Evaluation copy. Propeller-Powered Pendulum. Project PROJECT DESIGN REQUIREMENTS

Transcription

1 Propeller-Powered Pendulum Project 11 A pendulum is a weighted object suspended from a pivot point. As a pendulum moves, it swings out in a circular arc moving back and forth in a periodic motion. A pendulum usually operates under the influence of gravity; but in this Project, you will use a motorized propeller to power the pendulum s motion. The spinning blades of a propeller cause a pressure differential on the front and back surfaces resulting in a force that moves the object through the air called thrust. Propeller blades are attached to their hubs at an angle or pitch, much like the threads on a screw. Propeller blades are also twisted. When the propeller is spinning, each section of the blade travels at a different velocity, but the twist in the blade is meant to provide uniform lift along the length of the blade making for a more efficient propeller. PROJECT DESIGN REQUIREMENTS Build a physical pendulum driven by a DC motor, a propeller, and a digital controller. You should attach the motor and propeller to the end of a long bar. The Vernier Rotary Motion Sensor will be used for mounting the bar at its pivot point and for measuring the angle of the bar s swing. You will use the Vernier Digital Control Unit (DCU) to power the motorized propeller and initiate the swing of the bar. The program should pulse the power on and off as needed to keep the bar swinging. For safety reasons, you should limit the range of your bar s swing to approximately ±20. The bar angle should be displayed on the front panel, but the bar s motion should be controlled totally by the program. Evaluation copy Engineering Projects with NI LabVIEW and Vernier Vernier Software & Technology P11-1

2 Project 11 MATERIALS SensorDAQ, LabQuest, or LabQuest Mini LabVIEW computer USB cable Vernier Digital Control Unit (DCU) LabQuest or LabPro power supply Vernier Rotary Motion Sensor DC motor propeller jumper wires long metal bar (approx 50 cm) ring stand rod clamp rod ADDITIONAL MATERIALS (SENSORDAQ ONLY) Vernier Digital Proto Board Connector breadboard PROJECT SETUP Construct the propeller device 1. Connect a propeller to the shaft of a DC motor. 2. Connect the motor to the end of a long bar so that the motor shaft is perpendicular to the bar (see photo above). 3. Insert a rod through the mounting hole of the Rotary Motion Sensor and tighten the thumb screw. 4. Mount the rod to a ring stand with a rod clamp so that the shaft of the Rotary Motion Sensor is parallel with the ground. 5. Mount the long bar to the Rotary Motion Sensor about one-third of the way up from the motorized propeller. Note: If necessary, pre-drill a 1/8 hole in the bar to accept the thumb screw. 6. Connect the Rotary Motion Sensor to the first DIG channel on the interface. 7. Connect the interface to the computer. Connect the motor to the DCU 1. Plug the 9-pin cable into the socket on the side of the DCU. 2. Wire the motor to the DCU cable as shown in the figure below. You can find the color-coded pin-out for the DCU cable on the label attached to the cord. Figure 1 Wiring diagram for DCU-controlled circuit 3. Connect a power supply to the DCU. P11-2 Engineering Projects with NI LabVIEW and Vernier

3 Propeller-Powered Pendulum Connect the DCU to the interface SensorDAQ (See below if you are using LabQuest or LabQuest Mini) 1. Insert a Vernier Digital Proto Board Connector into a breadboard. 2. Wire the Digital Proto Board Connector to the SensorDAQ screw terminal using jumper wires as shown in the figure below. Figure 2 Digital Proto Board Connector pin-out to SensorDAQ screw terminal 3. Plug the DCU into the Digital Proto Board Connector. Note: The digital output lines of the screw terminal are on by default. You may have to disconnect the DCU, or power from the DCU, until you run the program for the first time. 4. The Rotary Motion Sensor should remain connected to the DIG channel on the side of the SensorDAQ. LabQuest or LabQuest Mini 1. Connect the DCU to channel DIG2 on the side of the LabQuest or LabQuest Mini. 2. The Rotary Motion Sensor should remain connected to channel DIG1. PROJECT BACKGROUND INFORMATION In this Project, you will write a LabVIEW program to make a driven physical pendulum. You can use the Digital Express VI (found in the Vernier functions palette) to monitor angle readings from the Rotary Motion Sensor to provide feedback and to maintain an acceptable swing range. You can power your motorized propeller with the Vernier Digital Control Unit (DCU). The DCU is an electronic device that allows you to control up to six digital output lines for on/off control of motors and other DC electrical components. The DCU plugs into one of the digital connections on the interface and is powered by a separate DC power supply. A 9-pin D-sub socket cable with bare wires on one end is supplied with the DCU for use in building projects. There are connections for all six digital lines, plus a power connection and two ground connections. The color code of the wires is identified on a label attached to the cable. Always keep the power limitations of the DCU and your DCU power supply in mind. You should not exceed 1000 ma total. Engineering Projects with NI LabVIEW and Vernier P11-3

4 Project 11 Controlling the DCU (SensorDAQ) If you are using a SensorDAQ, you must control the DCU from the screw terminal (screw terminal 1) using the DAQ Assistant Express VI. When the DAQ Assistant (located in the Measurement I/O DAQmx Data Acquisition palette) is placed on the block diagram a configuration window appears asking you to select the type of task. For this Project, you will be Generating a Signal. You should select the Line Output option from the Digital Output dropdown list. Next you must select the Physical Channel name. If your SensorDAQ is connected to the computer and powered on, you should select port0/line0. Unlike the Digital Express VI which sends an output pattern of 1 to turn on the DCU, you control the DCU from the DAQ Assistant with a 1-D Boolean array ( True tells the DAQ Assistant to turn on DCU line D1; False turns D1 off). Only the top row (the first element) of the array is used. The other rows of the array must remain empty (grayed-out). Figure 3 DAQ Assistant for DCU control To make sure that the two Express VIs operate in a sequential manner, wire them together using the Error lines. Controlling the DCU (LabQuest or LabQuest Mini) The Digital Express VI can be used to control the DCU if you are using a LabQuest or LabQuest Mini since these interfaces have two digital ports capable of accepting BTD connectors. You must send an output pattern indicating which digital lines should be on or off at any one time. An output pattern of 1 will turn on DCU line D1 and a pattern of 0 will turn all lines off. You can sample all 16 different output patterns in the configuration window of the Digital Express VI. You will need to place separate Digital Express VIs on the block diagram for the Rotary Motion Sensor and the DCU. In the configuration window under Channel Selection, choose DIG Channel 1 for configuring the Rotary Motion Sensor and DIG Channel 2 when configuring the DCU. Connect the two Digital Express VIs together using the stop (F) and stopped terminals. PROJECT TIPS 1. Avoid using the Abort Execution button to stop your VI because some of the DCU lines may remain on. 2. If using the SensorDAQ, end your program by turning DCU line D1 off. 3. Make sure that all wires are away from the rotating propeller blades and that the bar is able to swing freely. 4. Incorporate some sort of physical stop into your apparatus so that if you supply too much voltage to the motor, the bar does not spin around in circles. For example, the rod supporting the Rotary Motion Sensor could extend out far enough to stop the bar from rotating too far. P11-4 Engineering Projects with NI LabVIEW and Vernier

5 Propeller-Powered Pendulum 5. The Rotary Motion Sensor assumes the initial position of the bar is at 0 ; therefore, make sure the bar has stopped swinging before restarting the program. 6. Refer to Appendix E for additional information on the Vernier DCU, Rotary Motion Sensor, and Digital Proto Board Connector. PROJECT TROUBLESHOOTING 1. Make sure the DCU is receiving power. The green LED in the top of the DCU box will be lit when the DCU is powered on. 2. Double-check the DCU cable connections against the color-coded label attached to the cable. 3. Make sure you are using the same SensorDAQ that was connected to the computer when you configured the DAQ Assistant. Switching SensorDAQs will cause an error (# or ) when you run your program. See Appendix F for information about how to resolve this problem. Engineering Projects with NI LabVIEW and Vernier P11-5

6 Project 11 CHALLENGE DESIGN REQUIREMENTS (SENSORDAQ ONLY) Note: Do not attempt the Challenge until you have completed the Project Design Requirements. Write a LabVIEW program to allow a user to control the speed of the propeller motor and thereby gently raise the pendulum from the resting state to a specific angle. Use an analog output controller and the Vernier Power Amplifier. The propeller and motor should be mounted as they were in the Project, that is, at the end of a long bar, and the bar should be connected to the Rotary Motion Sensor. Your program should control the voltage delivered from a Vernier Power Amplifier to the motor and use a Vernier Rotary Motion Sensor to measure the angle of the bar. The user should be able to control the motor voltage, and indirectly the speed of the propeller, from the front panel. The bar angle should be displayed on the front panel. Note: The LabQuest or LabQuest Mini should not be used for the Challenge. The LabQuest has the ability to send a DC signal to the Power Amplifier, but you will not be able to satisfactorily control the bar due to the slow response when updating the output voltage. The LabQuest Mini cannot be used for this activity because it does not have the ability to output a voltage signal. ADDITIONAL MATERIALS Vernier Power Amplifier Vernier Analog Proto Board Connector CHALLENGE SETUP Connect the Rotary Motion Sensor to the interface 1. Connect the Rotary Motion Sensor to the DIG channel on the interface. 2. Remove the DCU from your apparatus. It will not be used in the Challenge. Connect the motor to the Power Amplifier 1. Connect the two terminals on the DC motor to the ±10V (red) and GND (black) ports on the Vernier Power Amplifier. 2. Connect the Power Amplifier to its external power source and flip the power switch to the On position. Connect the Power Amplifier to the SensorDAQ 1. Insert an Analog Proto Board Connector into a breadboard. 2. Plug one end of a BTA cable into the port marked Audio Input on the Power Amplifier and the other end into the Analog Proto Board Connector. P11-6 Engineering Projects with NI LabVIEW and Vernier

7 Propeller-Powered Pendulum 3. Use jumper wires to connect the SensorDAQ screw terminal to the Analog Proto Board Connector as shown in the figure below. Figure 4 Analog Proto Board Connector pin-out to the SensorDAQ screw terminal CHALLENGE BACKGROUND INFORMATION In the Project, we controlled the physical pendulum with a digital (on or off) output line and the DCU. In this Challenge, the user will control the rate at which the propeller turns with a variable voltage (analog output) control. The Vernier Power Amplifier is used. It can deliver the voltage to drive the motor at a range of speeds. The Power Amp Express VI (found on the Vernier functions palette) should be used to control the Power Amplifier when writing your LabVIEW program. This Express VI sends a DC voltage signal by default. You can use the Digital Express VI to monitor the angle readings from the Rotary Motion Sensor. CHALLENGE TIPS 1. Propel the bar in a direction away from the wires connecting the DC motor to ensure that these wires do not get tangled in the propeller. 2. Incorporate some sort of physical stop into your apparatus so that if you supply too much voltage to the motor, the bar does not rotate too far. For example, the rod supporting the Rotary Motion Sensor could extend out far enough to stop the bar. 3. Refer to Appendix E for additional information on the Vernier Power Amplifier and Analog Proto Board Connector. Engineering Projects with NI LabVIEW and Vernier P11-7

8 Project 11 EXTREME CHALLENGE DESIGN REQUIREMENTS (SENSORDAQ ONLY) Modify your VI created in the Challenge so that the propeller is automatically raised to an exact angle of 30 using the Power Amplifier as a power source. You should use Proportional-Integral- Derivative (PID) control so that your propeller reaches the desired angle quickly with a minimum of overshoot and/or oscillation. You should create Waveform Charts on the front panel for the motor voltage, desired angle of the propeller, and actual angle of the propeller. Both the desired and actual angle of the propeller should be displayed on the same Waveform Chart. Note: You cannot use the LabQuest or LabQuest Mini to perform PID control. The LabQuest has the ability to send a DC signal to the Power Amplifier, but you will not be able to satisfactorily control the bar due to the slow response when updating the output value. The LabQuest Mini cannot be used for this activity, because it does not have the ability to output a voltage signal. EXTREME CHALLENGE BACKGROUND INFORMATION When using manual control to raise the propeller to a desired angle, the operator knows instinctively to increase the speed of (voltage to) the propeller for more lift or decrease the propeller speed for less lift. However, the Extreme Challenge requires a method of automatic control for situations in which a human operator is absent. A feedback control system takes information on the current (and sometimes past) measurements to influence a system. In this case, the Rotary Motion Sensor monitors the bar angle and feeds the data back to the program which continuously adjusts the voltage to the propeller to keep the bar as close to the desired angle as possible (see the figure below). An ideal system would cancel out all errors and keep the propeller at exactly the desired angle, but this can be difficult due to measurement precision, delays in the controller response, and external air currents. Figure 5 Feedback control loop A PID (proportional, integral, derivative) controller is often used in control systems. It uses the weighted sum of three corrections to quickly and smoothly adjust the voltage to the desired condition. The proportional factor makes an adjustment to the process based on the current error; the integral factor makes an adjustment based on the sum of recent errors; and the derivative factor makes an adjustment based on the rate at which the error has been changing. All three terms are then summed and multiplied by the gain. Gain is the ratio of the signal output to the signal input in this instance, volts per degree. This equation can be shown as: de V t G K pe t Ki e t dt Kd Vbias dt where V(t) is the voltage, G is the gain, K p is the proportional constant, e(t) is the error, K i is the P11-8 Engineering Projects with NI LabVIEW and Vernier

9 t Propeller-Powered Pendulum integral constant, e dt is the summation of the error and the previous error, K d is the de derivative constant, is the time rate of change of the error, and Vbias is a starting voltage for dt 30. At first glance, this equation can appear daunting; but you do not need an extensive background in differential equations to implement this formula into your LabVIEW program. All of the terms can be simplified to basic arithmetic. The error in this exercise is simply the number of degrees difference (positive or negative) between the desired angle and the measured angle. e(t) = error = desired angle measured angle Using a Shift Register to store the current error value will allow you to use it in the next calculation as the previous error. You will then be able to easily compute ( e t dt ) (error + previous error) and de (error previous error). To get the rate of change in the error we should really use the change in the error value divided by the time between readings (dt). By default the Digital Express VI reads the Rotary Motion Sensor 10 times a second, and therefore, dt = 0.1 seconds/sample. The simplified result for the PID portion of the equation can now be written as: Kp error Ki error previous error Kd error previous error / 0. 1 Figure 6 Calculating the Error, Change in Error, and Sum of Errors using LabVIEW You can determine the bias and gain by doing some preliminary analysis of your bar position. First, by running your basic program with the manual voltage control (the Challenge for this chapter), you can find an approximation for the bias voltage. The bias or offset voltage is the voltage at which the bar angle is approximately 30. Engineering Projects with NI LabVIEW and Vernier P11-9

10 Project 11 Next you can specify the gain of the system. This is an estimate of the ratio of the change in voltage applied to the motor divided by the corresponding change in degrees of the pendulum. A quick way to estimate this is by running the program from the Challenge of this chapter with the manual voltage control. Take data on the change in voltage and the change in degrees of the pendulum and estimate the gain Note that in the PID equation all three terms (proportional, derivative, and integral) are multiplied by the gain. This is important in order for the PID equation to be tuned by any of the standard tuning methods. Tuning the PID equation Tuning the PID equation is a matter of finding the optimal K coefficients that will yield a responsive system with minimal overshoot or oscillation. The proportional term takes into consideration how far away the bar angle is from 30. As the difference grows or shrinks, the influence of the proportional correction grows or shrinks. The main problem with proportional control alone is that the bar will tend to oscillate. The derivative term can help minimize the overshoot problem. The integral term will tend to make the error go to zero, but it also will tend to make the overshoot worse. The best approach for determining the correct proportional, integral, and derivative values is trial and error. Make sure your equipment is in an isolated location so that if the long bar starts oscillating wildly, it will not hit other people or equipment near it. When you write your LabVIEW program, place a Waveform Chart on the front panel to monitor the actual angle of the bar in relation to the desired angle. You can use a Bundle function (found in the Programming Cluster, Class, & Variant palette) to plot both the desired and the actual bar positions on the same chart. 1. Set all three K coefficients to zero. Figure 7 Plotting two values on a Waveform Chart with a Bundle function 2. As you run the program, increase the proportional coefficient (K p ) until the bar s oscillation about the desired angle has a constant amplitude. Note that you are not trying to match the angle of the bar to the desired angle at this stage. You want a uniform oscillation in both the voltage and position graphs. Tip: Right-click on your PID front panel controls. From the Properties window, set the Data Entry Increment for the K constants to 0.01 to help you in tuning your PID system. 3. Next, cut K p in half and increase K i to accelerate the process. Note that the system will probably continue to oscillate, but too much K i will quickly make the system unstable. 4. Next increase K d until the system stabilizes to the desired angle. P11-10 Engineering Projects with NI LabVIEW and Vernier

11 Propeller-Powered Pendulum 5. At this point, you should stop and restart your program taking note of the amount of overshoot at the beginning of your system. Increasing the derivative parameter (K d ) and/or decreasing the integral parameter (K i ) a small amount should reduce the overshoot. 6. Continue stopping and restarting your system until the overshoot is as small as possible (an adjustment in K d ) and the system reaches the desired angle very quickly (an adjustment in K i ). EXTREME CHALLENGE TIPS 1. You may want to look up articles on PID control on the internet or in engineering books. 2. Incorporating the mathematics for a PID controller in the Extreme Challenge is not difficult, but finding the proper constants for the proportional, derivative, and integral input parameters can be tricky. You should program these values as controls, rather than constants, so that you can adjust them to suit your equipment. 3. Make the K coefficients adjustable by hundredths of a unit. EXTREME CHALLENGE TROUBLESHOOTING 1. If the bar appears to have reached a steady 30 angle, but the plot of the Rotary Motion Sensor angle is not overlaying the plot of the desired angle, check to see if you are starting the program while the propeller is still swinging. The Digital Express VI assumes the initial angle of the bar is 0. If the bar is not in a resting position on startup, the plot will be off. 2. A common mistake when tuning the PID system is to try to match the angle of the bar to the desired angle when adjusting just the proportional coefficient (K p ). Students will think they have tuned the system, but in actuality you will notice a significant amount of overshoot or delay in reaching the desired angle when you stop and restart the program. When adjusting the proportional coefficient, the bar should exhibit a uniform oscillation about the desired angle. The addition of the integral (K i ) and derivative (K d ) coefficients should be used to stabilize the bar. Engineering Projects with NI LabVIEW and Vernier P11-11

12 Vernier Lab Safety Instructions Disclaimer THIS IS AN EVALUATION COPY OF THE VERNIER STUDENT LAB. This copy does not include: Safety information Essential instructor background information Directions for preparing solutions Important tips for successfully doing these labs The complete Engineering Projects with NI LabVIEW and Vernier manual includes 12 projects as well as essential teacher information. The full lab book is available for purchase at: Vernier Software & Technology S.W. Millikan Way Beaverton, OR Toll Free (888) (503) FAX (503)