Assignment on Dynamics and Control

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Dynamics and Controls
Student’s Name
Institutional Affiliation
Date

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Table of Contents
Abstract................................................................................................................. 2
Introduction........................................................................................................... 2
System modeling................................................................................................... 5
Experiments........................................................................................................... 7
Discussion.............................................................................................................. 7
Conclusion............................................................................................................. 8
References............................................................................................................. 9
Abstract
This laboratory exercise investigated the control systems used in electronic devices and ways
of making control systems more stable.
Introduction
Vibrations can be defined as to and fro motions that occur about a central point
known as equilibrium (Findeisen, 2013). Vibrations are necessary for some applications
while in others, they are undesirable as they produce noise and other unwanted effects.
Vibrations in mechanical structures dissipate energy which lowers productivity and
sometimes introduces a risk component (Mori, 2017). This laboratory exercise will
demonstrate the necessity of damping vibrations and how control systems can be utilized to
control vibrations in mechanical systems. In this exercise, two different devices including
ECP model 205 and ECP model 210 will be used as aweel as the necessary software.
Control systems are encountered in many engineering fields, from electrical systems
to mechanical systems (Srikant, 2010). Control systems whether electrical or mechanical may
be classified into open-loop control and closed-loop control systems. Systems in which the
output signal does not affect the input signal are known as open-loop control systems (Nise,
N.S., 2010). In closed-loop control systems, part of the output is sampled and compared with

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the input signal to produce an error signal which is used to drive the system. This is known as
"feeding" back the output signal to the input. In this way, the system closely monitors the
output to ensure that any error introduced by external or internal factors is kept at a
minimum. There are two types of feedback namely negative feedback and positive feedback.
Negative feedback involves subtracting the sampled output from the reference signal (input)
while in positive feedback, the two are summed up (DiStefano, Stubberud and Williams
2012). However, negative feedback is used in most systems since positive feedback often
makes the system unstable.
A control system monitors the process variables which are the parameters of the
system which need to be kept in control. For example, the temperature of a furnace may be
maintained at the desired value using a control system that detects a rise or a fall in
temperature and adjusts the fuel input rate. The difference between the reference value and
the process variable (error signal) is used by the controller or compensator to keep the output
close to the set value (DiStefano, Stubberud and Williams 2012).
An open-loop system cannot reject any disturbances that may be introduced into the
system and cannot improve the response of unstable systems (Ahmad and Hasan 2014). A
closed-loop system, on the other hand, can reject most disturbances that may be introduced
into the system and can improve the stability of systems. Examples of closed-loop control
systems include car cruise control in which the velocity of the car is the controlled variable
and the control variable is the mixture of fuel and air (Levine 2018). Another example is
aircraft in which parameters such as the aircraft's pitch, yaw, and roll have to be controlled by
the control surfaces such as the rudder, ailerons, and flaperons to maintain the aircraft's static
and dynamic stability (Nise 2010).

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In this exercise, two experimental models including the ECP model 210 and ECP
model 205 are used. The ECP model 210 is a rectilinear apparatus. Some of the
characteristics of this model include trajectory tracking and regulation, inflexible body PID
control, phase and gain margins, lead/lag compensators and control for high order collocated
and non-collocated systems. The system also shows the primary features of flexible systems
such as natural frequencies, mode shapes, frequency, and transient responses. It also exhibits
both generic vibrations and lumped parameter dynamics. Other features of the model include
movable air damping, flexible masses, and exchangeable springs. Additionally, the model
exhibits a rigorous arrangement of vibrations and dynamics experiments incorporating both
one degree of freedom systems and higher order flexible systems.
The ECP 205 is a torsional model with a wide range of important practical systems,
including rigid bodies. Other features include coupled discrete vibrating systems both
collocated and non-collocated actuator control as well as flexible drive chains. The model has
three disks support by vertically suspended shafts that are torsionally flexible. The shafts are
then suspended on friction-resistant ball bearings. To alter the inertia of the discs, sliding
brass weights are incorporated. The shaft is connected through a rigid belt and pulley system
that is driven by a brushless servo motor. The angular displacement of the first disk is
measured using an encoder located at the shaft’s base. The angular displacements of the other
two disks are measured using two different encoders. This system agrees well with analytical
models and is very reliable and robust in the dynamics field.
Applications of open and closed-loop systems
Open-loop systems

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i) Electric bulb: the working of the electric bulb depends on the supply of an electric
current and is not affected by the bulb’s temperature and other environmental
parameters
ii) Cloth dryer: this is also an open-loop system since it only depends on the number
of clothes being dried. For instance, if the dryer is set to operate for 30 minutes, it
will stop after 30 minutes regardless of whether the clothes are dry.
Closed loop systems
i) Washing machine: This system has controllers to maintain the temperature of the
water, the drum speed, and the water level. The system has indicators to alert the
operator if any parameter diverges.
ii) Thermostat: This is a device that maintains a constant temperature in a room or a
house. The system constantly checks the temperature level and adjusts the heating
system if there is any deviation from a set value
System modeling
The rectilinear model features two to three trolleys connected using a spring and a damper
mechanism such as a dashpot connected to one of the trolleys. However, in this exercise,
electronic controls were substituted for the damping mechanism. The system is shown below.

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This system can be modeled using newton’s second law of motion yielding the following 1-
degree of freedom differential equation with m being the mass of trolley, k the stiffness
coefficient and c the damping coefficient,
m ̈x + c ̇x+ kx=F (t)
The transfer function on taking Laplace transforms becomes,
m s2 X (s)+ csX ( s)+kX ( s)=F (s)
X ( s )
F ( s) =
1
m
s2+ ( c
m ) s+ ( k
m )
For the torsional dynamic model, the equation of motion is still given by Newton’s second
law, with the linear parameters replaced by angular ones,
J ̈θ+c ̇θ=T (t )
Where T (t) is the torque generated by the dc motor, J is the moment of inertia of the disk
and θ is the angle of rotation of the disk.
J s2 θ (s )+ csθ( s)=T ( s)