**Part 5**

**Discrete Intelligent PID Controller** 

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

If there is a designed linear PID controller for a process control, we may use the equivalent fuzzy PID controller in its place in order to control the process with better control quality criteria. Based on the above notice, the method may be used also for tuning the fuzzy PID

The term of "pseudo-equivalence" is used because there is no direct equivalence between the nonlinear digital fuzzy PI controller, with linearization only in the origin, and a linear

The theory presented in this paper is used and proved by the author in practical control applications, as speed control of electrical drives for dc motors, synchronous and induction

Bao-Gang, H.; Mann, G.K.I. & Gosine, R.G. New methodology for analytical and optimal

Bao-Gang, H., Mann, G.K.I. & Gosine, R.G. A systematic study of fuzzy PID controllers

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Moon, B.S. Equivalence between fuzzy logic controllers and PI controllers for single input

Mohan, B.M. & Sinha, A. The simplest fuzzy PID controllers: mathematical models and

Mohan, B.M. & Sinha, A. Analytical Structures for Fuzzy PID Controllers?, *IEEE Trans. On* 

Santos, M.; Dormido, S.; de Madrid, A.P.; Morilla F. & de la Cruz, J.M. Tuning fuzzy logic

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Volosencu, C. Stabilization of Fuzzy Control; Systems, *WSEAS Transactions On Systems and* 

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analogue PI controller.

motors.

**7. References** 

**8** 

*Czech Republic* 

**Discrete PID Controller Tuning Using** 

*University of Pardubice & Institute of Chemical Technology Prague* 

PID controller (which is an acronym to "proportional, integral and derivative") is a type of device used for process control. As first practical use of PID controller dates to 1890s (Bennett, 1993), PID controllers are spread widely in various control applications till these days. In process control today, more than 95% of the control loops are PID type (Astrom et al., 1995). PID controllers have experienced many changes in technology, from mechanics

Especially microprocessors have influenced PID controllers applying significantly. They have given possibilities to provide additional features like automatic tuning or continuous adaptation – and continuous adaptation of PID controller via neural model of controlled system (which is considered to be significantly nonlinear) is the aim of this contribution. Artificial Neural Networks have traditionally enjoyed considerable attention in process control applications, especially for their universal approximation abilities (Montague et al., 1994), (Dwarapudi, et al., 2007). In next sections, there is to be explained how to use artificial neural networks with piecewise-linear activation functions in hidden layer in controller design. To be more specific, there is described technique of controlled plant linearization using nonlinear neural model. Obtained linearized model is in a shape of linear difference

The basic structure of conventional feedback control using PID controller is shown in Fig. 1 (Astrom et al., 1995), (Doyle et al., 1990). In this figure, the SYSTEM is the object to be controlled. The aim of control is to make controlled system output variable *yS*(*t*) follow the set-point *r*(*t*) using the manipulated variable *u*(*t*) changes. Variable *e*(*t*) is control error and is

Continuous-time PID controller itself is defined by several different algorithms (Astrom et

0 <sup>1</sup> ( ) () () ( ) *t p d i de t ut K et e d T*

*T dt* 

(1)

 

al., 1995), (Doyle et al., 1990). Let us use the common version defined by (Eq. 1).

**1. Introduction** 

and pneumatics to microprocessors and computers.

equation and it can be used for PID controller parameters tuning.

**2. Continuous-time and discrete PID controller** 

considered as PID controller input and *t* is continuous time.

**Piecewise-Linear Neural Network** 

Petr Doležel, Ivan Taufer and Jan Mareš
