Development of System Models - Manually Calculated System Equations - Mathematics Assignment Help

Assignment Task :

Introduction

The main aims of the computer modelling challenge are twofold; firstly, by completing the challenge you will increase your understanding of the theory and mathematics taught in term 1 by application. Secondly, you will gain experience of using an industry leading mathematical simulation package such as Matlab. All engineering challenge groups have the same challenge to complete although there will be some differences to provide originality in the challenge solutions. The key to successful completion of the challenge will be planning and teamwork. As a group, you need to invest time to properly understand what you have been asked to do and put a plan in place to achieve it. Group members need to agree to this plan and stick to it! When devising your challenge plan, you need to account for... 

• Research 

• Development of system models (hand calculated system equations) 

• Development of computer models (Matlab models) 

• Testing of computer models (time and frequency response testing) 

• Verification of simulation results (comparing simulated results to hand calculated results) 

• Reporting 

Task 1: Manually calculated system equations. 

1. Using the data shown for your group in table 1, lay out your system schematic and develop the system equations symbolically (no component values and no combining components) and calculate all mesh currents by hand. 

For example, if your group is required to have a single voltage source, two meshes, and four resistors, you could lay the system out as follows: 

2. Create a script file in Matlab and enter your system equations. Use the ‘input’ command to ask the user for the required component values. Using the same component values, verify that your numerical model and your Matlab model produce the same results. When verifying that your simulation results match your hand calculated results, you do not need to compare every piece of data calculated. For example, if you had a time base that went from 0s to 10s in 0.01s increments, you would have 1000 calculated data points. When doing your hand calculations, there is no need to calculate all 1000 data points, you could for example, calculate a data point every 0.5s yielding 20 data points. You just need enough hand calculated data points to prove that hand calculated data points match simulated data points along the full time base. 

3. Modify your script file in order that the results of your simulations are conveyed to the user via a string using the ‘sprintf’ command (a text message will be displayed to the user in the command window, the text message will contain numbers which will automatically change depending upon what the system is doing). 

Task 2: Development of system analysis software and GUI. 

4. Using the data shown for your group in table 2, lay out your system schematic. Develop a numerical and Matlab model that establishes the s-domain transfer function for the system. User data entry must be via a GUI. 

5. Develop the Matlab model and GUI in order that it demonstrates transient analysis in response to step and impulse responses. The user must be able enter a suitable time-base and the transient response must be automatically calculated and plotted. Ensure the plots have the correct units and have appropriate titles. Numerically verify that the step & impulse responses calculated by Matlab are correct. 

6. Develop the Matlab model and GUI in order that the stability of the system can be determined for a single value of gain and infinite gain. Numerically verify that the stability (over a range of gain) of the system calculated by Matlab is correct. 

7. Develop the Matlab model and GUI in order that the user can conduct a frequency response test 

upon the system or can determine the magnitude and/or phase for single input frequencies. 

8. Develop the Matlab model and GUI in order that the system can be converted to a state-space model. Conduct simulations to demonstrate that the output of the state-space model is the same as the transfer function; verify numerically. 

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