In the feedback system of Fig. 1, the dynamical model of a laser tracking system

In the feedback system of Fig. 1, the dynamical model of a laser tracking system G(s) is given by
G(s) = 48/s(s
2 + 12s + 48),
where time is in seconds, and output position is measures in meters. A unit step command or
disturbance represents a position change by 1 [m], and unit ramp presents a slope of 1 [m]/sec.
You task is: 1) to design a suitable controller C(s) that meets prescribed requirements given
below, and verify the feedback system’s performance by Matlab simulation(s).
• no steady-state error in tracking ramp commands;
• step-command response with settling time of no more than 2.8 [sec], and overshoot of no
more than 14%;
• rise times (10%-to-90%) of no less than 0.3[sec]; respectively;
• deviation in position of no more than 0.06 [m] during transient response to unit step disturbances, with 2% settling time of no more than 2.5 [sec].
Note that rise time limit ensures that feedback system’s response is not excessively fast, potentially
leading to saturation in electronics, mechanical or hydraulic components. If your design cannot
meet one or more of the objectives and you settle on a suitable trade-off, this has to be clearly
explained with relevant Matlab simulations. In other words, the listed objectives include some
that are absolutely restricted, as noted by either the specification language, or digits of prescribed
limits. Round off to the no. of digits in prescribed limits is acceptable, e.g., specification of 6.05
[sec] in settling time is met by ts ≤ 6.054..
Project Report Preparation Guidelines
The word document describes IEEE Tech Report style that also includes some required sections. These and other suggested sections listed below should convey the following information:
• Abstract: One or two paragraphs, giving a concise overview of the project and objectives,
and a brief summary of the achieved performance of the designed system.
• Introduction: more detailed overview of the project with some relevant background that is
necessary to understand the project requirements, goals and the approach. (This should be
in text form; no equations).
• Technical Background: detailed technical background and all information relevant to the
design process.
• Analysis and Design: most important section of the project, where you clearly show the
thought process in approaching the design problem; for example, how specifications led you
to the initial proper controller selection, perhaps intermediate designs, and the eventual
result. You should also convey how you decided on various adjustments to your design in
order to achieve the objectives.
• Experiments and Results: where you give and describe all simulations/results that support
your analysis and design.
• Summary and Conclusions: summarizing your work and the final design, as well as any
conclusion from the project.
Pay special attention to the overall organization of the report, and follow the IEEE technical
report guidelines as closely as possible. Read your report after writing it for typos, spelling
and grammar errors, incomplete sentences, etc. The grading of your report is weighted equally
according to the technical contents and writing style. Below are pointers to some do’s and don’ts
(based on previous years’ project reports).
• Use we or passive form, instead of I; e.g., instead of “I am supposed to design a system . . . ,”
say “We are supposed to design a …. . . . ,” or “In this project, a feedback system is to be
designed . . . .”
• Number your equations, and refer to them by number, as necessary. Introduce equations,
as soon as they are described. Avoid talking about an equation in some paragraph, and
give it much later (e.g., in the next one).
• All figures and tables should be properly numbered, labeled, and have detailed captions
to describe what is presented, e.g., “Figure 1: Block diagram of the feedback system with
given plant model and controller to be designed based on prescribed objectives.” Shouid be
properly referenced by figure number; e.g., “For the feedback system in Fig. 1, the system
G(s) is given by
G(s) = 1
s(s
2 + 3s + 1).
They do not have to be in the body of the report, and can be placed at the end. If within
the body, they should preferably appear on the top or bottom of the same or next page,
when first referenced in the text.
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• Bad Habit to avoid: Absolutely avoid making figures part of a sentence. So many times,
I have graded reports that say” The block diagram of the feedback system is ” and they put
the block diagram right below the sentence. Instead, you should say “The block diagram
of the feedback system is shown in Fig. 1,” and give Fig. 1 preferably somewhere on the
same/next page, or at the end of the report, with proper caption as explained above.
• The report should not contain detailed mathematical derivations. These should/could be included as supporting documents in numbered appendices. For example: With a proportional
controller C(s) = K, the transfer function of the feedback system, derived in appendix 1, is
T(s) = K
s
3 + 3s
2 + s + K
.
In the appendix, you may include derivations of the form:
T(s) = G(s)C(s)
1 + G(s)C(s)
=
k
s
3+3s
2+s
1 + k
s
3+3s
2+s
=
k
s
3 + 3s
2 + s + k
.
• With exception of detailed derivations in the appendices, you should use complete sentences
throughout the report even when using equations or mathematical expressions ; e.g., “The
transfer function of the system is
T(s) = K
s
3 + 3s
2 + s + k
,
where the gain K would be chosen to optimize the speed of response.”
• Avoid long run-on or convoluted sentences. The following 2 example have been taken from

Three Common Grammar Errors to Avoid

1. Long run-on sentence: ”The novel has lengthy descriptions of the passionate emotions
or confusion a character feels internally, while that is great for readers of the story, the
screenwriter is going to have to come up with a way to explain those emotions in a
visual manner without the extra prose description to help the audience follow along.”
To convey the same information properly, use conjunctions correctly and/or split the
run-on sentence into multiple related sentences:
”The novel has lengthy descriptions of the passionate emotions or confusion a character
feels internally, which is great for readers of the story. However, the screenwriter is
going to have to come up with a way to explain those emotions, in a visual manner
without the extra prose description, to help the audience follow along.”
2. Convoluted sentence: When, in situations like this, the communication requires a degree of formality, it only requires such a style to the degree in which it is requested;
otherwise, one runs the risk of writing in a manner that requires excessive concentration
from any given reader and thus obscures the original intent.
Instead, you would say: “It is sometimes necessary to use formal communication styles,
but only to a certain degree. Otherwise, the writing might distract from the actual
point of the writing.”
For project 1, consideration will be given for the fact that English is not the native language
of some students, and inexperience in technical report preparation. However, students should
carefully read and follow the above guidelines as closely as possible.
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