COMPENSATION TECHNIQUES FOR A VEHICLE SYSTEM DRIVEN BY INDEPENDENT DC MOTORS

Mohd Afzal Biyabani G200904750

Outline• Introduction• Objectives• Motivation• Problem Definition• Methodology

Identifier ModelController Model

Mathematical Representation

• Results and Simulation• Conclusion

Introduction

• An automated guided vehicle or automatic guided vehicle (AGV) is a mobile robot that follows markers or wires in the floor, or uses vision or lasers.

• They are most often used in industrial applications to move materials around a manufacturing facility or a warehouse.

• AGV systems offer several advantages over conveyor belts and forklifts, such as higher flexibility, less space utilization, and more safety.

• They are driverless and can effectively be interfaced with material handling subsystems or work cells.

AGV Advantages

• Reduce Manpower• Increase Productivity• Easy Installation• Less space utilization• Can operate in narrow paths• Eliminate Unnecessary Fork Lift Trucks• Reduce Product Damage• Maintain Better Control of Material Management

Problem Definition and Objectives:

Problem Definition:

The main tasks of AGVs are to pick up parts or items at certain points and drop them off at others. AGV systems offer several advantages over conveyor belts and forklifts, such as higher flexibility, less space utilization, and more safety and lower operating costs.

Objectives:

•To design an identifier model and a controller model in order to control the direction and the velocity of the vehicle.•To show that the proposed controller is robust to load changes as it follows different trajectories.

Methodology:

• Here we are controlling a vehicle which has a four-wheeled configuration as shown in the figure below. There are two controlled wheels on front and two uncontrolled wheels on back of the vehicle.

• Linear velocity of right and left wheel can be given as,(1)

(2)• Average linear velocity of both wheel can be written as,

(3)

• Change in direction of the vehicle with respect to angular velocities can be given as,

(4)

R RV R

L LV R

R LR L( )

2 2

V V RV

R L( )d R

dt L

• Let VX and VY be the velocity component in X and Y direction respectively,

(5)

(6)

• The vehicle has two wheels on front and each of the front wheels is independent and driven by a separately excited DC motor, through a gear box. The torque transferred from the motor to gearbox can be written as follows:

(7)where

(8)

x R Lcos( ) ( ) cos( )2

dx RV V

dt

R Lsin( ) ( )sin( )2y

dy RV V

dt

2

LOAD2m m

m m m

d dT J B T

dt dt

22 2

LOAD 2 22 | |m m m

Cm

d dT n J n B nF

dt dt

Substitute TLOAD into motor torque Tm we get,

(9)We can simplify the above equation as,

(10)

Where,

(11)Where Ƞ 1, Ƞ 2, Ƞ 3 are constants.

22 22 22

( ) ( ) ( )m mm m m C m

d dT J n J B n B nF sign

dt dt

2

1 2 32( )m mm m

d dsign T

dt dt

22

1 22

( )

( )m

m

B n B

J n J

2 2

2( )C

m

nF

J n J

3 22

1

( )mJ n J

• From equation (10) we can write the angular velocities of right and left wheel as respectively,

(12)(13)

Using above equations we can write the equations for average linear velocity and change in direction as,

(14)

(15)

R 1 R 2 R 3( ) Rsign T

L 1 L 2 L 3( ) Lsign T

R L 1 R L 2 R L 3 R L( ) [ ( ) ( ( ) ( )) ( )]2 2

R Rv sign sign T T

R L 1 R L 2 R L 3 R L( ) [ ( ) ( ( ) ( )) ( )]R R

sign sign T TL L

Control of the Vehicle System

Right wheel torque: TR = (1/2)*(uv+uϕ)Left wheel torque: TL = (1/2)*(uv-uϕ)

uv and uϕ are the velocity and direction input to the vehicle system.

Block Diagram:

Adaptive Compensator based on Fuzzy Identifier and Controller for the Vehicle System

• Fuzzy Identifier Model:Takagi–Sugeno fuzzy system may have any linear mapping as its output function. This fuzzy system can be considered as a nonlinear interpolator between R linear systems. One mapping is to have a linear dynamic system as the output function so that the ith rule has the following form

Here, uv (k) and uϕ (k) are the plant inputs and v(k) and φ(k)

are plant outputs.

• Using center-average defuzzification, we get the following identifier model outputs:

Let us define the following terms,

Where

Online Method:An on-line method, recursive least square (RLS) is used to adjustthe ai, bi, ci and di parameters since they enter linearly. The RLSalgorithm with update formulas is given by

Design of controllerFor the controller, we use Takagi–Sugeno rules in the form

The Gaussian input membership functions on the universes of discourse v(k) and φ(k) are used in the form

where v*(k) and φ*(k) are the reference values of v(k) and φ(k).

Design of Fuzzy Controller• The Gaussian input membership functions on the universes of

discourse v(k) and φ(k) are used in the form

Note that since there is only one input, the membership function certainty is the premise membership function certainty for a rule

Design of Fuzzy Controller

These cause saturation of the outermost input membership functions

Using a certainty equivalence approach for the controller systemWe assume,v(k)=v, (k), vi (k)= v, i (k) where vi (k) represents the ith component of the plant model.If the plant is operating near its ith rule and there is little or no affect fromits other rules, then v(k)=vi (k)

Design of Fuzzy ControllerApplying Z- transform to the above equation we get,

Choosing,

To get the placement of the pole; our controller designer in our indirect adaptive scheme will pick

Next, to have a zero steady-state error, we want

Design of Fuzzy Controller

• The above approach that is used to calculate the gains of the uv(k) can be used to obtain the gains of the controller uφ(k) and they can be defined as follows

Results and Simulations:

Results and Simulatios:

Design of Controller using Lead Lag Compensator

Result:

Conclusions:• The control system is tested for loading conditions and

complex references. It is demonstrated that the response of the proposed adaptive fuzzy control system is very fast and very robust against disturbance and change of references. The results show that the produced control signals prevent overshoots and deeps at the velocity and direction angle of the vehicle system when load and references are suddenly changed. Hence, the proposed model and controller is acceptable.