Designing a Speed Control system of a DC motor based on PID algorithm using MATLAB SIMULINK

DC motors have variable characteristics and are used extensively in variable-speed drives. DC motor can provide a high starting torque and it is also possible to obtain speed control over wide range.
Why do we need a speed motor controller?
For example, if we have a DC motor in a robot and we just apply a constant power to each motor on a robot, then the poor robot will never be able to maintain a steady speed. It will go slower over carpet, faster over smooth flooring, slower up hill, faster downhill, etc. So, it is important to make a controller to control the speed of DC motor in desired manner.
And that’s why we are now interested to design a control system named PID.
Now if we want to define the PID control system,then it will be like this

A block diagram of PID Control system

Now if we want to discuss about the algorithm behind this control system then,it constritutes of three basic part all comes from the following equation:

The Characteristics of P, I, and D Controllers
A proportional controller (

) will have the effect of reducing the rise time and will reduce but never eliminate

the steady-state error. An integral control (

) will have the effect of eliminating the steady-state error for a constant

or step input, but it may make the transient response slower. A derivative control (

) will have the effect of increasing

the stability of the system, reducing the overshoot, and improving the transient response.
The effects of each of controller parameters,

,

, and

on a closed-loop system are summarized in the table

below.
CL RESPONSE

RISE TIME

OVERSHOOT

SETTLING TIME

S-S ERROR

Kp

Decrease

Increase

Small Change

Decrease

Ki

Decrease

Increase

Increase

Eliminate

Kd

Small Change

Decrease

Decrease

No Change

Note that these correlations may not be exactly accurate, because

,

, and

are dependent on each other. In

fact, changing one of these variables can change the effect of the other two. For this reason, the table should only be used as a reference when you are determining the values for

,

and

.

For designing a good controller system the most important concerns are achieving:

----STABILITY
-----TRACKING
----ROBUSTNESS
----DISTURBNESS REJECTION
----OPTIMALITY

PID control system design:

So,here what we have got as the output result:

Here the yellow line representing our desired speed and the purple line represents what we have achieved So if we can see we have achieved a constant speed with both stability & tracking.We have able to minimize etxreme acceleration that will always face without a good controlling system.That’s why here we earned robustness.
So finally we can say,this a good controlling system that we intended to design.

Let’s take a look at the comparison between these two:

Without PID

And here with PID
Here we can easily observe that on the first diagram we have lost robustness,tracking!!!
But on the second we have achieved both one.