**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. https://doi.org/10.24846/v25i4y201605

**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**

- BOLOURCHI,, R. A. HESS,
**Nonlinear Model Reference Adaptive Control using Tap-delay Filters**, IEEE Transactions on Systems, Man and Cybernetics*,*vol. 22, no. 2, 1992, pp. 360-368. - BOULKROUNE,, M. M’SAAD, M. FARZA,
**Fuzzy Approximation-based Indirect Adaptive Controller for Multi-input Multi-output Non-affine Systems with Unknown Control Direction**, IET Control Theory & Applications*,*vol. 6, no. 17, 2012, pp. 2619-2629. - CHANG, Y., Z. JING, Z. LIU, S. HONGYE,
**Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance**, IEEE Transactions on Automatic Control*,*vol. 56, no. 7, 2011, pp. 1672-1678. - CHEN, L., L. YAN,
**Adaptive Dynamic Surface Control for Linear Multi-variable Systems**, Automatica*,*vol. 46, no. 10, 2010, pp. 1703-1711.

- FLIESS,, C. JOIN,
**Intelligent PID Controllers***.*6th Mediterranean Conference on Control and Automation, 2008, pp. 326-331. - FLIESS,, C. JOIN,
**Model-free Control**, International Journal of Control*,*vol. 86, no. 12, 2013, pp. 2228-2252. - HAO, J., P. A. IOANNOU,
**Robust Adaptive Control for a Class of MIMO Nonlinear Systems with Guaranteed Error Bounds**, IEEE Trans.on Automatic Control*,*vol. 48, no. 5, 2003, pp. 728-742. - HOJATI M., S. GAZOR,
**Hybrid Adaptive Fuzzy Identification and Control of Nonlinear Systems**, IEEE Trans. on Fuzzy Systems*,*10, no. 2, 2002, pp. 198-210. - HSU,-F.,
**Adaptive PI Hermite Neural Control for MIMO Uncertain Nonlinear Systems**, Applied Soft Computing*,*vol. 13, no. 5, 2013, pp. 2569-2576. - HSU, -F. C.-M. LIN, R.-G. YEH,
**Supervisory Adaptive Dynamic RBF-based Neural-fuzzy Control System Design for Unknown Nonlinear Systems**, Applied Soft Computing*,*vol. 13, no. 4, 2013, pp. 1620-1626. - HYEONGCHEOL L., M. TOMIZUKA,
**Robust Adaptive Control using a Universal Approximator for SISO Nonlinear Systems**, IEEE Trans. on Fuzzy Systems*,*8, no. 1, 2000, pp. 95-106. - JOIN,, F. CHAXEL, M. FLIESS,
**“Intelligent” Controllers on Cheap and Small Programmable Devices**, 2013 Conference on Control and Fault-Tolerant Systems, 2013, pp. 554-559. - LAFONT,, J.-F. BALMAT, N. PESSEL, M. FLIESS,
**A Model-free Control Strategy for an Experimental Greenhouse with an Application to Fault Accommodation**, Computers and Electronics in Agriculture*,*vol. 110, 2015, pp. 139-149. - LUNGU,, R. LUNGU, C. ROTARU,
**New Systems for Identification, Estimation and Adaptive Control of the Aircrafts Movement**, Studies in Informatics and Control*,*vol. 20, no. 3, 2011, pp. 273-284. - LUSU,, L. PARSA,
**Model Reference Adaptive Control of Five-Phase IPM Motors Based on Neural Network**, IEEE Transactions on Industrial Electronics*,*vol. 59, no. 3, 2012, pp. 1500-1508. - MENHOUR,, B. D’ANDRÉA-NOVEL, M. FLIESS, D. GRUYER, H. MOUNIER,
**A New Model-free Design for Vehicle Control and Its Validation through an Advanced Simulation Platform**, 14th European Control Conference (ECC), 2015, pp. 1-6. - MICHEL,, C. JOIN, M. FLIESS, P. SICARD, AND A. CHERITI,
**Model-free Control of****DC****/****DC****Converters***.*12th IEEE Workshop on Control and Modelling for Power Electronics (COMPEL), 2010, pp. 1-8. - PRECUP, E., RADAC, M. B., DRAGOS, C. A., PREITL, S., PETRIU, E. M.,
**Model-free Tuning Solution for Sliding Mode Control of Servo Systems***.*2014 8th Annual IEEE Systems Conference (SysCon), 2014, pp. 30-35. - SAN. S. G., J. WANG,
**Robust Adaptive Neural Control for a Class of Perturbed Strict Feedback Nonlinear Systems**, IEEE Transactions on Neural Networks*,*13, no. 6, 2002, pp. 1409-1419. - SCHAFER, R. W.,
**What is a Savitzky-Golay Filter?**, IEEE Signal Processing Magazine,*,*28(4), 2011, pp. 111-117. - VOJTESEK,, P. DOSTAL,
**Simulation of Adaptive LQ Control of Nonlinear Process**, Studies in Informatics and Control, vol. 21, no. 3, 2012, pp. 315-324. - WANG,, Y. TIAN, D. ZHENG,
**ESO-based iPI Common Rail Pressure Control of High Pressure Common Rail Injection System**, Studies in Informatics and Control*,*vol. 25(3), 2016, pp. 273-282. - YOUCEF, T., O. ITO,
**A Time Delay Controller for Systems With Unknown Dynamics**, Journal of Dynamic Systems, Measurement, and Control*,*vol. 112, no. 1, 1990, pp. 133-142. - YADMELLAT,, S. K. Y. NIKRAVESH,
**Stabilizing Unstable Equilibria using Observer-based Neural Networks with Applications in Chaos Suppression***.*2009 IEEE Symposium on Computational Intelligence in Control and Automation. 2009, pp. 96-103. - ZHANG,, S. S. GE, C. C. HANG,
**Design and Performance Analysis of a Direct Adaptive Controller for Nonlinear Systems**, Automatica*,*vol. 35, no. 11, 1999, pp. 1809-1817. - BOUSHAKI, R. Z., B. CHETATE, Y. ZAMOUM,
**Artificial Neural Network Control of the Recycle Compression System**,Studies in Informatics and Control, vol. 23(1), 2014, pp. 65-76.