Intuition
on Control Theory, Engineering and Systems Review w.r.t. Electrical and
Mechanical Application
The design of a
control mechanism as a realm is unique and demanding as is profoundly rooted in theory and the engineering
aspect to achieve the desired; control objective.
An engineer is required to articulate theoretical
techniques in the analysis of the
behavior of a system about input, system
dynamics and feedback approach. The ultimate aim corresponds with the ability of
output to follow design reference
specification successfully. Simply, an error is the basis for control
that is achieved through comparison of an output signal to design reference
(one approach). The error signal is feedback as input to the system
hence brings current output much closer
to the reference point. That is control
engineering.
Control
systems may be used in mechanical or
electrical systems. For efficiency of motion in electrical drives, mechanical
moving parts, and other electrical
systems. Over the ages, the design techniques have evolved and new fronts
achieved. In that regard, understanding the fundamentals of electrical and
mechanical systems are imperative features for a control engineer. What is the
merge point? Is there a smooth handshake between control systems with the electrical or mechanical system?
Control engineers acknowledge measurement, comparison,
computation and effecting the correction action. For example, a solar system which has interesting compenene ts that must work together. For more information, visit this site. That is more of control
engineering, but first, let us analyze
the contents making up control theory. Major branches summarize to linear and
nonlinear control. There are typically open-loop or closed loop control types. In addition, during engineering schemes
analysis, interfacing approaches add Single-Input-Single-Output (SISO) and
Multiple-Input-Multiple-Output (MIMO) into the works. Control theory cannot be regarded as complete without a study to analyse techniques into observability,
controllability, and stability.
Classical control theory has evolved to modern control
approaches. Classical control makes use of differential equations in defining
systems while modern control attracts the use of state space and matrices. Differential
equations are handy in modelling systems, studying the responses, yet, are
complex in analyzing responses to varying inputs. To counter the complexity, a
transformation into s-domain and z-domain make manipulation easier to process. Taking
an example, when analyzing a system described by sinusoids and its response to
impulse is a complex but determinable problem. Consider the input
and system
described by
which is
a convolution process. When Laplace transforms is performed on the function,
the convolution can be carried out as simple multiplication of the input and
the system properties.
Where A, B, C and D are a representation of
state,
input, output and transition matrices respectively. At this point, worthy to note is that solutions to the control
system in the time domain are complex and hence need for Laplace
transformation into the s-domain and the z-domain. More on that later.
The application of control systems is in electrical and
mechanical systems. For that reason, it is must understand fundamentals of the electrical and mechanical system. Electrical
engineering is composed of electrical power systems, electronics, and electromagnetics. Fundamentally, the movement of
charge makes electricity. Yes, the flow of the charge then makes electric
current. This paper won’t say much about Direct and Alternating Current (DC and
AC). Accurately, studied and stood the test of time, is Ohm’s law;
Where R, Resistance
I, Current
V, Voltage
Also, consider the power equation,
Where P, Power
I, Current
E, Voltage
Combination of Ohms’ law and power equation;
Designing the controllers from and for such electrical systems,
require a grip on this laws. Motor, generators, transformers and of course, there are others. Motor and generators
are both mechanical and electrical in operation. They transform from one energy
domain (electrical) into another (mechanical) and vice versa. They are very
handy tools.
You need to adore the following definition of mechanical
engineering;
If
it needs engineering, but it doesn’t
involve electrons, chemical reactions, the arrangement
of molecules, life forms, isn’t a
structure (building/bridge/dam), doesn’t move nor fly, a mechanical engineer
will take care of it but….
If it does involve electrons, chemical reactions, the
arrangement of molecules, life forms, is a structure, does move, fly, a mechanical engineer
may handle it.
Perfect! Did you get motion from the definition? Ignore the
others for now. Designs for moving parts and the help of others to move is the
integration point where control systems are
engineered. What to move, when to move, how to move is answered by the
control engineer. When the idea of motion is brought out, Newton’s laws of
motion presents itself.
You are right; it is the
second law. This is at its basic state
but during the design of mechanical
systems and their control mechanism, complex relations, say mass-spring-damper
system;
Or the motion of a bicycle, are derived and used in analyzing
the system. More on this later.
Open loop and closed loop control
Consider that control theory has aspects of the control loop. In that respect, and so far, two
types are fundamentally open loop and
closed loop control. The control action in open loop technique is independent of the process output. Also
referred to as non-feedback control. Having no
acknowledgment of the output, open loop control mechanism has no ability
to self-correct in the case of errors.
Sometimes adrift in preset values may
thus lead to larger deviations. It renders the design ineffective to handle
disturbances and cannot reliably complete the
desired task.
The transfer function for the linear system;
Assuming that a linear system is represented by the equation
below
Performing Laplace transformation on the system
Characteristics consistent with open loop control mechanism are
o
Does not offer comparative approach to
actual and required output
o
The settings for each input produces a
fixed point in controller operation
o
Disturbances of any level do not
necessarily affect the output automatically/directly
o
Has no self-regulation with regard to the
output value
o
Output is neither measured nor fed back
The drawbacks evident from open loop control require external
attention from an operator. It introduces anticipatory control so that the user
takes action to correctively control the process
before it deviates. Termed as feedforward control is the manual open
loop control able to react before the error occurs.
I hope you have not forgotten that we are reviewing control
theory/techniques. Computation of transfer function is accomplished when
initial conditions are equivalent to zero. In addition, note that transfer
function is considered the Laplace Transform of the impulse function.
Rationality of the function of a linear system holds true.
A rational function has its denominator d(s) (characteristic equation) and numerator
n(s) as polynomials,
Consider that G(s) is proper in the condition that
And G(s) is strictly proper in that condition that m<n, while
the difference n-m is the relative degree of the
transfer function. Poles are
the roots of d(s) while zeros are
roots of the n(s). A point to keep in mind here is that the poles and zeros location of the transfer function G(s) does determine the
behavior of the linear system completely. We will review the concept of
stability of equilibrium points using poles location more at an in depth later.
On the other hand, control action considering closed loop
control type is influenced by the process
output. Referred to as feedback control. Control theory brings on board the
feedback control which influences states and output of the process/dynamic
system. It is superior compared to open loop as the output is fed back to be input to the process and hence, closing the
loop.
That is too much theory. Is it? Yes. The goal of an engineer in
designing a control system, recall, is to measure, compare, compute and
correct. Measurement and comparison is consistent with closed loop control. The
supporting notion here is that with feedback, we are able to accurately control
a dynamic process. The difference between the measurement output and the
desired value reveals the error used in corrective control. It comes very handy
during external disturbance of the process as the design allows achieving and
maintaining of a desired output automatically through making comparison with a
measured output.
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G2
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G3
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G4
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Comparator
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H
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Input output
Feedback
loop
The main characteristics of closed-loop control are:
o
Ability to reduce errors automatically by
adjusting the systems input.
o
Improves systems stability.
o
Capable of increasing or reducing
sensitivity of a system.
o
Enhances robustness considering
disturbances/dynamic state of a process.
o
Capable of reliable, repeatable and
accurate performance.
The illustrations above may seem misleading because they are
rather simple. The design has to achieve some complexity due to dynamics in the
real world. Sensitivity of the controller is a factor to articulate or may lead
to instability. Instability causes oscillation of the controller and eventual
break. For an engineer to predict the issues that may ensue from the design,
considering the control specification is mandatory. They range from stability
specification, rejection of disturbance (step and other classes), time-response
(rise time, overshoot, and settling time). Robustness is a criteria in frequency
domain for consideration. An advise for
the engineers to keep in mind, regards the fact that, in cases where one does
not know what they require and does not develop a document on it, the result is
whatever someone else thinks they require.
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H(s)
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G(s)
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Comparator
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Where ;
U(s)-reference input,
H(s)-compensator
transfer function,
G(s)-plant
transfer function,
E(s)-error
signal,
Y(s)-output
Consider the following combination
Note that,
represents the closed loop system design,
while
represent the sensitivity transfer function.
The designer ought to ensure that
to
make
. The transfer function
and
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G(s)
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Comparator
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H(s)
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