TUNING OF PID CONTROLLER WITH FUZZY LOGIC

CONTENTSSerial No. Topic Slide No.1 Introduction 32 Fuzzy Logic 43 Example 54 PID Controller 65 Designing of PID Controller 76 Necessity of Tuning 87 ZEIGLER NICHOLS Method 98 Inferences from ZN

method of tuning10

9 PID tuning using fuzzy set-point weighting

11

10 Block diagram for PID tuning

13

11 Conclusion 1512 References 16

2

INTRODUCTION

->PID controllers constitute an important part at industrial control systems so any improvement in PID design and implementation methodology has a serious potential to be used at industrial engineering applications.

->The PID controllers which were invented in the 1900s are still used in more than 95% of industrial control loops .

-> They have survived many changes in technology from mechanics and Pneumatics to microprocessors via electronic tubes , transistors and integrated circuits .

-> Present day PID controllers are made by using microprocessors/microcontrollers and using Programmable logic control technology.

3

Fuzzy Logic

-> Fuzzy logic is an approach to computing based on ‘degrees of truth’ rather than the usual ‘true or false’(1 or 0) Boolean logic on which the modern computer is based.

-> Boolean logic is a subset of fuzzy logic.

-> the FL is based on the implementation of human understanding and human thinking in control algorithms.

-> Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. -> As the complexity of a system increases, it becomes more difficult and eventually

impossible to make a precise statement about its behaviour, eventually arriving at a point of complexity where the fuzzy logic method is the only way to get at the problem.

4

The Non-fuzzy Approach Suppose that the tip always equals 15% of

the total bill. tip=0.15

The fuzzy Approach This takes into account the quality of the service.

Because service is rated on a scale of 0 to 10, let the tip go linearly from 5% if the service is bad to 25% if the service is excellent.

tip=0.20/10*service+0.05

EXAMPLE Given a number between 0 and 10 that represents the quality of service at a restaurant (where 10 is excellent), what should the tip be?

5

PID CONTROLLER A proportional-integrating-derivative controller is a generic control loop feedback mechanism

widely used in industrial control systems. A PID controller calculates an "error" value as the difference between a measured process variable

and a desired set- point. The controller attempts to minimize the error by adjusting the process control inputs.

ALGORITHM

p – depends on present error I - depends on accumulation of past errors D - is a prediction of future errors

6

DESIGNING OF PID CONTROLLER An open-loop response is taken and the parameters to be improved are listed .

Values of Kp, Ki, and Kd are adjusted until we obtain the optimum response .

Constants Rise time Overshoot Settling Time ess

Kp ↑ Decrease Increase Small change Decrease

Ki ↑ Decrease Increase Increase Eliminate

Kd ↑ Small Change Decrease Decrease Small Change

7

NECESSITY OF TUNING

Tuning is the process of finding appropriate parameters for the PID controller . Tuning determines the overall performance of control loop which affects quality of product , cost etc .

A pid control system needs tuning if – a) Careful consideration was not given to the units of gains and other parameters. b) The process dynamics were not well-understood when the gains were first set, or the

dynamics have (for any reason) changed. c) Some characteristics of the control system are direction-dependent (e.g. actuator piston

area, heat-up/cool-down of powerful heaters).

8

ZEIGLER NICHOLS METHODThis method proposed by Ziegler and Nichols is based on experimentally determining thepoint of marginal stability.

Formula – u(t)= Kp [e(t)+Td de(t)/dt+1/Ti ∫e(t)dt]

Procedure – 1- The pid controller is turned into p controller by setting Ti=infinity and Td=0.2 – The gain Kp is set to zero.3 – The control loop is closed by setting the controller in automatic mode.4 - Kp was increased until there are sustained oscillations in the signals in the control system.

9

Inferences from ZN method of tuning1 – Ensures good load disturbance attenuation.2 – The algorithm and application is quite simple .

3– System maybe driven towards instability.4– poor phase margin, hence large overshoot and settling time for step response .5 – We don’t know in advance the amplitude of sustained oscillations.6- Does not work if operating point is unstable. 7 - Poor performance for processes with a dominant delay.8 - Closed loop very sensitive to parameter variations.

10

PID tuning using fuzzy set-point weighting Formula - u(t)= Kp [e(t)+Td de(t)/dt+1/Ti ∫e(t)dt]

->Set-point for the proportional action is weighted by means of a constant b <1 .

so we get u(t)= Kpep(t)+Kdde(t)/dt+Ki∫e(t)dt

where ep(t)=bysp(t)—y(t)

-> In this way, a simple two-degree of freedom scheme is implemented . -> one part of the controller is devoted to the attenuation of load disturbances, and the other

to the set-point following as shown in figure, where the following transfer functions are indicated:

Gff = Kp [b+1/(sTi)+Td] Gc = Kp[1+1/(sTi)+Td]

11

However, the use of set-point weighting generally leads to an increase in the rise time since the effectiveness of the proportional action is somewhat reduced.

This significant drawback can be avoided by using a fuzzy inference system to determine the value of the weight b(t) depending on the current value of the system error e(t) and its time derivative è(t).

the output f(t) of the fuzzy module is added to a constant parameter w, resulting in a coefficient b(t) that multiplies the set-point.

Gff

Gc

-1

PROCESSY

Ysp

Two degrees of freedom implementation

12

Block diagram for PID Tuning

13

START

Calculate Kp, Ti, Td according to the Ziegler Nichols method

The value of the constant parameter w and scaling coefficients Kin2 and Kout, are obtained by an iterative procedure

for obtaining minimum IAE .

Obtain suitable of fixed set point b for minimising IAE .

Select error and change in error as the input variables to the fuzzy inference

system.

Is the desired

performance obtained?

Fine-tune the fuzzy-logic

controller by slightly varying the parameters

and/or modifying the rules suitably

Simulate the models and compare the values of Ziegler

Nichols fixed b and fuzzy b.

END

No

Yes

The same procedure is repeated for three, five and seven membership functions for input variables . The

conventional, fixed weight and fuzzy-set-point weighted tuning procedures are compared.

14

CONCLUSION The results have clearly emphasized the advantages of fuzzy inference systems .

The main benefits in the use of FL appear when process non-linearities such as saturation are significant.

a balance is obtained between both rise time and overshoot in the response i.e lesser overshoot and smaller rise time are obtained simultaneously by using FL which is impossible using conventional methodologies .

The ease of tuning of fuzzy mechanism parameters plays a key role in the practical applicability of the methodologies, since it determines the improvement in the cost per benefit ratio with respect to standard methods.

15

References

1 - Gaddam Mallesham Akula Rajani ,“automatic tuning of pid controller using fuzzy logic”8th international conference on development and application system ; Suceava,Romania,May 25-27 , 2006.

2 - A Visioli of Diupartimento di Elettronica per l’Automazione,Brescia University ,“tuning of pid controllers with fuzzy logic” proceedings of ieee, Volume 148, issue-1,Pages:1-8 , jan 2001

3 - L.J.Nagrath and M.Gopal , “Control System engineering” , New age internatrional publication , 4th edition , 2006.

16

THANK YOU