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.

Block diagram of sampled-data timedelay fuzzy model based controller

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

DYNAMICS OF TRUCK-TRAILER WITH TIME DELAY

PLANT MODEL

The overall system is described as the equation before in which the membership function is defined as

MODEL RULES

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