CS TRANSNATIONAL MECHANICAL SYSTEM

ADITYA COLLEGE OF ENGINEERING & TECHNOLOGY
Thursday, May 7, 2020
CONTROL SYSTEMS
Presented by
Mrs. RAMA VASANTHA ADIRAJU
Sr.Asst.Professor
Department of Electronics and Communication Engineering
Time: 10.30 AM to 12.00 PMTopic
Mechanical Systems

II ECE- CONTROL SYSTEMS Mrs. RAMA VASANTHA ADIRAJU
Aditya College of Engineering & Technology
Thursday May 7, 2020
• Introduction
• Translational mechanical system
• Rotational mechanical system
• Force – Voltage analogy
• Force – Current analogy
• Transfer function calculation
• Feedback systems
OVERVIEW OF PRESENTATION

• A system which is combination of mechanical components and are controlled
to perform a particular task is called Mechanical system
INTRODUCTION

Mechanical
systems
Machinery in industries
Robotic hand
Automobiles

MECHANICAL
SYSTEM
TRANSLATIONAL ROTATIONAL
TYPES OF MECHANICAL SYSTEMS:
FORCE TORQUE

FORCE Vs TORQUE
FORCE
• To MOVE an
object
• Produces
ACCELERATION
TORQUE
• To ROTATE an
object
• Produces
ROTATIONSVs

FORCE Vs TORQUE
Vs
Symbol Variable Units
θ Angular
displacement
radian
ω Angular
velocity
rads-1
α Angular
acceleration
rads-2
T Torque Newton-metre
Symbol Variable Units
x Displacement Meter
v Velocity ms-1
a Acceleration ms-2
F Force Newton

• Translational mechanical systems move along a straight line.
• These systems mainly consist of three basic elements.
• Those are:
 Mass
 Spring and
 Dashpot or damper.
TRANSLATIONAL MECHANICAL SYSTEMS:

• If a force is applied to a translational
mechanical system, then it is opposed
by opposing forces due to mass,
elasticity and friction of the system.
• They follow Newton's Second Law
of Motion, the algebraic sum of the
forces acting on the system is zero.
TRANSLATIONAL MECHANICAL SYSTEMS:

 Mass is the property of a body, which stores kinetic energy.
 If a force is applied on a body having mass M, then it is opposed by an opposing force due to
mass.
 This opposing force is proportional to the acceleration of the body.
MASS
Assume elasticity and friction are negligible.

DASHPOT:
• If a force is applied on dashpot B, then it is opposed by an opposing force due to friction of
the dashpot. This opposing force is proportional to the velocity of the body.
Assume mass and elasticity are negligible.

SPRING
• Spring is an element, which stores potential energy.
• If a force is applied on spring K, then it is opposed by an opposing force due to elasticity of spring.
This opposing force is proportional to the displacement of the spring.
Assume mass and friction are negligible.

TRANSLATIONAL MECHANICAL SYSTEMS

TF calculation for translational system:
Find the transfer function, X(s)/F(s), for the system
in Figure (a).

SOLUTION:
• Draw the free body diagram
• Place on the mass all forces felt by the mass.
• Assume the mass is travelling toward the right.
• Apply Laplace transform.

SOLUTION:
Apply Laplace transform
The equation in Laplace form is
(Ms2
 fvs  K)X (s)  F(s)

SOLUTION:
Solving for the transfer function
Ms2
 fvs  K
1
F(s)
G(s) 
X (s)

The equation in Laplace form is
(Ms2
 fvs  K)X (s)  F(s)

MECHNAICAL ROTATIONAL SYSTEM:
• Rotational mechanical systems move about a fixed axis.
• These systems mainly consist of three basic elements.
• Those are:
a. Moment of inertia
b. Spring and
c. Dashpot.

 Moment of inertia stores kinetic energy.
 f a torque is applied on a body having moment of inertia J, then it is opposed by an opposing
torque due to the moment of inertia.
 This opposing force is proportional to the ANGULAR acceleration of the body.
Moment of Inertia
Assume elasticity and friction are negligible.

DASHPOT:
• If a force is applied on dashpot B, then it is opposed by an opposing force due to friction of
the dashpot. This opposing force is proportional to the ANGULAR velocity of the body.
Assume mass and elasticity are negligible.

SPRING
• Spring is an element, which stores potential energy.
• If a force is applied on spring K, then it is opposed by an opposing force due to elasticity of spring.
This opposing force is proportional to the ANGULAR displacement of the spring.
Assume mass and friction are negligible.

MECHNAICAL ROTATIONAL SYSTEM:

Electrical Analogies of Mechanical Systems
 Two systems are said to be analogous to each other if the following two conditions are satisfied.
 The two systems are physically different
 Differential equation modelling 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.
 They are
 Force Voltage analogy (F-V)
 Force Current analogy (F-C)

Translational Mechanical
System
F-V analogy F-I analogy
Force(F) Voltage(V) Current(i)
Mass(M) Inductance(L) Capacitance(C)
Frictional Coefficient(B) Resistance(R) Reciprocal of Resistance(1R)
Spring Constant(K) Reciprocal of
Capacitance (1/c)
Reciprocal of Inductance(1/L)
Displacement(x) Charge(q) Charge(q)
Velocity(v) Current(i) Voltage(V)
Electrical Analogies of Mechanical Systems

Electrical Analogies of Rotational Mechanical Systems
Rotational Mechanical
System
F-V analogy F-I analogy
Torque(T) Voltage(V) Current(i)
Moment of Inertia(J) Inductance(L) Capacitance(C)
friction coefficient(B) Resistance(R) Reciprocal of Resistance(1/R)
spring constant(K) Reciprocal of
Capacitance (1/c)
Reciprocal of Inductance(1/L)
Angular Displacement(θ) Charge(q) Magnetic Flux(ψ)
Angular Velocity(ω) Current(i) Voltage(V)

Electrical Analogies of Rotational Mechanical Systems
FORCE-VOLTAGE V L R 1/C I
FORCE-CURRENT I C 1/R 1/L V
TORQUE-VOLTAGE V L R 1/C I
TORQUE-CURRENT I C 1/R 1/L V
Mechanical
System
Electrical
System
MASS
M
SPRING
K
DASHPOT
B
INPUT
FORCE F
/TORQUE T
OUTPUT
DISPLACEMENT
X / ANGULAR
DIAPLACEMENT θ

F-V ANALOGY

FEEDBACK

•If the value of (1+GH) is less than 1, then the overall gain increases. In this case, 'GH' value is
negative because the gain of the feedback path is negative.
•If the value of (1+GH) is greater than 1, then the overall gain decreases. In this case, 'GH' value is
positive because the gain of the feedback path is positive.

Effect of Feedback on Sensitivity
Sensitivity of the overall gain of negative feedback closed loop control system (T) to the variation
in open loop gain (G) is defined as

•If the value of (1+GH) is less than 1, then sensitivity increases.
•If the value of (1+GH) is greater than 1, then sensitivity decreases.
Effect of Feedback on Stability
 A system is said to be stable, if its output is under control. Otherwise, it is said to be unstable.
 In below equation, if the denominator value is zero (i.e., GH = -1), then the output of the
control system will be infinite. So, the control system becomes unstable.
 Therefore, we have to properly choose the feedback in order to make the control system
stable.

CS TRANSNATIONAL MECHANICAL SYSTEM

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