Find the transfer function for system

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Reference no: EM132174943

I. Assessment Requirements

In this course work (CW) you may use the concepts you learned during your lectures and your laboratory works together with your ability in performing further research in bringing more details if necessary. In your report, provide the answers to the following questions:

II. Assessment Details

I. Provide your understanding about Proportional (P), Integral (I) and Derivative (D) analogue controllers, their differences, advantages, and disadvantages. Then, clarify why their combinations, such as in PID controllers, can be useful.

II. Based on your understanding from the lecture notes, your laboratory practice, by further research, and with the help of a block diagram, explain how a PID temperature control system works.

III. A digital control system has the following difference equation:

y[n] = 2.0 x[n] - x[n-1] + 1.2 y[n-1] - 0.48 y[n-2]

a. Find the transfer function H(z) for this system.
b. Draw the digital Circuit for H(z)
c. Use MATLAB to draw the pole-zero diagram for the above system.
d. Use MATLAB to derive and plot the impulse response of the system.
e. With the help of MATLAB find and explain the response of the system to the input x[n]=(1-0.5e-n)u[n], where u[n] is a step function. What is the steady- state solution, i.e. when n becomes very large.

IV. Use MATLAB to design a 4th order lowpass Butterworth digital filter with a bandwidth of 0.35 (normalised with respect to Πfs). Then,
a. Find the parameters of the equivalent analogue filter through bilinear transformation considering a sampling frequency of 10 Hz.
b. What are the passband and stopband frequencies of both analogue and digital Butterworth filters.
c. Draw the pole-zero diagram of the digital filter.
d. Apply the input x[n] = 2sin(10Πt) + 5cos(24Πt) to the system and comment on the output. Use frequency response to enhance your conclusions.

V. This question is to investigate the stability of analogue and digital systems.
a. Provide the conditions for stability of the systems in both analogue and discrete (digital) domains.
b. Consider the following three analogue systems and comment on their stability:

i. H(s) = s/(s+0.2)
ii. H2(s) = 1/(s2 + 1)
iii. H3(s) = (s - 1)(s2-0.4s-0.05)

c. Convert all above filters into discrete (digital) domain using sampling frequency of 1 Hz and

i. Impulse invariant transformation
ii. Bilinear transformation

Draw the pole-zero diagrams, and comment on the stability of the equivalent digital systems.

d. Use MATLAB, find the impulse and unit step responses of the digital system, draw the outputs, and comment on the shapes of the responses.

VI. Consider the following analogue plant

H(s) = 2/(s + 0.8)

a. Convert H(s) to the equivalent digital system using bilinear transformation using a sampling frequency of 10 Hz. Draw the pole-zero diagram, impulse response, and frequency response of the system.

b. Control the analogue plant using the following feedback system.

1276_figure.jpg


Consider G(s) to be a constant K; Drive Y(s)/R(s) and determine for what range of K values the system remains stable. Y(s) and R(s) are the s-transform of y(t) and r(t) respectively.

c. Using a sampling frequency of fs = 2 Hz and for the two values of K = - 0.3 and K = - 0.5 determine the equivalent digital systems using bilinear transformation.

d. Draw the pole-zero diagram for the two digital systems in Part c and discuss on the overall stability of each system.

e. Find the unit step response of the two systems in part c. and explain about the steady-state response if any.

Verified Expert

The project is about the pole zero location to predict the stability. It also explains the design of a Butterworth filter. The s plane is mapped on to the z plane by means of impulse invariant and bilinear transformation.All are simulated in matlab and corresponding matlab plots are shown.This helps to predict the stability of a system.

Reference no: EM132174943

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Reviews

inf2174943

12/24/2018 1:07:58 AM

6) a) Frequency response of the system. b)Consider G(s) to be a constant K; Drive Y(s)/R(s) and determine for what range of K values the system remains stable. Y(s) and R(s) are the s-transform of y(t) and r(t) respectively. d)discuss on the overall stability of each system. e)Find the unit step response of the two systems in part c.and explain about the steady-state response if any. 3)b) Draw the digital circuit for H(z) 4) d)comment the output. Use frequency response to enhance your conclusions. 5)d) Comment on the shapes of the response 6)c)determine the equivalent digital systems using bilinear transformation. please add more references. The solution which has been provided to me was very easy to understand. The guidance provided to me was accurate and it justify the topic as well.

inf2174943

12/24/2018 1:07:40 AM

all the lecture notes on you email In question no 1) Difference 3) b) Draw the digital circuit for H(z) e)What is the steady- state solution, i.e. when n becomes very large. 4) when B.W =0.35 a) explain bilinear Transformation considering Sampling Frequency of 10Hz d)Apply the input x[n]=2sin(10?t)+5cos(24?t)to the system and comment the output. Use frequency response to enhance your conclusions. 5) d. UseMATLAB,find the impulse and unit step responses of the digital system, draw the outputs, and comment on the shapes of the responses.

len2174943

11/23/2018 4:37:03 AM

References & Sources of Information - Range of academic and current business and management references - Citing and referencing sources. A wide range of good quality academic sources have been used, including academic journal articles, books, trade publications, websites, company sources, and reputable data Referencing and citations are accurate throughout. Some good quality sources of information have been used, including at least one academic paper from a reputable journal. The student has clearly not just relied on what they can find on the Internet. References have been drawn from some good quality sources (reputable websites, books, newspapers) but there are no references from academic journals. There are some referencing / citing errors. Only poor quality (e.g. Wikipedia or similar) or no references have been included.

len2174943

11/23/2018 4:36:57 AM

Presentation of report English – Style, spelling, grammar graphs, tables, Literate and appropriate to content. Excellent use of tables and figures for illustrations * Enjoyable to read and of publishable standard Generally correct, but some minor grammar / spelling errors. Good use of tables and figures for illustrations A number of spelling / grammar errors – obvious reliance on automatic spell checker. Limited use of tables and figures for illustrations Difficult to read, with some incoherent sentences. Many errors. No tables or figures.

len2174943

11/23/2018 4:36:51 AM

Critical Evaluation Critical evaluation and discussion of the key issues impacting on the The motives of the study are analysed/evaluated with insight. Analysis is supported by Analysis/evaluation is made in a thoughtful way with attempts to refer to published works to The issues are described, but no critical analysis/evaluation is made. Analysis is purely There is no analysis/ evaluation at all, and all that is described are the student’sCritical Evaluation Critical evaluation and discussion of the key issues impacting on the The motives of the study are analysed/evaluated with insight. Analysis is supported by Analysis/evaluation is made in a thoughtful way with attempts to refer to published works to The issues are described, but no critical analysis/evaluation is made. Analysis is purely There is no analysis/ evaluation at all, and all that is described are the student’s Critical Evaluation Critical evaluation and discussion of the key issues impacting on the The motives of the study are analysed/evaluated with insight.

len2174943

11/23/2018 4:36:21 AM

Analysis of research using lab work Understanding of actual operating conditions and practical performance analysis A clear understanding of the purpose of the lab work and how it can be used to buttress research findings with respect to performance analysis. Correct conclusions are drawn. *The level of understanding beyond expectations. Good understanding of research and lab work. Some attempts have been made to use published works in analysis of lab tasks. Satisfactory understanding of wireless communications performance analysis. Limited reference to published work to support what is written. Lack of understanding of the relevance of network performance measures. Lack of support with published materials.

len2174943

11/23/2018 4:36:15 AM

Range of technologies covered Quantity and quality of background research, analysis of key information, number of wireless technologies covered in report All key topics have been included, with meaningful analysis of each in the context of the assignment. Correct analysis and comparison of at least 3 different wireless technologies * The module topics have been included in an integrated way, rather than just different sections. All of the key topics have been included, with thorough analysis for most. Correct analysis and comparison of at least 2 different wireless technologies Most of the key topics have been included, but the analysis for some may be incomplete or superficial. Limited analysis and comparison of about 2 wireless technologies Many of the key topics may not be included or the paper is written in such a way that it is not clear which module topics are included. Only one technology mentioned and no form of comparison

len2174943

11/23/2018 4:36:06 AM

Class/grade Assessment criteria Distinction (Excellent) Commendation (Very Good) Pass (Good) Fail (insufficient) Grade/ Comment *Exceptional Distinction High C Mid C Low C High P Mid P Low P Marginal fail Mid Fail Low Fail High D Mid D Low D Abstract and Introduction General overview and understanding of wireless technologies Clear and fact based introduction to the investigation, knowledge of area of application and current technical challenges experienced with use of technology. Research gaps The introduction clearly describes the investigation, good knowledge of area of application and current technical challenges experienced with use of technology. Enough information about the investigation. Some knowledge of wireless technologies and applications. It is not clear about the rationale for the investigation, poor understanding of wireless communications.

len2174943

11/23/2018 4:35:57 AM

A summary of key points: ? This is an individual assignment ? Need to submit a Technical report ? An electronic copy of the report (in WORD document) must be uploaded to the module dropbox in NOW not later than 4pm 3rd 8.

len2174943

11/23/2018 4:35:50 AM

As an engineer, you are required to submit a well-structured technical report detailing the process and outcomes of the above research. The good practice of citations and referencing must be evident throughout the report. The Harvard referencing system should be used. The marking scheme: ? In this course work you need to answer all the questions precisely. They have more or less the same mark weightage. ? Each question has 15% of the total 100% mark. ? 10% of the mark will be given to presentation, clarity, writing style, consistency in format particularly for the list of references. ? Mark will be deducted for over-size (more than 13 pages; 12 pages for the content and 1 covering page) submissions. ? Mark will be deducted for late submissions accordingly. Zero mark will be given to those submitted more than 3 days after the deadline.

len2174943

11/23/2018 4:35:44 AM

Students are expected to show knowledge of underlying principles of wireless communication while demonstrating the ability to undertake research and critically analyse information. They are also to demonstrate ability to use results from practical experiments/lab work in buttressing research findings. Wireless technologies are used in different industrial, private and public sectors and are also certified mainly by the IEEE standards. Students are expected to demonstrate knowledge of these standards and the report should include industries or sectors where chosen wireless technologies are predominantly used, analysis of difference between advertised performance and practical operating conditions.

len2174943

11/23/2018 4:35:38 AM

The assignment is designed to provide an opportunity for students to engage in reflective learning through a process of research and peer interaction, while allowing individuals to demonstrate their level of knowledge and understanding in the subject area. Students are expected to demonstrate a good understanding of the key topics associated with the assignment. The report should include evidence of background research and critical appraisal of relevant articles and case studies. Attempts should be made to gather information from a range of sources (book, journals, magazines, newspaper articles, internet etc) with proper acknowledgement.

len2174943

11/23/2018 4:35:27 AM

Citing and Referencing You may need to carry out independent research into the technologies you are analysing. You can use sources which are noted in the module content/module recommended textbook, but you should not use exactly the same data. If references are included in your work – including information sourced from the Internet - you must cite them appropriately in your work

len2174943

11/23/2018 4:34:32 AM

SUBMISSION REQUIREMENTS: Reports: Use font 11pt Calibri, written on one side of A4 only, single spacing. Harvard referencing system must be used. Page limit: Strictly 12 sides maximum (in total including figures and references). You may add a covering page for information about your name, student number, module name, etc.

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