two-order or one-order model and a lumped unknown dynamics (LUD) disturbance which contains the high-term and parametric uncertainties by the differential algebra and estimation method online. However, its performance of an iPID control depends on the precision and rapidity for estimating the LUD disturbance. Besides, it also influences the parameter in the ultra-local model. In order to compensate the estimation error of LUD disturbance, we put forward an extra radial basis function (RBF) neural network observer to estimate it. This extra observer cannot only ensure to acquire the estimation error rapidly, but also has an ability of self-learning. In addition, this iPDNN method can ensure the closed-loop system stability under the Lyapunov stability theory. Finally, in order to demonstrate its performance, an inverted pendulum plant has been applied and the results indicate this method is of efficiency.

**Keywords:** adaptive control; mode- free control; PID.

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**CITE THIS PAPER AS**:

Haoping WANG, Shanzhi LI, Yang TIAN*, Abdel AITOUCHE, **Intelligent Proportional Differential Neural Network Control for Unknown Nonlinear System**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 25(4), pp. 445-452, 2016.

**Introduction**

As a classical algorithm, adaptive control has been applied in many types of industrial systems including nonlinear and time-vary systems and also attracts many scholars’ attentions. Because of the advantage of self-adaptation, adaptive controller can tolerate the uncertainties and external disturbances in closed-loop system [7, 11, 19, 21]. In the adaptive control system, a common method for dealing with uncertainties including the parameters or structure is to design an adaptive parameter estimates algorithm or an auxiliary controller [3, 4, 14]. A nonlinear system is difficult to use a mathematical equation for modelling because of the lack of knowledge of plant or disturbances [9, 10].

As for the issues, many research results have been put forward for applying a range of different perspectives. Their methods can be classified into two types according to the approximation form. The first type is called a direct approximation method such as model reference adaptive control (MRAC) [1, 15], which is used as a reference model to obtain the disturbance immediately. In this type of system, by comparing with the nominal model or reference model, the disturbance can be acquired directly. The other type used an indirect method [2, 8, 26]. In this type of system, it requires knowing about the information of structure and some parameters. Its performance depends on the model parameters.

Recently, as a new type of adaptive control, model-free control and its corresponding intelligent proportion integration differentiation (iPID) controller which has been applied successfully to the real-time systems, such as DC-DC converters [17], vehicle control [16], agricultural greenhouses [13], High pressure common rail injection system [22] etc., was firstly introduced in the references [5]. It requires only the systems input gain, and the output measurements. The critical issue for this kind model free control is resided on how to obtain and compensate rapidly the lumped unknown dynamics (LUD) which it covers the high-order term, uncertain parameters, external and or internal perturbations. Reference [17] puts forward an algebraic identification technique to estimate the LUD. In reference [20], a Savitzky-Golay filter is proposed to obtain the LUD for a servo system. However, these methods regard the gain of input as a known constant and ignore its parameter-vary. In addition, its performance depends on the quality of the observer which requires the ability of rapidity and reliability. Moreover, these methods cannot guarantee the stability in closed-looped system [12, 16].

Considering these factors, an extra sliding model control is adopted into the model free control for compensating the estimation error of LUD [18]. However, the gain of input is also neglected, which stems from the ultra-local model. Thus in this paper, a radial basis function neural network is introduced to make up for the estimation error of the LUD. The referred neural network has an ability of universal approximation and been applied to a nonlinear system for estimation LUD. Combining the advantage of neural network, the novel model-free control strategy which is called as an intelligent Proportion Differential Neural Network (iPDNN) controller ensures not only the stability, but also has a high efficiency for trajectory tracking performance.

The paper is organized as follows. In section 2, the problem of a classical model free control is introduced. In section 3, an improved model free iPDNN control is proposed while in section 4, to validate the proposed method, an inverted pendulum numerical system is implemented. Finally, some conclusion remarks are given in section 5.

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