what does derivative and integration means in real world

embpic

Joined May 29, 2013
186
i get confuse in the term of derivative and integration. as this topic studied in college but cant relate with real life.
means where this terms actually use.

MrChips

Joined Oct 2, 2009
19,373
The simplest usage of derivative and integration is in their application to speed (velocity) and distance traveled.

derivative = differentiation = difference = change

If a car's speed changes from 60mph to 62mph in 1 second, the change is 2mph per second. This is the derivative of the speed. The car is accelerating at 2mph/s.

integration = integral = total = sum

If we were to record the speed of the car at each second, how far does the car travel from time 20 second to time 22 second? We integrate.

Suppose the speed of the car is steady at 60mph.

60mph = 88 feet per second.

The car travels 88 feet in the first second and 88 feet in the second second.
Total distance traveled in the 2-second interval is 176 feet.

What happens if the car is accelerating from 60mph to 62mph during the 2-second interval?
What is the distance traveled during that 2-second interval?

To keep the calculation simple,

suppose in the first second the average speed is 88 feet per second. Distance traveled is 88 feet.

Suppose in the second second the average speed is 90.9 feet per second. Distance traveled is 90.9 feet.

To find distance traveled we integrate the speed over the duration of interest.
Distance traveled is 88 + 90.9 = 178.9 feet.

In summary,

integration = sum
derivative = difference

WBahn

Joined Mar 31, 2012
24,848
The derivative is a measure of how much one thing changes as some other thing changes.

Speed is a measure of how much position (distance) changes as time changes, so it is the derivative of position with respect to time. As you go up in altitude, the air pressure changes. How much it changes with a particular change in altitude is the derivative of pressure with respect to altitude.

Integration is simply a totalizing or summing process.

The amount of water added to a bucket is the sum of all the water added to it since the bucket was last empty. Mathematically, this is the integral of the flow rate into the bucket over time. The total lift of the wings on a plane is the air pressure difference between lower and upper surfaces integrated over the total area of the wings.

Roca

Joined Apr 18, 2014
3
The simplest usage of derivative and integration is in their application to speed (velocity) and distance traveled.

derivative = differentiation = difference = change

If a car's speed changes from 60mph to 62mph in 1 second, the change is 2mph per second. This is the derivative of the speed. The car is accelerating at 2mph/s.

integration = integral = total = sum

If we were to record the speed of the car at each second, how far does the car travel from time 20 second to time 22 second? We integrate.

Suppose the speed of the car is steady at 60mph.

60mph = 88 feet per second.

The car travels 88 feet in the first second and 88 feet in the second second.
Total distance traveled in the 2-second interval is 176 feet.

What happens if the car is accelerating from 60mph to 62mph during the 2-second interval?
What is the distance traveled during that 2-second interval?

To keep the calculation simple,

suppose in the first second the average speed is 88 feet per second. Distance traveled is 88 feet.

Suppose in the second second the average speed is 90.9 feet per second. Distance traveled is 90.9 feet.

To find distance traveled we integrate the speed over the duration of interest.
Distance traveled is 88 + 90.9 = 178.9 feet.

In summary,

integration = sum
derivative = difference
Well, I wish someone explained it to me like you did, when I was on my first courses. Totally agree with that.

embpic

Joined May 29, 2013
186
sir i have again little doubt that what is action of Integral, derivative in PID action.

tshuck

Joined Oct 18, 2012
3,535
PID uses the error to determine what value should be applied to the controlled device(plant) to make the input minus the feedback quantity equal to zero (indicating the controlled parameter is at the commanded input).

A PID controller uses the error (current error, rate of change of the error[derivative], and accumulated error[integral]) multiplied by some constant values($$k_{p}$$, $$k_{d}$$, & $$k_{i}$$) to determine the output parameter. In tuning a PID, one selects the $$k_{p}$$, $$k_{d}$$, & $$k_{i}$$ to accomplish the controller requirements (e.g. rise time, overshoot, response type, etc.)

In digital systems, the derivative is no more than the difference between the current error and the previous error, where the integral is the current error added to previous errors.