1. Software version

matlab2013b

2. Theoretical knowledge of this algorithm

Here, the distance is explained according to the basic work of the fuzzy controller , It is assumed that this system is a temperature control system .

first ： Fuzzification process

surface 1 Membership function of fuzzy set

error e

-50

-30

-15

-5

0

5

15

30

50

Error rate de

-150

-90

-30

-10

0

10

30

90

150

control u

-64

-16

-4

-2

0

2

4

16

64

Quantification level

-4

-3

-2

-1

0

1

2

3

4

state variable

Related membership function

PB

0

0

0

0

0

0

0

0.35

1

PS

0

0

0

0

0

0.4

1

0.4

0

ZE

0

0

0

0.2

1

0.2

0

0

0

NS

0

0.4

1

0.4

0

0

0

0

0

NB

1

0.35

0

0

0

0

0

0

0

Fuzzy rules ：

Fuzzy control rules are essentially a set of fuzzy conditional statements obtained by summarizing the control experience of operators . The principle of determining fuzzy control rules is to ensure that the output of the controller can optimize the dynamic and static characteristics of the system output response .

Here is an example , The rules satisfied are ：

rule 1： If error e yes NB, And the error changes de yes PB, Then control U by PB;

rule 2： If error e yes NB, And the error changes de yes PS, Then control U by PB;

rule 3： If error e yes NB, And the error changes de yes ZE; Then control U by PB;

rule 4： If error e yes NB, And the error changes de yes NS, Then control U by PB;

rule 5： If error e yes NS, And the error changes de yes ZE, Then control U by PS;

rule 6： If error e yes NS, And the error changes de yes PS, Then control U by ZE;

rule 7： If error e yes NS, And the error changes de yes PB, Then control U by NS;

rule 8： If error e yes ZE, And the error changes de yes ZE, Then control U by ZE;

rule 9： If error e yes ZE, And the error changes de yes PS, Then control U by NS;

rule 10： If error e yes ZE, And the error changes de yes PB, Then control U by NB.

rule 11： If error e yes NS, And the error changes de yes NS, Then control U by PS;

rule 12： If error e yes NS, And the error changes de yes NB, Then control U by PB;

rule 13： If error e yes ZE, And the error changes de yes NS, Then control U by PS;

rule 14： If error e yes ZE, And the error changes de yes NB, Then control U by PB.

Thus, the fuzzy rule table is ：

U

NB

NS

ZE

PS

PB

NB

PB

PB

PB

PS

NB

NS

PB

PS

PS

ZE

NB

ZE

PB

PS

ZE

NS

NB

PS

PB

ZE

NS

NS

NB

PB

PB

NS

NB

NB

NB

second ： Fuzzy reasoning process

Set systematic error e The quantized value of is l, Error variation de The quantized value of is -2 .

The non-zero membership function can be obtained as ：

error e      ：μZE(1)= 0.2      μps(1)= 0.4;

Error variation de ：    μNS(-2)= 1

Only the following two rules are valid

If error e yes ZE, And the error changes de yes NS, Then control U by PS;

If error e yes PS, And the error changes de yes NS, Then control U by ZE;

third ： Clarity process

The output fuzzy set of the control quantity obtained by the minimax reasoning method is

μps(1,-2)=min(0.2,1)= 0.2

μZE(1,-2)=min(0.4,1)= 0.4

The above is the working process of fuzzy control system .

3. Partial source code

here , According to the input and output requirements in the subject , All definitions NB,NS,Z,PS,PB, The membership function we will use here is trimf Function of type . Membership functions are as follows ：

That is, what is selected here is NB,NS,Z,PS,PB These five types of membership functions .

The rule table here is ：

NB

NS

Z

PS

PB

NB

NB

NB

NB

NS

Z

NS

NB

NB

NS

Z

PS

Z

NB

NS

Z

PS

PB

PS

NS

Z

PS

PB

PB

PB

Z

PS

PB

PB

PB

According to the basic structure of inverted pendulum ：

In actual work , angle 1 It will shake back and forth for adjustment , angle 2 It is relatively stable in one position . So as to achieve balance .

We build the following model ：

4. Simulation conclusion

You can see through simulation , The error and error change rate of fuzzy control are ：

angle 1 And angle 2 The simulation of is as follows ：

Membership functions are as follows ：

Surface As shown below ：

The simulation results are as follows ：

Through simulation , Finally, we can see that the final error of this system is -0.33, The change rate of error is 0.

Through simulation , The output results of the comparison controller can be obtained as follows ：

According to the above simulation results , The convergence speed of the signal after passing the fuzzy controller is fast , And there is almost no overshoot .

A28-04

Technology
Daily Recommendation
views 14
views 6
views 6
views 6
views 5