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DC Motor Modeling & Digital Control

This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation In Slide Show, click on the right mouse button Select “Meeting Minder” Select the “Action Items” tab

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DC Motor Modeling & Digital Control

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  1. This presentation will probably involve audience discussion, which will create action items. Use PowerPoint to keep track of these action items during your presentation • In Slide Show, click on the right mouse button • Select “Meeting Minder” • Select the “Action Items” tab • Type in action items as they come up • Click OK to dismiss this box • This will automatically create an Action Item slide at the end of your presentation with your points entered. DC Motor Modeling & Digital Control .

  2. Project Milestones • Project Proposal • DC Motor Model & Simulations • DC Motor Control Hardware • Digital Circuit Hardware & Software • Xilinx Webpack • Development Board

  3. Project Proposal • Digital DC Motor Speed Controller • Vary a Pulse Width Modulation Signal to change the DC motor speed. • Control Flow Set Point PWM Volts + - Error Digital Controller Motor Driver Motor Motor Used as Tachometer Volts Feedback A/D Converter

  4. Project Schedule • Week Ending June 14 • Preliminary Project Presentation • DC Model and Simulations • Week Ending June 21 • Basic Understanding of Project Board • Pulse Width Modulation VHDL Code • Simulate PWM VHDL Code in ModelSim • Code Static Set Point • Week Ending June 28 • Continue Understanding of Project Board • Download Implementation Code to FPGA • Look at PWM signal using oscilloscope

  5. Project Schedule • Week Ending July 5 • Bread Board Motor Circuitry (Open Loop Only) • Evaluate Open Loop Performance • Output PWM signal to motor driver • Connect Motor to driver • Week Ending July 12 • Model digital controller using DC motor model • Begin VHDL Code of Difference Equation • Simulate Difference Equation • Week Ending July 19 • Bread Board Motor Feedback Circuitry (Closed Loop) • Download Implementation Code to FPGA • Evaluate Closed Loop Performance • Output Error Signal to oscilloscope • Does the Error Signal approach zero

  6. DC Motor Speed Model & Simulations • The electric circuit of the armature and the free body diagram of the rotor describe the DC motor. • The motor torque, T, is related to the armature current, i, by a constant factor Kt. The back emf, e, is related to the rotational velocity by the following equations: where Kt is the armature constant and Ke is the motor constant

  7. DC Motor Speed Model & Simulations • Based on Newton's law combined with Kirchhoff's law the following equations can be derived using the physical parameters: • Physical Parameters • moment of inertia of the rotor (J) = 0.01 kg.m^2/s^2 • damping ratio of the mechanical system (b) = 0.1 Nms • electromotive force constant (K=Ke=Kt) = 0.01 Nm/Amp • electric resistance (R) = 1 ohm • electric inductance (L) = 0.5 H • input (V): Source Voltage • output (theta): position of shaft • The rotor and shaft are assumed to be rigid

  8. DC Motor Speed Model & Simulations • Develop Transfer Functions: • Eliminating I(s) results in an open-loop transfer function, where the rotational speed is the output and the voltage is the input

  9. DC Motor Speed Model & Simulations • Design Requirements: • motor should rotate at the desired speed • steady-state error of the motor speed should be less than 1% • motor must accelerate to its steady-state speed as soon as it turns on. • a settling time of 2 seconds. • an overshoot of less than 10% • A unit step reference input (r) should generate a motor speed output: • Settling time less than 2 secondsOvershoot less than 10%Steady-state error less than 2%

  10. DC Motor Speed Model & Simulations • The step response of the open loop system indicates that when one volt is applied, the motor will only attain 0.2 rad/sec. Also, it takes the motor 7 seconds to reach its steady-state speed; this does not satisfy the 2 second settling time criterion

  11. PID Control & Simulations • PID Control • Adding just a proportional gain of 100 to the uncompensated system produces the following response. ……………… • The steady-state error is approximately 0.95 volts or 5% and the overshoot is about 20%. • The settling time is well within 2 seconds (0.72 sec)

  12. PID Control & Simulations • PID Control • Adding an integral term will eliminate the steady-state error and a derivative term will reduce the overshoot • Let the integral term and the derivative term equal 1. • The response is a very sluggish but does attain zero steady state error after 225 seconds. The gains must be tuned.

  13. PID Control & Simulations • Increase Ki to 100 to reduce the settling time • This integral reduced the settling time to within 1 second. • The overshoot increased to approximately 30% well over the 10% mark. • Increase the derivate gain.

  14. PID Control & Simulations • Increase Kd to 10 to reduce the overshoot.

  15. The discrete control system will be designed by converting the continuous transfer function to a discrete transfer function The c2dm command in Matlab requires the following four arguments: the numerator polynomial (num), the denominator polynomial (den), the sampling time (Ts) and the type of hold circuit. The zero-order hold circuit will be utilized with a sampling time of 0.12 seconds, which is 1/10 the time constant of a system with a settling time of 2 seconds???????? Continuous to Discrete Conversion

  16. Continuous to Discrete Conversion Uncompensated System • The Matlab c2dm conversion results in • S-Plane • Z-Plane

  17. DiscretePID Control & Simulations • Derive the discrete PID controller with bilinear transformation mapping • The c2dm command in Matlab requires the following four arguments: the numerator polynomial (num), the denominator polynomial (den), the sampling time (Ts) and Tustin Method • The closed-loop response of the system is unstable

  18. DiscretePID Control & Simulations • Look at the root locus of the compensated system • rlocus(numaz,denaz) • From this root-locus plot, the denominator of the PID controller has a pole at -1 in the z-plane. We know that if a pole of a system is outside the unit circle, the system will be unstable

  19. DiscretePID Control & Simulations • This compensated system will always be unstable for any positive gain because there are an even number of poles and zeroes to the right of the pole at -1. • Therefore that pole will always move to the left and outside the unit circle • Since that pole comes from the compensator, the location can be relocated

  20. DiscretePID Control & Simulations • This design will cancel the zero at -0.62 • The plot shows that the settling time is less than 2 seconds and the percent overshoot is around 10%. In addition, the steady state error is zero. Also, the gain, K, from root locus is 158.7665. Therefore this response satisfies all of the design requirements.

  21. Costs • List new projections of costs • Include original estimates • Understand source of differences in these numbers -- be ready for questions • If there are cost overruns • summarize why • list corrective or preventative action you’ve taken • set realistic expectations for future expenditures

  22. Technology • List technical problems that have been solved • List outstanding technical issues that need to be solved • Summarize their impact on the project • List any dubious technological dependencies for project • Indicate source of doubt • Summarize action being taken or backup plan

  23. Resources • Summarize project resources • Dedicated (full-time) resources • Part-time resources • If project is constrained by lack of resources, suggest alternatives • Understand that customers may want to be assured that all possible resources are being used, but in such a way that costs will be properly managed

  24. Goals for Next Review • Date of next status update • List goals for next review • Specific items that will be done • Issues that will be resolved • Make sure anyone involved in project understands action plan

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