Hi,

This question has been studied in the past and recently revised, please take a look at attached file.

Best regards

Well, in the PID controller,

1. If the output is directly proportional to the error, then it is termed as proportional (P) controller,

2. If the output is proportional to the differentiation of the error, then it is called as derivative (D) controller and

3. If the output is proportional to the integral of the error, then it is called as integral (I) controller.

Similarly, in the Electrical circuit analogy,

1. If voltage is directly proportional to the current flowing, then it represents resistive load (Rs),

2. If voltage is directly proportional to the derivative of the current flowing, then it represents inductive load (L) and

3. If voltage is proportional to the integral of the current flowing, then it represents capacitive load (C).

In the mechanical analogy,

1. If stress is directly proportional to the strain, then it represents the spring load (S),

2. If stress is directly proportional to the derivative of the strain, then it represents damper load (Dm) and

3. If stress is directly proportional to the integral of the strain, then it represents complaint load (Cm). [It is usually represented for viscoelastic material by fractional order models]

So if we frame a mapping among these analogies, we will get

(output, error, P, D, I) = (voltage, current, Rs, L, C) = (stress, strain, S, Dm, Cm)

I hope it will be helpful.

A hydraulic cylinder's movement depends on integral of flow. So it can be used as integral term of a PID controller mechanically

Refer the below journal.

i work based on below journal regard optimization of pID controller