Week 7 Challenge
Aim :- Complete the vehicle model.
Objective :- Load the vehicle parameters using Matlab Workspace.
The model output should be the vehicle velocity.
Theory :-
Here we are going to make two subsystems,
1. Driver Subsystem.
2. Vehicle Model Subsystem.
1. In the Driver subsystem we are going to provide Actual velocity and Desired velocity inputs,and the outputs will be the Acceleration and Braking.
For the minimization of the error in the system we are going to use PID Controller with help of this controller we can get actual output. PID stands for Proportional gain,Integral gain,Derivative gain.
In the Proportional gain the correction factor is multiplied to the error.
Equation which represents Proportional gain,
`Cout = Kp.e(t) +Co`
Where,
`Cout` = Controller output.
`Kp` = controller gain.
`e(t)` = Error(Change with time).
`Co` = controller output when error is zero.
In Integral gain it gives any residual error in the system output.
Equation which represents Integral gain,
`Cout = Kiint_0^t e(t)dt + Co`
Where,
`Ki` = Integral Gain.
In Derivative gain it works to detect the rate of change of error .This helps to point out if the error is going to increase rapidly in the near future
Equation which represents Derivative gain,
`Cout = Kd (de(t))/dt +Co`
Where,
`Kd` = Derivative gain
Implementing this equations in the subsystem we are able to get Acceleration and Braking as a output.
Driver Subsystem Simulink Model,
2. In the Vehicle Model subsystem we are going to provide Acceleration and Traction force inputs,and the outputs will be the Velocity.
In this subsystem we are going to calculate all the resistance forces which is apply on the vehicle when its moving or stationary.There are mainly four forces whichvwill bevapplied on the vehicle.
- Rolling Resistance.
- Aerodynamic Drag Resistance.
- Grade Resistance.
- Lateral Forces.
In lateral forces this force is applied laterally(side body) on the vehicle body while its moving.So we are not considering this force.We are only considering remaining three forces.
To get the value of the velocity in this model we going to subtract the total resistance from the traction force.
To calculate total resistance we need to add all three resistance forces.To calculate all three resistance forces there are some standard equations with the help of them we can calculate them.
Rollling Resistance Eq,
`Fp = M*g*mu*cos(alpha)`
Where,
`mu` = Coefficient of rolling resistance.
Aerodynamic Drag Resistance Eq,
`Fa = 1/2 * rho * Af * Cd * V^2`
Where,
`Cd` = Drag Coefficient.
`rho` = Air density.
Grade Resistance Eq,
`Fg = M * g * Sin(alpha)`
Vehicle Model Subsystem Simulink Model,
Complete model with Velocity as a Output.
In the above figure as we can see the simulation ran for 598 sec.The velocity value here we get is 142.6 .