Mechanical translational rotational systems and electrical analogous circuitsin control systems

Mechanical Translational & Rotational
Systems and Electrical analogous Circuits in
control systems
Presented by
Mr. C.S.Satheesh, M.E.,
Assistant Professor, Department of EEE,
Muthayammal Engineering College (Autonomous),
Namakkal (Dt), Rasipuram – 637408
MUTHAYAMMAL ENGINEERING COLLEGE
(An Autonomous Institution)
(Approved by AICTE, New Delhi, Accredited by NAAC, NBA & Affiliated to Anna University),
Rasipuram - 637 408, Namakkal Dist., Tamil Nadu, India.

Electrical analogy of mechanical and thermal
systems
 Two systems are said to be analogous to each other if the following
two conditions are satisfied.
1. The two systems are physically different
2. Differential equation modeling of these two systems are same
 Electrical systems and mechanical systems are two physically
different systems.
 There are two types of electrical analogies of translational
mechanical systems.
1. Force voltage analogy and
2. Force current analogy.

Mechanical Translational systems
 Mechanical Translational systems can be obtained
by using three basic elements
1. Mass
2. Spring
3. Dash-pot

Analogous electrical elements in force voltage analogy for the
elements of mechanical translational system.
In force voltage analogy, the mathematical equations of translational
mechanical system are compared with mesh equations of the electrical system.
 Force, f = Voltage, e
 Velocity, V = current, i
 Displacement, x = charge, q
 Frictional coefficient, B = Resistance, R
 Mass, M=inductance, L
 Stiffness, K = Inverse of capacitance 1/C
 Newton‘s second law à Kirchhoff‘s voltage law.

Analogous electrical elements in force current analogy for the
elements of mechanical translational system.
In force current analogy, the mathematical equations of the translational mechanical
system are compared with the nodal equations of the electrical system.
 Force, f à current, i
 Velocity, V à Voltage, e
 Displacement, x à flux, Ф
 Frictional coefficient, B à Conductance, G =1/ R
 Mass, M à capacitance C
 Stiffness, K à Inverse of inductance, 1/L
 Newton‘s second law = Kirchhoff‘s current law.

Analogous electrical elements in torque voltage analogy for
the elements of mechanical rotational system.
In this analogy, the mathematical equations of rotational mechanical system are
compared with mesh equations of the electrical system.
 Torque, T = Voltage, e
 Angular Velocity, ω =current, i
 Angular Displacement, θ =charge, q
 Frictional coefficient, B = Resistance, R
 Moment of Inertia, J = inductance, L
 Stiffness of the spring, K = Inverse of capacitance 1/C
 Newton‘s second law = kirchhoff‘s voltage law.

Analogous electrical elements in torque current analogy for
the elements of mechanical rotational system.
 Torque, T = current, i
 Angular Velocity, ω = Voltage, e
 Angular Displacement, θ = flux, Ф
 Frictional coefficient, B = Conductance, G =1/ R
 Moment of Inertia,J = capacitance C
 Stiffness of the spring, K = Inverse of inductance, 1/L
 Newton‘s second law = kirchhoff‘s current law.

Force Balance Equation Of An Ideal Mass, Dashpot And
Spring Element.
Let a force f be applied to an ideal mass M. The mass will offer an opposing force
fm which is proportional to acceleration.
f= fm = M d2X/dt2
Let a force f be applied to an ideal dashpot, with viscous frictional coefficient B. The
dashpot will offer an opposing force fb which is proportional to velocity.
f= fb = B dX/dt
Let a force f be applied to an ideal spring, with spring constant K. The spring will offer
an opposing force fkwhich is proportional to displacement.
f= fk = K X

Mechanical translational rotational systems and electrical analogous circuitsin control systems

 The Speed of DC motor is directly proportional to armature voltage
and inversely proportional to flux in field winding.
 In armature controlled DC motor the desired speed is obtained by
varying the armature voltage. This speed control system is an electro-
mechanical control system. We will discuss transfer function of armature
controlled dc motor.
 The electrical system consists of the armature and the field circuit but
for analysis purpose, only the armature circuit is considered because the
field is excited by a constant voltage
Transfer Function of Armature Controlled DC Motor:

The mechanical system consist of the rotating part of the motor and
load connected to the shaft of the motor. The armature controlled DC
motor speed control system is shown in the below figure.

Transfer Function of Field Controlled DC Motor:
The speed of a DC motor is directly proportional to armature
voltage and inversely proportional to flux. In field controlled DC motor the
armature voltage is kept constant and the speed is varied by varying the flux
of the machine.
Since flux is directly proportional to field current, the flux is varied
by varying field current. Here we will learn derivation of transfer function
of field controlled dc motor.
The speed control system is an electro-mechanical control system.
The electrical system consists of armature and field circuit but for analysis
purpose, only field circuit is considered because the armature is excited by a
constant voltage.

The mechanical system consists of the rotating part of the motor and the
load connected to the shaft of the motor. The field controlled DC
motor speed control system is shown in the below figure. For this field
controlled DC motor we shall find transfer function.

References :
 A.Nagoorkani, Control Systems,
RBA Publications.
51

Mechanical translational rotational systems and electrical analogous circuitsin control systems

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