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SAMPLED-DATA FUZZY CONTROLLER FOR TRUCK-SAMPLED-DATA FUZZY CONTROLLER FOR TRUCK-TRAILER WITH TIME DELAYTRAILER WITH TIME DELAY
Authors:H.K.Lam,Frank.H.F.LeungAuthors:H.K.Lam,Frank.H.F.Leung
Presented ByPresented ByS.Anitha KumariS.Anitha Kumari
200831322200831322
INTRODUCTION
• Sampled-data fuzzy control system with time delay is formed by a non-linear plant with time delay and a sampled-data fuzzy controller connected in closed loop.
• Adv:As this controller can be implemented by a microcontroller or a digital computer the implementation time and cost can be reduced
• Disadv:The sampling activity and time delay which are the potential cause of system instability will complicate the system dynamics and make the stability analysis much more difficult than that for a pure continuous-time fuzzy control system
CONTROL TECHNIQUES
Control techniques to handle nonlinearsystems with time delay using fuzzy are
• Delay-independent
• Delay dependent
Delay-independent-Stability conditions not related to time-delay information. Once time-delay fuzzy control system is stable,it is stable for any value of time delay
Delay dependent- The time-delay information is considered, which leads to a complicated analysis procedure compared with that of the delay-independent approach.
FUZZY PLANT MODEL
• Time delay is an inevitable source causing system instability
• Let p be the number of fuzzy rules describing the non-linear plant with time delay.The i-th rule is
Rule i:IF f(x(t)) is M1 AND…AND f1(x(t)) is M2
THEN
The overall system dynamics are described by
.
.
1
( ) ( ) ( ) ( )
( ) ( ( ))( ( ) ( ) ( )
di d i
p
i di ii di
X t x t x t u t
t x t x t x t u t
A A B
X A A B
.
1
( ) ( ( ))( ( ) ( ) ( )p
i di ii di
t x t x t x t u tX A A B
SAMPLED DATA FUZZY CONTROLLER
A sampled data fuzzy controller with
Fuzzy rules is designed based on the fuzzy model of the nonlinear plant.The jth rule of the controller is of format
Rule j:IF is AND…AND is
THEN
The sampled data fuzzy controller can be represented as
( ( ))1g x t 1
jN ( ( ))g x t
( ) ( )j ju t G x t
jN
1 1
( ) ( ( )) ( ( )) ( ( ))p p
j k jk sj k
u t m x t m x t G x t t
PLANT MODEL
The overall system is described as the equation before in which the membership function is defined as
2 2
1 1
( ) ( ( )) ( ( )) ( ( ))j k jk sj k
u t m x t m x t G x t t
A four rule sampled data fuzzy controller is employed to stabilize the truck trailer with time delay
SYSTEM STATE RESPONSE & CONTROL SIGNALS OF TRUCK TRAILER WITH TIME DELAY UNDER FUZZY CONTROLLER WITH J1 & J2