matlab assignmentMM401 Lecture Slides (Set 1) Assignment 2 Two Parts 1. 2DOF mass-spring-damper...

Question

matlab assignmentMM401 Lecture Slides (Set 1)  Assignment 2 Two Parts  1. 2DOF mass-spring-damper system.  Forced vibration. Phasor analysis  using Excel 2. Modelling of DC electric motor  using Simulink and Matlab.  Submission  • Submit Simulink model and Matlab  code (together in a zipped folder). • Submit Excel workbook.  • Submit report as PDF file. Part 1  • Forced analysis of 2DOF system with  • Two input sinusoidal forces with  same frequencies but different  phases  • Damping  • Modify Phasor Analysis workbook to  analyse system. Part 1  Diagram shows system, where  ?1 = 1 kN/m  ?1 = 200 kg/s   ?2 = 2 kN/m f1(t) Part 1  ?  ?2 = 50 kg/s  ?1 = 55 kg  ?2 = 10 kg  ?1= 4 sin(?? + 60°) N  ?2 ? = 2sin ?? − 155° N  • Adapt Phasor Analysis workbook (checking it carefully  first) to:  • Allow all model parameters to be entered and changed  m 2  m 1  k 2  k 1  c 2 f 2 ( t )  c 1 Part 1  • For the parameters given, calculate and plot amplitudes  and phases of the displacements of both masses  against   ? showing the frequency response clearly  • For the parameters given, calculate and plot the  amplitude of the force in spring ?2 against ?. Be careful!  • Label all plots and include units.  • In report: Part 1  • Draw FBDs  • Write equations of motion  • For specified parameter values, give mass,  damping, and stiffness matrices (i.e. with  numbers)  • Specify clearly how you calculated the  amplitude of the force in the spring.  • Include plots Part 1  • In report:  • You will analyse the difference the phasor analysis makes  to the results. To do that, include equivalent plots for the  situation where the two forces are in antiphase (i.e. where  one force amplitude is negative), and where damping is  zero. That system could be analysed without using phasor  analysis. Compare the two sets of results.  • From the results, discuss the conditions under which a  phasor analysis of the system is required for accurate  results (in a situation where you’re just looking for rough Part 1  estimates of the vibration amplitudes and the maximum  spring force). Part 2  • Small brushed DC electric motor:  • One current through rotating armature, ??,  and one through stator coil, ?? Part 2 ?? = ?? Part 2  ?? = ???  where ? = ?? ?? .  The value of ?  depends on the coil  dimensions.  ? ?? is the magnetic  flux.  Motor properties: Part 2  ?? = 40Ω  ?? = 5mH  ? = 24gcm2  ? = 1× 10−6 Nms/rad  Assume that ?? = 24 V giving ? = 0.058 N ∙ m/A.  • Create state-variable Simulink model  for the system Part 2  • The load torque is ?|?|?, where, for  initial tests, ? = 1 × 10−6 N ∙ m ∙ s2.  • For all tests, start model with system  turned on at ? = 0, and run for 200 s  • You will vary the motor speed in two ways:  • By setting ?? equal to a constant value  between 0 an 24V  • Using Pulse Width Modulation (PWM). Part 2  • Use Pulse Generator block for PWM, with  frequency of 490Hz (as supplied by  Arduino) and amplitude of 24 V. Vary the  pulse width from 0% to 100%  • Measure the motor speed over time, and  find the steady-state speed  • Measure total heat generated in armature  coil (i.e. 0200׬??2????). Part 2  • Test 1:  • Use Matlab code to run model with  constant armature voltage, and plot both  steady-state speed and total heat  generated against ?? for ?? from 0 to 24 V  • Also, plot ?? and ? against ? for ?? = 12V  and ?? = 24V (don’t need to do that with  same code). Part 2  • Test 2:  • Use Matlab code to run model with PWM,  and plot both steady-state speed and total  heat generated against pulse width for  pulse width from 0 to 100%  • Also, plot ?? and ? against ? for pulse width  equalling 50% and equalling 100% (don’t  need to do that with same code). Part 2  • Test 3:  • Create a linearized incremental version of  the model with constant ??, with the  operating point at the steady-state speed  • Plot ?? and ? against ? for ?? = 12V and ??  = 24V (don’t need to do that with same  code).  • Test 4: Part 2  • Change the nonlinear model with constant  ?? by adding a PID controller block (with  default settings) to control speed. Set  desired ? to 100 rad/s. Note that ?? must  be between 0 and 24V (you can use a  Saturation block)  • Plot ??, ?? and ? against ?.  • Test 5: Part 2  • Change model so desired ? is reduced to 10  rad/s, and so that load changes over time with    ? ? = 1 × 10−4 1 + sin ? N ∙ m ∙ s2  • Plot ??, ?? and ? against ?.  • Your report should contain:  • Images of the Simulink models and any Matlab code  used Part 2  • The state variable equations for both the linearized and  nonlinear models, and the derivation of formulas for the  operating point parameters  • Details of the time-stepping methods used and  justification  • A discussion of time stepping for the different tests • The  requested results, with all plots properly labelled • A  discussion of the results from the tests. Submission    – Submit report as a PDF file.   – Submit your Excel workbook

Nihal · Accepted Answer

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MM401 Lecture Slides (Set 1) Assignment 2 Two Parts 1. 2DOF mass-spring-damper system. Forced vibration. Phasor analysis using Excel 2. Modelling of DC electric motor using Simulink and Matlab....

Answer To: MM401 Lecture Slides (Set 1) Assignment 2 Two Parts 1. 2DOF mass-spring-damper system. Forced...

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