代做EENG20005 Coursework Script Part 4 DC machines调试Matlab程序
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Part 4 DC machines
Summary
Build analytical models of DC machines and evaluating its steady-state and transient-state characteristics.
Learning outcomes
1. Learning how to use Simulink to model a Brushed Permanent Magnet (PM) DC machine and predict its performance.
2. Learning how to model field-wound DC machines and simulate its performance.
3. Analyse, compare, and evaluate the characteristics and output performance of the DC machines.
Tools
MATLAB 2024a and Simulink.
Learning materials
1. An incomplete Simulink model draft.
2. A guidebook for MATLAB - “Matlab_primer”.
3. Tutorial – introduction of Simulink and modelling support.
Case 4A Simulink modelling of brushed Permanent Magnet DC machines
You will be modelling a permanent magnet DC machine using equivalent circuit diagrams and Simulink models and simulating its performance. Fig 3 shows the draft Simulink model that has been provided for you to begin modelling as you progress through the tasks.
(a) Brushed PM DC machines model overview.
(b) Brushed PM DC machines incomplete model draft.
Fig. 3: An incomplete Simulink model draft.
Task 4.1
Draw the equivalent circuit diagram of a brushed Permanent Magnet (PM) DC machine for both steady-state and dynamic-state, and in both cases work out the voltage equations.
Briefly describe each component in both equivalent circuits. Discuss the differences between the two circuits.
Task 4.2
Derive both the steady-state and dynamic-state torque equations for the same brushed Permanent Magnet (PM) DC machine. Describe each component in the torque equation and briefly explain its physical meaning.
Task 4.3
Calculate the no load speed (in revolutions per minute, rev/min or RPM) and stall torque (in Nm) for a permanent magnet DC machine connected to a 50V battery as supply, with the following parameters:
Armature Resistance, Ra = 1Ω
Armature Inductance, La = 2.5 mH
Electro-mechanical Conversion Constant, ke = 2.5 × 10一2 VS rad一1(or Nm A一1)
Rotor mass moment of inertia, J = 0.005 kg m2
Rotor viscous friction constant, B = 0.02 Nm S
You can do these calculations by hand or through MATLAB code.
Task 4.4
Using the incomplete Simulink model provided, build the brushed Permanent Magnet (PM) DC machine. Calculate all the key parameters in the dynamic-state equations of the brushed Permanent Magnet (PM) DC machine by using the parameters given in Task 4.3.
In your report, present screenshots or images of your model, distinctly showing the top-level model, the voltage-current control loop, and the torque-speed control loop (You can refer to Fig. 3 of this document as an example). Briefly discuss how these loops work and the relationships between different variables, such as speed, current, torque, voltage, etc.
Task 4.5
Using the Simulink model built in Task 4.4, simulate the no-load speed and present your simulation result in your report. For this simulation, set the run-time to 20 seconds. Does the no-load speed operating point from task 4.3 correspond to the simulation results? If not, why?
Task 4.6
Using the Simulink model built in Task 4.4, add a varying mechanical load torque that opposes the electro-magnetic torque to simulate the motor having to do some mechanical work. The varying load torque will be a square wave varying from 0 to 0.2Nmwith a time period of 4 seconds. Provide a screenshot of your modified Simulink model. Run your modified Simulink model, and plot the speed and current. Discuss and explain the simulation results; for example, you could discuss the angular speed (ω) curve, the armature current (Ia), and the electromagnetic torque (Tem )) Think of the following questions and discuss your results accordingly:
1. What does the current (Ia) curve look like and why? Discuss how and why its shape changes.
2. What does the angular speed (ω) curve look like and why? Explain the factors impacting the angular speed (ω) and how it changes during the start-up period (dynamic state).
Case 4B Simulink modelling of Wound Field DC machines
You will be modelling a wound-field DC machine using equivalent circuit diagrams and Simulink models and simulating its performance.
Task 4.7
Derive the dynamic equations for a brushed DC machine that has a wound field (rather than a permanent magnet field). Use M as the parameter that is equivalent to the mutual coupling and iF to represent the field current. Use the other parameters such as resistances, mass moments of inertias, coefficient of viscous friction, etc. Please note that these parameters should be consistent with Task 4.1 and Task 4.2). Assume that the machine rotor is infinitely stiff (i.e., no need to model torsional stiffness) and that there is no load torque.
Task 4.8
Calculate the value of the mutual coupling parameter (M) required to achieve a performance same as that of the machine in Task 4.3 (shown below) when the field current is 10A. The DC machine is connected to a 50V battery supply.
1- Armature Resistance, Ra = 1Ω
2- Armature Inductance, La = 2.5 mH
3- Electro-mechanical Conversion Constant, ke = 2.5 × 10一2vS rad一1(orNm A一1)
4- Rotor mass moment of inertia, J = 0.005 kg m2
5- Rotor viscous friction coefficient, B = 0.02 Nm S rad一1
Task 4.9
Use the equations from Task 4.7 to convert your PM brushed DC machine Simulink model into a wound field brushed DC machine model. Provide screenshots of your Simulink model.
Task 4.10
Use the equations from Task 4.7 to predict how the no-load speed will change if you reduce the field current to 5A in the steady state. Calculate the new stall torque with this configuration. Validate this using your Simulink model and discuss your results.
Case 4C Case Study of a Wound Field DC machine.
In this case, you will be using both Simulink modelling and simulation techniques and theoretical calculation to study and evaluate a wound field DC machine. A separately excited DC motor delivers rated torque at a rated speed of 600 rpm and has the parameters indicated below:
- Rated output power = 1500 kW.
- Rated Supply Voltage (for both wound-field and armature) = 600 V.
- Rated Armature Current = 2650 A.
- Rated Field Current = 83 A.
- Armature Resistance = 0.003645Ω .
- Armature Inductance = 0.1 mH.
- Rotor Co-efficient of Viscous Friction = 15 Nm s rad-1.
Tasks 4.11 to 4.15 are related to this.
Task 4.11
Case Description:
Determine the machine’s torque constant and hence derive the mutual inductance of the machine at rated conditions. You can do this either by hand calculations or through MATLAB code.
Task 4.12
Calculate the machine’s efficiency at rated conditions. You can do this either by hand calculations or through MATLAB code.
Task 4.13 (Advanced Task)
Plot a steady-state torque speed curve/envelope for this machine up to 1500 rpm. For this, use a MATLAB code instead of a Simulink model. Discuss your results.
Task 4.14 (Advanced Task)
Plot an efficiency curve for the machine when it is supplying maximum torque at each speed over the speed range given in Task 4.13. For this, use a MATLAB code instead of a Simulink model. Discuss your results.