1) The document discusses the force-voltage analogy between mechanical and electrical systems. It describes how Newton's laws of motion can be mapped to equations for electrical circuits. 2) Key analogies presented are: force to voltage, mass to inductance, damping to resistance, spring constant to capacitance. 3) Equations of motion for mechanical translational and rotational systems are shown to be analogous to equations for electrical circuits, with positions mapped to charge.

1. Subject :Control Engineering (2151908)
Topic: Force Voltage Analogy
GANDHINAGAR INSTITUTE
OF TECHNOLOGY(012)

2. Content
• Introduction
• Force-Voltage analogy
• Transition System
• Rotational System

3. Introduction
There are two main Electrical analogous system:
1.Force-Voltage analogy
2.Force-Current analogy
Now that we have discussed mechanical system as well
as electrical system. It is worth nothing that exists a
analogy-similarity in their equations.
According to Newton’s law. The applied force will be
used up to cause displacement in the spring.
Acceleration to the mass against the friction force.

4. • According to Newton’s law. The applied force will be
used up to cause displacement in the spring.
Acceleration to the mass against the friction force.
• Apply Laplace Transform we get:
• r(t)= Ms2
Y(S) + s b(s) Y(s) + K X(s)
• This equation is called equilibrium equation of the
Mechanical system.
M
2
t
y t( )
d
d
2
⋅ b
t
y t( )
d
d
⋅+ k y t( )⋅+ r t( )
Force-Voltage analogy

5. The force is analogus to voltage
•v(t) = Ri +L + . dt
put i=
v(t) = R + L + q

6. Force Voltage Analogy

7. • Standard Equation for a Transition system is,
• The following analogies
– r -V
– M - L
– b - R
– k - 1/c
– y -Q
M
2
t
y t( )
d
d
2
⋅ b
t
y t( )
d
d
⋅+ k y t( )⋅+ r t( )

8. • Standard equation for a Rotational system is
T = J (d2
φ/dt2
) B . (dφ/dt)K φ
• The following analogies
– T – I
– J – C
– B – 1/R
– K – 1/L
– Φ – Q