School of Computing, Creative Technologies and Engineering Assessment Brief MAIN COURSEWORK Module name and CRN Mathematical Modelling and Simulation 21408 Module Leader Bal Singh Semester B Level 4 Approx. No of Students 30 ASSIGNMENT TITLE: Modelling and Analysis of Engineering Systems ASSIGNMENT WEIGHTING: 100% (% of Module Marks) HAND-OUT DATE: Jan 2016 SUGGESTED STUDENT EFFORT: 144 hours SUBMISSION DATE: ● Assignment 1: Sunday 05 March 2017 11:59 pm ● Assignment 2: Sunday 07 May 2017 11:59 pm SUBMISSION INSTRUCTIONS: ● VLE upload, NOTES: The usual University penalties apply for late submission. Submission of an assignment indicates that you, as a student, have completed the assignment yourself and the work of others has been fully acknowledged and referenced. By submitting this assessed work, you are declaring that you are fit to submit, and you will therefore not normally be eligible to submit a request for mitigation for this work. For further information, please refer to your course handbook or University Assessment Regulations. FEEDBACK MECHANISM: ● Typed feedback via VLE LEARNING OUTCOMES ADDRESSED BY THIS ASSIGNMENT: On successful completion of this module, students will be able to: ● Demonstrate an understanding of mathematical modeling of commonly used dynamic systems ● Use computer tools for the analysis and simulation of dynamic systems. 2 DETAILS OF THE ASSESSMENT Overview: This module aims to develop students’ proficiency in analysing and modeling dynamic systems in real life and industrial context. The focus will be to use computer tools to understand dynamic system behaviour under various signal excitation conditions. Assignment 1: A written report on first 4 lab experiments (40 marks) Deadline: Sunday 05 March 2017 11:59 pm During first five weeks of the module, you will be introduced to dynamic systems commonly used in electrical and electronic systems. You will obtain transfer functions of such systems using the State Space modelling technique. Matlab will be used to examine the response of each system to various excitation signals. Detailed instructions will be handed out for each of the lab experiments. You will model and analyse the following 4 systems: 1. First order systems consisting of resistive and capacitive elements 2. First order systems consisting of resistive and inductive elements 3. Second order systems consisting of resistive inductive and capacitive elements 1 4. Second order systems consisting of resistive inductive and capacitive elements 2 For each of the above circuit configurations, you will perform the following tests: ● Transient response: You need to apply a step input to the State Space model and observe the system output. The analysis should be performed for a time period long enough for the system to reach the steady state. ● Frequency response: You need to apply a range of frequencies at appropriate voltage level to the State Space model and observe the system output. The analysis should be performed at least 1 decade below and 2 decades above the resonant frequency of the system. Your report should include the discussion of system behaviour for each case and their relevance to real life applications. In particular you should discuss: ● The settling time and its significance. ● -3 dB point on the frequency response curves and its significance. ● The slope of the frequency response and its interpretation. ● The effect of cascading two systems together. In your report, you must also include circuit diagrams, system equations, State Space representation of each system, input/output plots and commented Matlab code for performing tests. 3 Assignment 2: A written report on the following projects (60 marks) Deadline: Sunday 07 May 2017 11:59 pm Part 1 For this exercise you will design, model and test a switch mode power supply filter using the skills you have gained in the first assignment and other course modules. The following figure shows the filter section of a switch mode power supply where V1 can be assumed to be a DC switched waveform between 0 and 12 V. First calculate the component values for L1 and C1 for the following operating conditions: ● Output voltage = 5 V ● Maximum load current = 20 A ● Allowable inductor ripple current = 2 A ● Switching frequency = 100 kHz Obtain a State Space model for the circuit perform transient, frequency sweep and steady state analyses. Document your results to demonstrate that they meet the design specification. It is rarely possible to find exact same value components as calculated in your design. It is normally an engineering compromise and commercially available components of nearest preferred values are substituted. Look in suppliers’ catalogues to identify suitable nearest value components and run your test again to see that the performance is not severely compromised. In our earlier design, we assumed the inductor and capacitor to be ideal; having no internal impedance. In practice, however, these components have finite internal equivalent series resistance values. Find these values from the manufacturer’s datasheets and modify your circuit model. Run the analysis again and explain clearly how these parameters affect the system performance. 4 Part 2 Phase angle control is a technique used to control the voltage across a given load in order to control the power delivered to it. The following figure shows a simple arrangement where the firing angle (phase angle) of the thyristor SCR is controlled to control the voltage across the load R1. The input voltage V1 is 240 V at 50 Hz and the load resistor R1 has a value of 10 Ω. Write a Matlab program to simulate the behaviour of this control scheme to plot the load voltage for phase angles of 0, 15, 30, 45, 90, 105 and 135 degrees. Extend the Matlab code to calculate and plot Total Harmonic Distortion in the load current as a function of the thyristor phase angle. Explain the effect of such control system on the current drawn from mains. Modify the circuit to include an appropriate value of inductance in series with the load to minimise the line current harmonic content. Recalculate the THD in the line current and explain how the inductor is affecting this. Can you suggest a better control system? MARKING SCHEME The marking scheme is at the end of this document. LATE SUBMISSION OPPORTUNITIES Students who fail to submit assessments by the prescribed date without good cause shall be penalised as given below: ● 1 to 9 days late: 5% of the possible total mark will be deducted from the mark achieved by the student for every day on which the work remains un-submitted. ● 10 days late or more: a mark of zero will be recorded. “Days” include weekdays and vacations, but exclude weekends, bank holidays and other days when the University is closed. REASSESSMENT and DEFERRAL OPPORTUNITIES Reassessment Component 1: 5 If your result for the whole of Component 1 is recorded as Non-Submission or your mark for Component 1 and for the whole module is below 40%, you will have opportunity to take reassessment with a submission date of 7 July 2017 and your mark capped at 40% (see Reassessment information below). If you are granted deferral through the mitigation process, you may complete the reassessment in July 2017 with a full range of marks available. For component 1, you need to submit a written report for the analysis and simulation of the following dynamic systems: 6 For each of the above circuit configurations, you will perform the following tests: ● Transient response: You need to apply a step input to the State Space model and observe the system output. The analysis should be performed for a time period long enough for the system to reach the steady state. ● Frequency response: You need to apply a range of frequencies at appropriate voltage level to the State Space model and observe the system output. The analysis should be performed at least 1 decade below and 2 decades above the resonant frequency of the system. Your report should include the discussion of system behaviour for each case and their relevance to real life applications. In particular you should discuss: ● The settling time and its significance. ● -3 dB point on the frequency response curves and its significance. ● The slope of the frequency response and its interpretation. 7 ● The effect of cascading two systems together. In your report, you must also include circuit diagrams, system equations, Sate Space representation of each system, input/output plots and commented Matlab code for performing tests. Refer to lecture slides and tutorial worksheets to get additional support. Reassessment component 2: If your result for the whole of Component 2 is recorded as Non-Submission or your mark for Component 2 and for the whole module is below 40%, you will have opportunity to take reassessment with a submission date of 8 July 2016 and your mark capped at 40% (see Reassessment information below). If you are granted deferral through the mitigation process, you may complete the reassessment in July 2016 with a full range of marks available. Part 1: You are required to design, model and test a switch mode power supply filter using the skills you have gained in the first assignment and other course modules. The following figure shows the filter section of a switch mode power supply where V1 can be assumed to be a DC switched waveform between 0 and 12 V. To generate a waveform in Matlab, we would need a sampling interval fast enough to minimise errors in synthesised waveform. Our switching frequency is 100 kHz which results in a switching period of 10 µs. If we take 10 samples in each cycle, our sampling interval will be 1 µs. ● Using Matlab, create a time vector from 0 s to 100 µs in increments of 1 µs. ● Create a square wave of 12 V amplitude using this time vector [Hint: v = 12*square(2*pi*f*t)] ● Iterate through the waveform to remove the negative part of the waveform ● Repeat this for the duty ratios calculated above [Hint: v = 12*square(2*pi*f*t, Duty_Ratio) where Duty_Ratio is a value between 0 and 100] 8 ● Calculate the mean value of the waveform in each case. Does it tie up with your calculations? Converter Design First calculate the component values for L1 and C1 for the following operating conditions: ● Output voltage = 5 V ● Maximum load current = 20 A ● Allowable inductor ripple current = 2 A ● Switching frequency = 100 kHz Some of the parameters are available but we will use our engineering judgement to specify the missing ones. For example, we will assume that: ● The allowable ripple current on the output cap is 0.5 V Using these parameters: 1. Calculate the value for the load resistance (vo/Io=5/20) 2. Using the skills learned so far, calculate the inductor and capacitor values. Refer to Week 7 lecture slides for more info. 3. Obtain a state space model for the converter 4. Use step and bode functions to obtain appropriate responses 5. Use a PWM signal to plot the output voltage. For this, you need to use the lsim function: y=lsim(a,b,c,d,v',time); [v’ transposes v]. 6. Plot y using: figure(1) subplot(211),plot(time,y(:,1)),title('Buck Converter - Inductor Current'); subplot(212),plot(time,y(:,2)),title('Buck Converter - Output Voltage'); Part 2: Phase angle control is a technique used to control the voltage across a given load in order to control the power delivered to it. The following figure shows a simple arrangement where the firing angle (phase angle) of a triac is controlled to control the voltage across the load R1. The input voltage V1 is 240 V at 50 Hz and the load resistor R1 has a value of 10 Ω. 9 Where V1 = 100*sin(2**50*t) and R1 = 10 . In this system, the conduction of a sinusoidal input is delayed for a given period between 0 and waveform half cycle time period. By doing this, the energy delivered to the device is controlled. The resulting waveform looks like the one shown below for a given delay angle: This waveform will contain a fundamental component at the input frequency but also higher frequency harmonics. To quantify the harmonic distortion, we will calculate Total Harmonic Distortion or THD in the resulting waveform. To calculate the harmonic distortion, we need to calculate the power delivered into the load. The power in a given load is given by: Where I is the root mean square or RMS value of the current. To obtain the RMS value: ● Square the function ● Take the mean value ● Take the square root 10 Note: More of this is covered in this week’s lecture. Let us first verify our theory by evaluating the THD in a pure sine wave. Since a pure sine wave contains on ONE harmonic, there shouldn’t be any distortion. Create a sine wave using: fs = 10e3; ts = 1/fs; t=0:ts:0.02-ts; i=100*sin(2*pi*50*t); figure(1),plot(i), grid on Next, calculate its RMS value using: >> Irms=sqrt(mean(i.*i)) Irms = 70.7107 THD by definition is given by: 𝑇𝐻𝐷= (𝐼𝑟𝑚𝑠!−𝐼1𝑟𝑚𝑠!) 𝐼1𝑟𝑚𝑠 ×100 Where Irms is the RMS value of the complete waveform and I1rms is the RMS value of the fundamental component. Calculate the RMS value of the fundamental component. Using: >> I=fft(i)/length(i); >> I1rms=2*abs(I(2))/sqrt(2) I1rms = 70.7107 Next, calculate THD using: >> THD = sqrt((Irms^2-I1rms^2))/I1rms*100 THD = 0.0000 No surprise here, no distortion results in 0 THD. Let’s introduce some distortion and observe THD: fs = 10e3; ts = 1/fs; t = 0:ts:0.02-ts; i = 100*sin(2*pi*50*t); for n=1:length(i)/4 i(n)=0; 11 i(n+length(i)/2)=0; end This should generate a waveform as shown below: Calculate the THD the same way: Irms=sqrt(mean(i.*i)) I=fft(i)/length(i); I1rms=2*abs(I(2))/sqrt(2) Irms = 50.4975 I1rms = 42.5061 THD = 64.1371 Is this acceptable? Carry out literature searches to answer this question. Next, create waveforms for delay angles of 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 and 165 degrees. Calculate the THD in each case and plot it as a function of the delay angle. This should go into your report. Thinking about the filters analysed in your previous assignment, can you suggest a solution to filter out some of the harmonics? Use the function lsim to pass a distorted waveform through such a filter to improve the current waveform. Refer to the following source to propose a suitable solution: http://rfemcdevelopment.eu/en/emc-basics/conduced-emissions 12 MARKING SCHEME Outstanding (80%+) A mark of 80% or above is awarded to those students who begin to critique the current/existing framework and propose alternative ways to find an innovative solution. They will present these solutions by providing justification supported by evidence from authoritative sources. Excellent (70%+) A mark of 70% or above is awarded to those students who demonstrate extensive and relevant practice to carry out assignment tasks and demonstrate an outstanding grasp of theoretical concepts. You will have demonstrated an evidence of extensive research done in order to relate the assignment tasks to real life applications. You will also have extensively evaluated the capabilities and limitations of computer tools used for the simulation and analysis of engineering systems. Very good (60-69%) A mark of 60% to 69% is awarded to those students who demonstrate appropriate practice to carry out assignment tasks and demonstrate a good grasp of theoretical concepts. You will have demonstrated an evidence of relevant research done in order to relate the assignment tasks to real life applications. You will also have evaluated the capabilities and limitations of computer tools used for the simulation and analysis of engineering systems. Good (50-59%) A mark of 50% to 59% is awarded to those students who demonstrate relevant practice to carry out assignment tasks and demonstrate a reasonable grasp of theoretical concepts but there may be there may be gaps in knowledge. You will have demonstrated an evidence of relevant research done in order to relate the assignment tasks to real life applications. You will also have evaluated the capabilities and limitations of computer tools used for the simulation and analysis of engineering systems. Satisfactory (40-49%) A mark of 40% to 49% is awarded to those students who will have attempted to carry out assignment tasks and demonstrated some grasp of theoretical concepts. You will have demonstrated some evidence of research done in order to relate the assignment tasks to real life applications. You will also have carried out some evaluation of the capabilities and limitations of computer tools used for the simulation and analysis of engineering systems. Fail (<40%) A mark of less than 40% is awarded to those students who will have demonstrated a little effort to carry out assignment tasks and demonstrated a limited grasp of theoretical concepts. There is a little or no evidence of research done in order to relate the assignment tasks to real life applications. A very little or no evaluation of the capabilities and limitations of computer tools used for the simulation and analysis of engineering systems. Unsatisfactory (<30%) A mark of less than 30% is awarded to those students who will have demonstrated very little effort to carry out assignment tasks and demonstrated a no grasp of theoretical concepts. There is no evidence of research done in order to relate the assignment tasks to real life applications. A very little or no explanation of any analytical work carried out.