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

1. 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.

REFERENCES

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