**Part 6**

**Fractional Order PID Controllers** 

210 Introduction to PID Controllers – Theory, Tuning and Application to Frontier Areas

There is introduced the technique above, which performs continuous adaptation of PID controller via neural model of controlled system. Neural model is used for controlled system continuous linearization and that linearized model is used for discrete PID controller tuning using pole assignment. The technique is suitable for highly nonlinear systems control, while

The work has been supported by the funds of the framework research project MSM 0021627505, MSM 6046137306 and by the funds of the project of University of Pardubice SGFEI06/2011 "Artificial Intelligence Control Toolbox for MATLAB". This support is very

Astrom, K. J. & Hagglund, T. (1995). *PID controllers: theory, design and tuning,* International

Bennett, S. (1993). *A history of control engineering, 1930-1955,* IET, ISBN 0-86341-280-8,

Doyle, J., Francis, B. & Tannenbaum, A. (1990). *Feedback control theory,* Macmillan Publishing,

Dwarapudi, S.; Gupta, P. K. & Rao, S. M. (2007). Prediction of iron ore pellet strength using

Doležel, P.; Taufer, I. & Mareš, J. (2011). Piecewise-Linear Neural Models for Process

300, ISBN 978-80-227-3517-9, Tatranská Lomnica, Slovakia, June 14-17, 2011 Haykin, S. (1994). *Neural Networks: A Comprehensive Foundation,* Prentice Hall, ISBN 0-02352-

Hecht-Nielsen, R. (1987). Kolmogorov's mapping neural network existence theorem, *Proc 1987 IEEE International Conference on Neural Networks,* Vol. 3, pp. 11-13, IEEE Press Hunt, K. J., Ed. (1993). *Polynomial methods in optimal control and filtering.,* IET, ISBN 0-86341-

Isermann, R. (1991). *Digital Control Systems,* Springer-Verlag, ISBN 3-54010-728-2,

Montague, G. & Morris, J. (1994). Neural network contributions in biotechnology, *Trends in* 

Nguyen, H.; Prasad, N.; Walker, C. (2003). *A First Course in Fuzzy and Neural Control*,

*biotechnology,* Vol. 12, No 8., pp. 312-324, ISSN 0167-7799

Chapman & Hall/CRC, ISBN 1-58488-244-1, Boca Raton, USA

Society for Measurement and Control, ISBN 1-55617-516-7, Durham, North

artificial neural network model, ISIJ International, Vol. 47, No 1., pp. 67-72, ISSN

Control, *Proceedings of the 18th International Conference on Process Control '11*, pp. 296-

it brings no advantages to control of the systems which are close to linear ones.

**7. Conclusion** 

**8. Acknowledgement** 

gratefully acknowledged.

Carolina, USA

Stevenage, UK

0915-1559

761-7, New Jersey, USA

295-5, Stevenage, UK

Heidelberg, Germany

ISBN 0-02330-011-0, New York, USA

**9. References** 

**9** 

*3ESIEE-Amiens* 

*1,3France 2South Africa* 

**PID Control Theory** 

*2Tshwane University of Technology/FSATI* 

Kambiz Arab Tehrani1 and Augustin Mpanda2,3

. () *P K error t <sup>P</sup>* (1)

*Saint-Quentin, Director of Power Electronic Society IPDRP,* 

*1University of Nancy, Teaching and Research at the University of Picardie, INSSET,* 

Feedback control is a control mechanism that uses information from measurements. In a feedback control system, the output is sensed. There are two main types of feedback control systems: 1) positive feedback 2) negative feedback. The positive feedback is used to increase the size of the input but in a negative feedback, the feedback is used to decrease the size of the input. The negative systems are usually stable. A PID is widely used in feedback control of industrial processes on the market in 1939 and has remained the most widely used controller in process control until today. Thus, the PID controller can be understood as a controller that takes the present, the past, and the future of the error into consideration. After digital implementation was introduced, a certain change of the structure of the control system was proposed and has been adopted in many applications. But that change does not influence the essential part of the analysis and design of PID controllers. A proportional– integral–derivative controller (PID controller) is a method of the control loop feedback. This

The role of a proportional depends on the present error, I on the accumulation of past error and D on prediction of future error. The weighted sum of these three actions is used to adjust Proportional control is a simple and widely used method of control for many kinds of systems. In a proportional controller, steady state error tends to depend inversely upon the proportional gain (ie: if the gain is made larger the error goes down). The proportional response can be adjusted by multiplying the error by a constant *Kp*, called the proportional

A high proportional gain results in a large change in the output for a given change in the error. If the proportional gain is very high, the system can become unstable. In contrast, a

**1. Introduction** 

method is composing of three controllers [1]:

**1.1 Role of a Proportional Controller (PC)** 

gain. The proportional term is given by:

1. Proportional controller (PC) 2. Integral controller (IC) 3. Derivative controller (DC)
