Evaluation copy. PID Ping-Pong Ball Levitation (SensorDAQ only) Project

Transcription

1 PID Ping-Pong Ball Levitation (SensorDAQ only) Project 12 Evaluation copy Levitation is a process in which an object is suspended against gravity by a physical force. Many methods can be used as the levitating medium, including magnetic repulsion, viscous liquids, sound waves, and air currents. In this Project, we will use an air stream provided by a fan to provide the levitating force on a ping-pong ball. Controlling the ping-pong ball is not easy, so it requires a good control system, which you can build using LabVIEW. The photo above shows the setup for the Challenge. Engineering Projects with NI LabVIEW and Vernier Vernier Software & Technology P12-1

2 Project 12 PROJECT DESIGN REQUIREMENTS (SENSORDAQ ONLY) In this Project, you will build a device to levitate a ping-pong ball in a long vertical tube using the force of air. You will use a small DC fan powered by a Vernier Power Amplifier to provide the lift force for the ping-pong ball. The fan should be secured to the bottom of the tube in such a way that there is an air-tight seal between the sides of the fan and the tube, but that the top and bottom of the fan are open to provide air intake and exhaust. Your LabVIEW program should allow the user to control the speed of the fan (the lift force on the ball) from the front panel via a voltage control to the fan motor. When program execution ends, the fan should automatically turn off. Note: This Project can only be done with SensorDAQ. The LabQuest and LabQuest Mini cannot be used. The LabQuest has the ability to send a DC signal to the Power Amplifier, but you will not be able to satisfactorily control the ball height due to the slow response when updating the output voltage. The LabQuest Mini does not have the ability to output a voltage signal. MATERIALS SensorDAQ LabVIEW computer USB cable Vernier Power Amplifier Vernier Analog Proto Board Connector small DC fan ring stand 3-finger clamp jumper wires Styrofoam block long hollow plastic tube ping-pong ball PROJECT SETUP Build a levitation chamber 1. Cut a hole through the Styrofoam block the same diameter as the long plastic tube. Insert the tube into one end of the block (it should fit snugly with no air leaks). 2. Insert or mount the DC fan to the other end of the Styrofoam block. The lead wires of the fan should extend away from the tube and block. 3. Use a ring stand and 3-finger clamp to support the tube and block so that the tube is oriented vertically, and the Styrofoam block is positioned about 2 5 cm (1 3 in) above the ground to allow air flow to the fan. Connect the fan to the Power Amplifier and interface 1. Connect the positive (red) lead of the fan to the ±10V (red) terminal on the Power Amplifier. Connect the negative (black) lead of the fan to the GND (black) terminal. 2. Connect one end of a BTA cable to the port marked Audio Input on the Power Amplifier and the other end into an Analog Proto Board Connector. Use jumper wires to connect the SensorDAQ screw terminal to the Analog Proto Board Connector as shown to the right. Figure 1 3. Connect the Power Amplifier to its external power source and flip the power switch to the On position. P12-2 Engineering Projects with NI LabVIEW and Vernier

3 PROJECT BACKGROUND INFORMATION PID Ping-Pong Ball Levitation In this Project, the user will be controlling the rate at which the air moves past the ping-pong ball with a variable voltage control on the fan. The Vernier Power Amplifier should be used for this Project because it has the ability to output a constantly varying signal unlike a digital device (such as Vernier Digital Control Unit) which provides strictly on/off control. The Power Amplifier also allows you to drive loads that typically draw more power than the signal source can deliver. The Power Amp Express VI (found on the Vernier functions palette) should be used when writing your LabVIEW program. PROJECT TIPS 1. One method of cutting the hole in the Styrofoam block is to push and twist the plastic tube through it. 2. The long tube should be vertically aligned when viewed from all directions to minimize friction between the ball and the tube. 3. Provide 2 5 cm (1 3 in) of air space underneath the fan for air intake. 4. Avoid using the Abort Execution button to stop your VI or the fan may continue spinning. 5. Refer to Appendix E for additional information on the Vernier Power Amplifier and Analog Proto Board Connector. PROJECT TROUBLESHOOTING 1. You can test-run your fan motor from the configuration window of the Power Amp Express VI to ensure that all of your electrical connections are working properly. 2. Check the direction of air flow from the fan. It should be blowing air up into the tube, not exhausting air out the bottom of the tube. 3. Check for air leaks between the fan and the Styrofoam block. Engineering Projects with NI LabVIEW and Vernier P12-3

4 Project 12 CHALLENGE DESIGN REQUIREMENTS Note: Do not attempt the Challenge until you have completed the Project Design Requirements. Add a Vernier Motion Detector to the top of the tube. Then modify your VI created in the Project to levitate the ping-pong ball at an exact distance of 30 cm away from the Motion Detector using Proportional-Integral-Derivative (PID) control. Your device should raise the ball to this position as quickly as possible with a minimum of oscillation. You should create Waveform Charts on the front panel for the motor voltage, desired position of the ball, and actual position of the ball. Display both the desired and the actual position of the ball on the same Waveform Chart. ADDITIONAL MATERIALS Vernier Motion Detector rod clamp CHALLENGE SETUP Connect a Motion Detector to the levitation device 1. Position the Motion Detector about 5 cm above the top of the tube using a rod clamp. The gold circular sensor should be centered exactly above the tube opening and pointing downward. Tip: The Motion Detector has a pivoting head to aid in positioning the sensor. Simply rotate the detector head away from the detector body. 2. Set the sensitivity switch on the Motion Detector (if it has one) to the short-range (cart) setting. The sensitivity switch is located under the pivoting detector head. 3. Connect the Motion Detector to the DIG port on the interface. CHALLENGE BACKGROUND INFORMATION In the Challenge, you are asked to levitate the ping-pong ball at an exact distance away from the Motion Detector. When using a front panel control, as in the Project, the user can raise the ball to the desired position fairly quickly by increasing the voltage to the fan for more lift and then decreasing the voltage to maintain that lift. However, in this Challenge, the program needs a method of control in the absence of a human operator. A Proportional-Integral-Derivative (PID) controller uses the weighted sum of three error terms to quickly and smoothly adjust the ball to the desired position. The proportional term takes into consideration how far away the ping-pong ball is from the desired position. As the difference grows or shrinks, the influence of the proportional term grows or shrinks. The main problem with proportional control alone is that the ball will tend to oscillate up and down. You could increase the voltage to the fan at a very slow rate to avoid oscillating the ball, but your goal is to get the ball to its desired position as quickly as possible. Addition of the integral term will accelerate the ball towards the desired position; but since the integral term is accelerating the process, it can cause the ball to overshoot and even fly out of the tube. A derivative term is added to reduce the amount of overshoot. 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 P12-4 Engineering Projects with NI LabVIEW and Vernier

5 integral constant, PID Ping-Pong Ball Levitation e t dt is the summation of the current error and the previous error, K d is the de derivative constant, is the time rate of change of the error, and Vbias is an initial voltage. dt This equation may appear intimidating, but you do not need an extensive background in differential equations to use it in your LabVIEW program. All of the terms can be simplified to basic arithmetic. Let s start with the error since it is used three times in the equation. The error in this exercise is simply the difference (positive or negative) in centimeters between the actual position of the ball in relation to the Motion Detector and the desired position. Remember, the detector is above the ball, so you should not think of the ball s position in terms of its height above the floor. error = measured position desired position If the ball is too low, the measured distance from the Motion Detector will be too large and the error will be positive. Using a Shift Register in your LabVIEW program to store the current error, 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 Motion Detector 20 times a second, and therefore, dt = 0.05 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/ Figure 2 Calculating the Error, Change in Error, and Sum of Errors using LabVIEW You can find values for additional terms by doing some preliminary analysis of your ping-pong ball in the tube. First, by running the program from the Project of this chapter with the manual voltage control, you can find an approximation for the bias voltage. The bias or offset voltage is the voltage required to keep the ping-pong ball near the desired position. 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 height of the ball. A quick way to Engineering Projects with NI LabVIEW and Vernier P12-5

6 Project 12 estimate this is by running the program from the Project of this chapter with the manual voltage control. Take data on the change in voltage and the change in ball position and estimate the gain. 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 best approach is trial and error. Make sure your equipment is in an isolated location so that if the ping-pong ball happens to fly out of the tube, 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 ball s position in relation to the desired position. You can use a Bundle function (found in the Programming Cluster, Class, & Variant palette) to plot both the desired and the actual ball positions on the same chart. Figure 3 Plotting two values on a Waveform Chart with a Bundle function 1. Set all three K coefficients to zero. 2. As you run the program, increase the proportional coefficient (K p ) until the ball s oscillation about the desired position has a constant amplitude. Note that you are not trying to match the position of the ball to the desired position at this stage. You want a uniform oscillation in both the voltage and position graphs. Tip: From the Properties window, set the Data Entry Increment for the K constants to 0.1 to help you in tuning your PID system. 3. Next, cut K p in half and increase K d gradually until the system stabilizes to the desired position. 4. Next, increase K i to see if you can improve performance. K i will tend to make the make the error approach zero, but too much K i will quickly make the system unstable. 5. At this point, you should stop and restart your program taking note of the amount of overshoot at the beginning of your system. 6. Make minor adjustments in the coefficients and 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 position very quickly (an adjustment in K i ). CHALLENGE TIPS 1. You may want to look up articles on PID control on the internet or in engineering books. 2. Make sure that you define the error as the difference between the measured position and the desired position, so that the error comes out positive when the ball is too low. 3. Make sure that you have programmed the mathematics correctly or your system will be unstable and impossible to tune properly. P12-6 Engineering Projects with NI LabVIEW and Vernier

7 PID Ping-Pong Ball Levitation 4. Make sure that the Motion Detector is sensing the entire length of the tube. If the detector is positioned too far above the tube, it will detect the lip of the tube and not the ping-pong ball. 5. Refer to Appendix E for additional information about the Vernier Motion Detector. CHALLENGE TROUBLESHOOTING A common mistake when tuning the PID system is to try to match the position of the ball to the desired position when adjusting the K p coefficient. You may think you have tuned the system, but in actuality you will notice a significant amount of overshoot or delay in reaching the desired position. When adjusting the K p coefficient, the ball should exhibit a uniform oscillation about the desired position. The addition of the K i and K d coefficients should be used to level out the ball. Engineering Projects with NI LabVIEW and Vernier P12-7

8 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)