Fuzzy Bang-Bang Relay (FBBR) Control System

foulchilianΤεχνίτη Νοημοσύνη και Ρομποτική

20 Οκτ 2013 (πριν από 3 χρόνια και 8 μήνες)

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1

Fuzzy Bang
-
Bang Relay (FBBR) Control System


Abstract

A new fuzzy Bang
-
Bang relay controller (FBBRC) is proposed in this paper. The inputs to the FBBR are configured
on standard fuzzy sets based on Mamdani implications. The output of FBBR is a two level state. Largest of maxima
(LOM) defuzzification method is

used for two level state output. Non
-
linear Bang
-
Bang control, results in optimal
time control of continuous system. Conventional Bang
-
Bang control uses switching relays or hard limiter saturation
functions, and do not have fuzzy linguistic rules flexibil
ity in their input. The stability and optimality of the FBBRC
can be established with Lyapunov’s stability criterion and Pontrygin minimum principle (PMP) respectively.
Because of its simplicity in design and cost effectiveness the Bang
-
Bang control is des
ired for spacecraft
-
satellite
attitude, heating and valves on/off controls. Comparison between the proposed FBBRC and the standard fuzzy logic
controller (FLC) show that FBBRC gives a better response. Finally, a practical application of FBBRC is
demonstra
ted by controlling the angular position of a single axis pneumatic rotary actuator in real
-
time, using
Matlab
-
Simulink xPC target environment.



1) Introduction

Bang

Bang or on/off action constitutes simple and inexpensive control systems. Bang
-
Bang
con
trol systems usually results when attempting to force continuous
-
time systems from initial
state to the origin in minimal time, under bounded control signal of fixed magnitude. There are
many control applications that require two level states “on” or “off”

controller output. Bang
-
Bang fuzzy logic controllers have been developed in past. Bang
-
Bang fuzzy controller developed
by Chiang and Jang made its debut in Cassini spacecraft’s deep space exploration project. The
controller proves its supremacy over the c
onventional Bang
-
Bang controller. Other applications
include minimum time fuzzy satellite attitude controller crane hoisting/lowering operation and
process control valves operation However, these applications are not well suited to the standard
linear cont
rol design methodologies.


Simple hardware relays or hard limiter programming functions are used for implementation of
Bang
-
Bang control system. In absence of deadband in Bang
-
Bang control, hysteresis is
commonly used to compensate for the deadband action.

In presence of deadband, the input to
control system is disabled in its band limits, resulting in steady state error. Hysteresis provides
neat solution, but lacks the robustness as it is fixed or chosen to optimize performance for one
particular nominal p
lant operating condition.


2

The solution lies in the flexible hysteresis of the Bang
-
Bang control action. M
azari and

M
ekri

show how the flexible fuzzy hysteresis band (HB) is used to optimize the pulse width modulator
(PWM) for reduction of harmonic curr
ent pollution. Nowadays, digital processors are readily
available to implement the fuzzy and neural network controller in the industry. Fuzzy controllers
are flexible, simple to build and provide robustness to Bang
-
Bang controller.


6) Conclusion


A simp
le fuzzy Bang
-
Bang relay controller (FBBRC) is conceptualized in this paper. Its
operation is demonstrated with a simulated model and real system application. The simulated
model is a linear model without uncertainties and is used for development, stabilit
y, and
optimality analysis. The real system parameters are not used in simulation model as its
uncertainties are not modeled and are not focus of study in the present work. Fuzzy controllers
are known for absorbing the non
-
linearity of the systems and as t
he results shows it works well
for the real system.


Comparison between the FBBRC and standard FLC shows that FBBRC can reset the beam in
optimal time and with smaller overshoot. In FBBRC, Largest of Maxima (LOM) defuzzification
method yields direct Bang
-
Bang output from fuzzy controller which is similar to hardware
relays, SCR
-
traic, thyristor or solenoid. The hysteresis of these relays are fixed in contrast to
fuzzy relays, where the linguistic rule based overlapping of membership provides robustness in
case of uncertainties and flexible hysteresis. The stability and optimality of FBBRC were
satisfied by SMC

lyapunov criterion and optimal Bang
-
Bang control theory respectively.



The FBBRC developed in section 2
-
4 was successfully applied to the real time

application
system in section 5. The real
-
time control is achieved by using Matlab
-
simulink xPC target
environment. In the application program it was demonstrated how the controller output is divided
into two level voltage required for the operation of pn
eumatic solenoid valves. Simple procedure
to implement the FBBRC is provided for the interested readers. To arrest high velocity beam
motion, the response time of FBBRC can be further study, by changing the fuzzy rules polarity
of immediate adjacent diagon
als, next to the main diagonal. Adaptive fuzzy tuning of
membership FBBRC function can be investigated to enhance the performance of the controller.