fuzzy control simulation of the ball and the beam system

seteney šuaže (seteney_guase@hotmail.com)
Sat, 30 Jan 1999 21:56:31 +0100 (MET)

Dear Sir,
While searching on the net , I have found your name and thought maybe
you could help me.
What I want to implement by simulation is to design a "fuzzy pd" or
"fuzzy P" and etc. based controller for the well known "ball and the
beam system"( or just determines u 's membership function value as input
to the new step) to set the parameters to the desired levels(in my case
getting r around zero and theta around zero too.) I am writing the code
in C++.
But I have dealt problems while constructing the rules. In fact I
could not succeed in defining the rules. First I put limiters to r then
to theta together. But I can not say , i.e. if error is
small(error=x_1-desired=x_1 , since desired=zero) and error_dot(x_2) is
positive medium, then Kp=... and Kd=...) and u=Kp*x_1+K_d*x_2. I hope
you have understood the problem.

system state equations are as follows:

x_1=r x_2=r_dot x_3=theta x_4=theta_dot
B=.7143(might be altered) and G=9.81 m/sec^2

x_1_dot=x_2
x_2_dot=B*x_1*(x_4)^2 - B*G*sin(x_3)
x_3_dot=x_4
x_4_dot=u

If you have designed such a controller , please inform me of
that(or you have seen, anywhere, the fuzzy rule base for the system).
Hoping to hear good news from you soon.
Best Wishes,
Seteney Šuaže

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