Anna University,Regulation 2017,EEE,IC -8451-CONTROL SYSTEMS

1. IC 8451&CONTROL SYSTEMS
Department of Electrical and Electronics Engineering
Approved by AICTE | Affiliated to Anna University | Accredited by NAAC | Accredited NBA | Recognized by UGC under 2(f) and 12(B)
Chennai Main Road, Kumbakonam- 612 501.
ARASU ENGINEERING COLLEGE
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Prepared by
Mrs.K.KALPANA.,M.E.,(Ph.D.).,
Department of Electrical and Electronics
Engineering

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 Electrical Analogous of mechanical rotational systems
 There are two types of electrical analogies of rotational mechanical
systems. Those are torque voltage analogy and torque current analogy.
 Torque Voltage Analogy
 In torque voltage analogy, the mathematical equations of rotational
mechanical system are compared with mesh equations of the electrical
system.
Rotational Mechanical System Electrical System
Torque(T) Voltage(V)
Moment of Inertia(J) Inductance(L)
Rotational friction coefficient(B) Resistance(R)
Torsional spring constant(K) Reciprocal of Capacitance
(1/c)
Angular Displacement(θ) Charge(q)
Angular Velocity(ω) Current(i)

4.  Torque Current Analogy
 In torque current analogy, the mathematical equations of the
rotational mechanical system are compared with the nodal
equations of the electrical system.
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Rotational Mechanical System Electrical System
Torque(T) Current(i)
Moment of inertia(J) Capacitance(C)
Rotational friction coefficient(B) Reciprocal of Resistance(1/R)
Torsional spring constant(K) Reciprocal of Inductance(1/L)
Angular displacement(θ) Magnetic flux(ψ)
Angular velocity(ω) Voltage(V)

5.  Analogous elements in Torque voltage analogy
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Analogous elements in Torque current analogy

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 EXAMPLE PROBLEM 1
 Write the differential equations governing the mechanical system shown in
fig. Draw the torque voltage and torque current electrical analogous circuits
and verify by writing mesh and node equations.
 The free body diagram of J1 is shown in fig. The opposing Torques are TJ1,Tb1,
Tk1

8.  The free body diagram of J2 is shown in fig. The opposing
Torques are Tj2,Tb2, Tk1, Tk2
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9.  Torque voltage analogous circuit
 The electrical analogous elements for the elements of mechanical
systems are
T- e(t), J1 -L1, J2 -L2 , B1-R1, B2-R2, K1-1/C1, K2-1/C2
 The mesh equations are
 Torque -voltage analogous circuit
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10.  Torque current analogous circuit
 The electrical analogous elements for the elements of
mechanical systems are
T - i(t), B1 - 1/R1, B2 - 1/R2 , J1 - C1,J2 -C2, K1 - 1/L1, K2 - 1/L2
The node equations are
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11.  Torque current analogous circuit
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12.  EXAMPLE PROBLEM 2
 Write the differential equations governing the mechanical
system shown in fig. Draw the torque voltage and torque
current electrical analogous circuits and verify by writing
mesh and node equations.
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13.  The free body diagram of J1 is shown in fig. The opposing
torques are marked as TJ1, Tb1, Tk1
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Free body diagram of J2 is shown in fig. The opposing Torques are marked as
Tj2 , Tb1, Tb2 & Tk1.

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The free body diagram of J3 is shown in fig. The opposing torques are marked as
Tj3, T b2 and Tk3

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TORQUE VOLTAGE ANALOGOUS CIRCUIT
MESH EQUATIONS

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TORQUE VOLTAGE ANALOGOUS CIRCUIT
TORQUE CURRENT ANALOGOUS CIRCUIT

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NODE EQUATIONS
TORQUE CURRENT ANALOGOUS CIRCUIT

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HOME WORK PROBLEM
Write differential equations governing mechanical system shown in fig. Draw
torque voltage and torque current electrical analogous circuits and verify by
writing mesh and node equations.