Application of a PID controller in a Speed

Control of a Car.

By

Atchyuth Sonti

Hello,guys now i am going to tell you how a PID controller is used in the

automobiles.This is an important concept in the field of control systems and

lets see why it should be used and how each stage of it contributes to the speed

control.I am going to use matlab(simulink) for illustrating this particular

concept.

Lets me consider that i am having a SUV. Let the parameters of the car be

1.Weight of 1000 kg.

2.Engine force of 5000 N.

3.Drag coefficient of 50.(this in simple terms can be explained as sum of

friction and other opposing forces).

The specifications which my design should meet be

1.A speed of 10m/s.( =36kmph).

2.Rise time should be <5 sec.(this is popularly called as pick up).

3.Steady state error of <2% ( the steady state speed should be in between 9.8m/s

and 10.2m/s).

So now let us construct a simple car model

To execute this particular thing we need to have both matlab file(.m) and

simulink file(.mdl).

We do this because we will have maximum compatibility for changing values

and analyse the circuit with different parameters.

Generally the M file consists of the list of parameters which affect the system

and mdl file consists the signal flow diagram of the system.

Simple Car Model

The (.m) file

The simulink (.mdl) file for the simple car model is given below.

This is the way you need to design the files and for simulink file to take the

values from the m file u need to run the m file first followed by the mdl file. This

makes the things simpler.

The output which is generated by this model will be of this type.

The output of the simple car model.

Analysis

1.A speed of 10m/s.

2.Rise time should be <5 sec.

3.Steady state error of <2%.

When the above output is analysed it is following all the design specifications

except the rise time. i.e the above car doesn’t have proper pick up or

acceleration.(the design takes 100 sec where it should take less than 5 sec).If

employed this becomes one of the worst design.

Now let us add the parts of the controller and analyse its effect(s).

The “P” controller.

Now we shall make two subsystems

1. Car.(the above car mode is now put in this particular subsystem).

2. Controller.

We shall start with the P controller and go on adding the complexity to the

controller.

For our convenience we converted the force into a reference velocity of 10m/s.

This reduces the tedious calculations.

The m file for the above system is

The output of the P controller is

This is the output with a p controller

Analysis

1.A speed of 10m/s.( =36kmph).

2.Rise time should be <5 sec.(this is popularly called as pick up).

3.Steady state error of <2% ( the steady state speed should be in between

9.8m/s and 10.2m/s).

The PI controller.

In PI controller an integral controller comes into action with the P controller.

Now we completely made another subsystem called a controller and we add

different components into that controller.

For our reference this is the subsystem car.

And this is the subsystem of the controller.

The m file for the above system where we include all the parameters of “PI” is

This is the output of the “PI” controller.

As all of u can see here we are not getting a perfect value. This states that the

above system is unstable. This is the major disadvantage for this particular

system. This instability makes this particular system impractical.

1.A speed of 10m/s

2.Rise time should be <5 sec

3.Steady state error of <2%.

The PID controller

Finally we arrive to the PID controller .As the name implies we need to

implement a differential controller to the above “PI” controller.

This is the signal flow graph implemented in the form of a simulink mdl file.

The parameters for the above diagram are driven by this particular m file which

has all the parameters.

When the above files are executed you will get a output of this sort.

Analysis

1.A speed of 10m/s.

2.Rise time should be <5 sec.

3.Steady state error of <2%.

Thus all the design requirements are met through this particular design.

This makes the applications of the electronics in automobiles.

Moreover this particular model is implemented in many of the luxurious cars.

The thing which makes “luxurious” cars “luxurious” is the embedded

electronics in them.

There are many electronic components implemented in the cars like

ABS,ECU and air bag control etc which employs many of the electronic

components and make the automobiles more comfortable, safe and smart.