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Aim : Create a MATLAB model of electric car which uses lithium ion battery and induction motor. Choose suitable blocks from Powertrain block set. Prepare a report about your model including following: 1. System level configurations 2. Model parameters 3. Results …
abhijeet dhillon
updated on 16 Jul 2020
Aim :
Create a MATLAB model of electric car which uses lithium ion battery and induction motor. Choose suitable blocks from Powertrain block set. Prepare a report about your model including following:
1. System level configurations
2. Model parameters
3. Results
4. Conclusion
Solution :
We will first conisder all the forces acting on a vehicel and derive the torque required :
1.Rolling Resistance Force :
Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface. It is mainly caused by non elastic effects; that is, not all the energy needed for deformation (or movement) of the wheel, roadbed, etc. is recovered when the pressure is removed.It is given by the formula :
Fr= Coefficient of rolling resistance*weight of the vehicle
2.Aerodynamic drag:
It the total drag acting on the vehicle and its the sum of sking friction drag as well parasite drag.It is given by the formula:
Fd=1/2*Cd*v^2*A*RHO
3.Accelaration Force:
This the force which produces the acceleration in the vehicle and is given by the formula:
F=ma
Angular acceleration force :
This is the force which is required to overcome the angular inertia present in the gears etc and it is given bu the formula:
Fa=I*G^2*a/r^2*n
where G= Gear ratio
I= Inertia of vehicle
r= radius of wheel
n= efficiency of drivetrain
a=acceleration
Now the tractive force is given by
Fte= G*T/r
The total tractive force is equal to the sum of all the forces mentioned above in order for the vehicle to move forward and it is given by:
Fte= Frr + Fad + Fhc + Fla + Faa
Assuming the following parameters of the car , matlab code is written which calculates the total tractive force required by the car :
Weight of Car (W)= 500 kgs
Coefficient of Rolling Resitance (R1)= 0.002
Efficiency Of Drivetrain (n)= 0.9
Gear Ratio(G) = 5
Coefficient Of Drag (Cd) = 0.3
Radius Of Wheel (r) = 0.250 m
Inertia(I) = 31.25 Kg.m^2
Matlab Code :
clc
clear all
R1 = 0.002 %coefficient of resistance
W= 500 %weight of car(kgs)
p=1.2 %Density of air
Cd=0.3%coefficient of drag
A=1 %area of car(m2^2)
V=linspace(5,50,500)%speed range
r=0.250%radius of car
a=2 % acceleration
I= 31.25 % inertia
G= 5 % gear ratio
n = 0.8 % drivetrain efficiency
F1 = W*R1 % ROLLING REISISTANCE FORCE
F2=0.5*A*Cd*p*(V).^2%drag force
F3=W*a%acceleration force
F4=I*G^2*a/r^2*n % inertial force
Ft = F1 + F2 + F3 + F4 % tractive force required
T = Ft.*r % Torque Required
w=V./r
plot(w,T)
title('Torque Required vs Speed ')
xlabel('speed')
ylabel('Torque')
Results :
Hence we will require this torque - speed curve to satisfy the load acting on the vehicle .Hence keeping this in mind a electric vehicle system is designed below as shown below :
Now we will create a model in simulink as shown below:
Following components were used in the model:
1.Tyre:
N :It denotes the normal force acting on the tire
A:It denotes the axle
H:It denotes the hub
S:It denotes the slip
The vertical load is the normal weight beacause of the vehicle weight and is calculated as shown below:
Total vehicle weight = 500 kgs
Weight acting on rear=250 kgs
Weight acting on front = 250 kgs
Weight acting on each tyre = 125 kgs = 1250 N
A rolling resistance coefficient of 0.015 is chosen as shown above .
2.Vehicle Body :
It takes account the normal force from the wheels ,connections to the hub and all the forces acting on the vehicle body.
3.Simple Gear :
The output of the gearbox is connected to the hub of the wheel and the input is connected to the dc motor.A gear ratio of 3 is given as shown below :
4.DC Motor :
This provides the required torque.
No Load Speed : ]The no load speed is the RPM at which the DC Motor's shaft rotate when there is no load attached to it (no torque applied to the output shaft). It is the maximum output speed of the motor.
Rated voltage — Motors are designed to yield optimal performance when operating at a specific voltage level, or a combination of voltage levels in the case of dual-voltage or tri-voltage motors. This value is known as the nameplate voltage. In recognition of the fact that voltage changes on your power distribution system occur due to changing load conditions within your facility and on the utility supply that feeds your facility, motors are designed with a 10% tolerance for voltage above and below the rated nameplate value. Thus, a motor with a rated nameplate voltage of 460V should be expected to operate successfully between 414V and 506V.
Rated full-load speed — This is the motor's approximate speed under full-load conditions, when voltage and frequency are at the rated values. A somewhat lower value than the actual laboratory test result figures is usually stamped on the nameplate because this value can change slightly due to factors like manufacturing tolerances, motor temperature, and voltage variations. On standard induction motors, the full-load speed is typically 96% to 99% of the no-load speed
5.Battery
This is the source of the power to the dc motor .A finite battery source with the following specifications .
6.Power Converter :
We will be using h bridge converter which make sure the motor operates in the forward motoring ,reverse motoring etc.
Power Converter :
A converter is an electrical circuit which accepts a DC input and generates a DC output of a different voltage, usually achieved by high frequency switching action employing inductive and capacitive filter elements.A power converter is an electrical circuit that changes the electric energy from one form into the desired form optimized for the specific load. A converter may do one or more functions and give an output that differs from the input. It is used to increase or decrease the magnitude of the input voltage, invert polarity, or produce several output voltages of either the same polarity with the input, different polarity, or mixed polarities such as in the computer power supply unit.
H- Bridge :
In general an H-bridge is a rather simple circuit, containing four switching element, with the load at the center, in an H-like configuration:
The switching elements (Q1..Q4) are usually bi-polar or FET transistors, in some high-voltage applications IGBTs. Integrated solutions also exist but whether the switching elements are integrated with their control circuits or not is not relevant for the most part for this discussion. The diodes (D1..D4) are called catch diodes and are usually of a Schottky type.
The top-end of the bridge is connected to a power supply (battery for example) and the bottom-end is grounded.
In general all four switching elements can be turned on and off independently, though there are some obvious restrictions.
Though the load can in theory be anything you want, by far the most pervasive application if H-bridges is with a brushed DC or bipolar stepper motor (steppers need two H-bridges per motor) load. In the following I will concentrate on applications as a brushed DC motor driver
7.Driver
This block is responsible for the driving commands such as acceleration ,decceleration etc.
The reference velocity is the velocity is the ideal velocity and it is the velocity which we want and it is used for reference .\
The velocity feedback which is Velfdbk is the actual velocity which we are getting with our current vehicle characterictics .If there is a difference between the reference velocity and the actual velocity , it creates an error this error is fed into the PID controller shown below which changes the motor speed through PWM signal generation created through the accclecmd and deccelcmd which is the acceleration and deccleration which is a digital signal standing between 1 and 0 .1 meaning that the that command should be used for full use and vice versa.
PID Controller :
A PID controller is an instrument used in industrial control applications to regulate temperature, flow, pressure, speed and other process variables. PID (proportional integral derivative) controllers use a control loop feedback mechanism to control process variables and are the most accurate and stable controller.
PID controller maintains the output such that there is zero error between process variable and set point/ desired output by closed loop operations. PID uses three basic control behaviors that are explained below
Proportional or P- controller gives output which is proportional to current error e (t). It compares desired or set point with actual value or feedback process value. The resulting error is multiplied with proportional constant to get the output. If the error value is zero, then this controller output is zero
I-Controller:Due to limitation of p-controller where there always exists an offset between the process variable and set point, I-controller is needed, which provides necessary action to eliminate the steady state error. It integrates the error over a period of time until error value reaches to zero. It holds the value to final control device at which error becomes zero.Due to limitation of p-controller where there always exists an offset between the process variable and set point, I-controller is needed, which provides necessary action to eliminate the steady state error. It integrates the error over a period of time until error value reaches to zero. It holds the value to final control device at which error becomes zero.
D-Controller:I-controller doesn’t have the capability to predict the future behavior of error. So it reacts normally once the set point is changed. D-controller overcomes this problem by anticipating future behavior of the error. Its output depends on rate of change of error with respect to time, multiplied by derivative constant. It gives the kick start for the output thereby increasing system response.
8.Drive Cycle
A drive cycle to the velocity ref is applied as shown below :
Now we will be simulating for the drive cycle as shown below :
As you can see that the P gain is very much accurate but the steady state error caused is not being corrected by the I controller as well as the change is not happening hence there is a need to increase the I gain as well D gain as shown below :
As you can see the breaking is not occurring fast enough therefore we need to increase the PI gain .
Hence after increasing the PI gain we have reached a very accurate result to our desired speed.
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