This document provides an overview of tuning a PID controller with fuzzy logic. It introduces fuzzy logic and discusses how it can be applied to PID tuning. Specifically, it discusses using fuzzy set-point weighting to tune the PID controller by determining the proportional weighting factor b(t) using a fuzzy inference system based on the error e(t) and change in error. It also discusses traditional Ziegler-Nichols tuning and compares the performance of fixed versus fuzzy set-point weighting tuning. The conclusion is that fuzzy logic provides benefits like balancing rise time and overshoot to obtain better performance than traditional methods.

1. TUNING OF PID CONTROLLER WITH
FUZZY LOGIC

2. CONTENTS 2
Serial No. Topic Slide No.
1 Introduction 3
2 Fuzzy Logic 4
3 Example 5
4 PID Controller 6
5 Designing of PID Controller 7
6 Necessity of Tuning 8
7 ZEIGLER NICHOLS Method 9
8 Inferences from ZN 10
method of tuning
9 PID tuning using fuzzy set- 11
point weighting
10 Block diagram for PID 13
tuning
11 Conclusion 15
12 References 16

3. INTRODUCTION 3
->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.

4. Fuzzy Logic 4
-> 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.

5. EXAMPLE 5
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?
The Non-fuzzy Approach The fuzzy Approach
Suppose that the tip always equals 15% of This takes into account the quality of the service.
the total bill. Because service is rated on a scale of 0 to 10, let
tip=0.15 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

6. PID CONTROLLER 6
 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

7. DESIGNING OF PID CONTROLLER 7
 An open-loop response is taken and the parameters to be improved are listed .
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
 Values of Kp, Ki, and Kd are adjusted until we obtain the optimum response .

8. NECESSITY OF TUNING 8
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).

9. ZEIGLER NICHOLS METHOD 9
This method proposed by Ziegler and Nichols is based on experimentally determining the
point 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.

10. Inferences from ZN method of tuning 10
1 – 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.

11. PID tuning using fuzzy set-point weighting11
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]

12. 12
 However, the use of set-point weighting
Ysp
generally leads to an increase in the rise Gff
time since the effectiveness of the
proportional action is somewhat reduced.
 This significant drawback can be avoided
by using a fuzzy inference system to Y
determine the value of the weight b(t) Gc PROCESS
depending on the current value of the
system error e(t) and its time derivative è(t).
-1
 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.
Two degrees of freedom implementation

13. 13
Block diagram for PID Tuning

14. START
Fine-tune the
fuzzy-logic No Is the
14
controller by
slightly varying desired
the parameters performance
Calculate Kp, Ti, Td according to and/or
modifying the obtained?
the Ziegler Nichols method
rules suitably
Yes
Simulate the models and
Obtain suitable of fixed set point compare the values of Ziegler
b for minimising IAE . Nichols fixed b and fuzzy b.
Select error and change in error as the
input variables to the fuzzy inference END
system.
The same procedure is repeated for
The value of the constant parameter w three, five and seven membership
and scaling coefficients Kin2 and Kout, functions for input variables . The
are obtained by an iterative procedure conventional, fixed weight and fuzzy-
for obtaining minimum IAE . set-point weighted tuning
procedures are compared.

15. CONCLUSION 15
 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.

16. References 16
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.

17. THANK YOU