Control Engineering
(2151908)
G-14
Equivalent Mechanical circuits
Prepared by:- 130110119005
 The equivalent mechanical network is drawn as follows:1. Total number of nodes=Total number of Displacements=
Total number of masses
2. Take one reference node in addition to represent the ground
line(or reference)
(a) Mass has only one displacement x(t). Connect it between
the node x and the reference node.
(b)Spring and Damper have two possible displacements x1 (t)
And x2(t). Connect these elements between x1(t) and x2(t) or
between x1(t) and the reference node.
4. Draw the nodes and connect the different elements
accordingly
5. The excitation to the system f(t) is represented alongwith the
direction at the appropriated node where it is acting.
6. Apply the usual method of nodal analysis (as in KCL) and
develop the system equations at each node using Newton’s third
law of motion
Example 1
Mechanical translation system. Consider the spring
-mass-dashpot system shown in Fig. . Let us obtain
the transfer function of the system
(
7
.
7
)
by assuming that the force F(t) is the input and the
displacement y(t) of the mass is the output.
Example 2
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Seismograph.
figure shows a schema of seismograph. A seismograph indicates
the displacement of its case relative to the inertial reference. It
consists of a mass m fixed to the seismograph case by a spring of
stiffness k , b is a linear damping between the mass and the case.
Let us define:
xi = displacement of the seismograph case relative to the inertial
reference (the absolute frame)
x0 = displacement of the mass m within the seismograph relative
to its case
y = x0 – xi = displacement of the mass m relative to the case.
Note that y is the variable we can actually measure.Since gravity
produces a steady spring deflection, we measure the
displacement x0 of mass m from its static equilibrium position.
Considering xi as input an y as output, the transfer function is
Example 3
Multivariable mechanical system.
Consider the system shown in Fig. We assume that
the system, which is initially at rest, has two
inputs F1(t) and F2(t) and two outputs x1(t) and x2(t).In
this problem we would like to demonstrate formulation
of a multivariable system transfer-function description.
where the transfer-function matrix
The equations describing the multipole diagram model
of the system given in are
F1
1 b1 + sm1 + k1/
s
2
–b1
–b1
b1 + sm2 + k2/
s
F2
–1
–1
Example 4
Dynamic Vibration Absorber
• A dynamic vibration absorber consists of a mass and an
elastic element that is attached to another mass in order to
reduce its vibration. The figure is a representation of a
vibration absorber attached to a cantilever support
Example 5
• Rolling Machine:
• A model of a commercial rolling machine
(for metals processing) has been created
and is shown above.
• The model comprises a cylinder with a
mass, m, with a radius, r that spins about
an axle. The cylinder rolls without slip on
the lower surface.
• Attached to the axle housing are a
damper (b) , a spring (k) and a force
source( f).
Cont.
• From MATLAB, plotting TF for step input, we
get,