AC : INTRODUCTION TO INSTRUMENTATION AND CON- TROL SYSTEMS USING A PENDULUM MOUNTED AIR ROCKET

Transcription

1 AC : INTRODUCTION TO INSTRUMENTATION AND CON- TROL SYSTEMS USING A PENDULUM MOUNTED AIR ROCKET Michael Keller, University of Tulsa Michael Keller is an assistant professor of mechanical engineering at the university of tulsa. His research and teaching interests are in solid mechanics, both experimental and theoretical, and materials science. Jeremy S. Daily, University of Tulsa c American Society for Engineering Education, 211

2 Abstract Introduction to Instrumentation and Control Systems Using a Pendulum Mounted Air Rocket Courses on engineering instrumentation and measurement typically have two objectives: 1) introducing the students to essential and modern engineering instrumentation and 2) developing the ability of students to plan, execute, and analyze engineering experiments. The project described in this paper encompasses all of these objectives and introduces students to practical aspects of control systems. The multi-week laboratory exercise requires the students to interface with laboratory hardware and modern instrumentation with only limited guidance from the instructor. The self-guided problem solving approach to instrumentation gives students a deeper understanding of the nuances and complexity of developing and implementing multi-component instrumentation systems. Additionally, the students are required to develop a limited control system that fires an air rocket in response to position or acceleration feedback in order to achieve the highest swing height. Since this class precedes the formal controls systems course in our curriculum, conceptual control system theory is provided in a one-on-one basis in the lab. In essence the laboratory serves as a just-in-time controls course and sets up the formal mathematical controls course that follows. This paper includes the detailed design of the air rocket thrust laboratory apparatus and computerized data acquisition setup. Schematics and specifications of the instruments are included along with a typical student data and analysis. Finally, student surveys were conducted and analyzed to assess the both general and specific outcomes of the laboratory experience. Introduction Measurement and instrumentation courses are typically the catch-all course for topics in experimental design and execution in mechanical engineering curriculum. Course objectives include the introduction of modern data acquisition systems and techniques, the development and presentation of statistical techniques for data analysis, and the introduction of formal uncertainty analysis. These three course topics are employed in nearly every rigorous engineering experiment that a student would perform in either an industrial setting or during advanced graduate research. However, most laboratory experiments are canned and handed to the student with a detailed procedure that can be easily followed. The emphasis on these experiments is not the experiment, but the analysis of the data generated from a particular experiment. Essentially, these laboratories can quickly degenerate into a show-and-tell theater portion followed by individual student work during the data analysis and report writing phases. 1 Recently, self-directed and autonomous learning experiences have been realized to be integral to the learning process. In order to introduce these aspects into an instrument and measurement course setting, a defined, but undirected instrumentation lab was recently designed and implemented in the Department of Mechanical Engineering at The University of Tulsa. This lab was based on an existing air-rocket lab that had been almost entirely demonstrative in previous iterations. 3,2 In this lab, a fire-extinguisher air rocket is attached to a bearing-suspended pendulum, instrumented and mounted to a frame. Students are directed to connect, calibrate, and write a data acquisition program in LabVIEW in order to collect data during a short duration fire

3 of the rocket, typically lasting 1 to 3 seconds. The data gathered during this lab is used to generate an impulse vs. initial pressure curve to determine the potential for using an air rocket to power comical human flight. After the data acquisition program is completed, a follow-on lab period is devoted to the programming of a simple control system in LabVIEW with the goal of achieving the highest swing height for a given initial pressure. This is the capstone lab of the course and comes after 4 dedicated LabVIEW programing labs and two previous, directed labs using LabVIEW to interface with data acquisition (DAQ) hardware. Some previous familiarity with the practical aspects of DAQ implementation is critical to the success of this experiment. Description of the Lab Exercise The goal of this is lab is two-fold. 1) Determine the thrust characteristics of a simple, pendulum attached, pressurized air rocket and 2) construct a simple control system that attains the highest possible swing height for a given initial rocket pressure. This experiment introduces the students to data acquisition and signal output for both analog and digital sensors. The controls aspect, while technically simple, introduces students to the concept of feedback and boolean logic. The physical experimental apparatus is shown in Fig. 1. Students are given only basic information about the sensors that might be gathered from a data sheet. Table 1 lists the information that the students are given for each sensor. All sensors are terminated at a terminal strip at the top of the rocket frame. An example pinout is listed in Table 2 and is provided to the students. After a brief introduction to the lab and a description of each of the sensors, the students are given three LabVIEW Figure 1: Physical arrangement of the rocket test compact DAQ modules, a bridge sensor stand, with the transducer locations indicated. module (NI 9237), a digital input/output module (NI 941), and a differential digital input module (NI 9411). Hook up wire is available for the students as well as all the required break-out boards and basic equipment. The students are verbally directed to spend the first lab period physically connecting the sensors to the DAQ hardware and writing LabVIEW programs to take data from the sensors and generate a digital signal to operate the solenoid valve. The second lab period is spent calibrating the pressure transducer and accelerometer and taking the data required for the analysis of the rocket

4 impulse. The third lab period is spent designing and implementing the control system. Details of the data analysis are provided below. After the data analysis is performed, the students are also required to complete a detailed uncertainty analysis of the experiment based on given uncertainty values. The details of the uncertainty analysis are also given in a section below. Table 1: Given information at the start of the lab for each sensor Sensor Accelerometer Encoder Pressure Gage Strain Gages Information Strain-gage-based and bridge type (full) 496 counts per revolution Wheatstone bridge type (-2 psi) Full bridge configuration Data Analysis Table 2: Example pinout given to students # Color Description 2 Red Strain gage top EX (+) 19 White Strain gage middle AI (+) 18 Black Strain gage bottom RS (+) 17 Red Strain gage top EX (-) 16 White Strain gage middle AI (-) 1 Black Strain gage bottom RS (-) 14 Lt.Blue, Bl/Wt Accelerometer EX(+) 13 Blue Accelerometer EX(-) 12 Lt.Brown, Br/Wt Pressure Sensor Out(-) 11 Brown Pressure Sensor Out(+) 1 White, Or/Wt Pressure Sensor EX(-) 9 Orange Pressure Sensor EX(+) 8 Lt.Green, Gr/Wt Accelerometer Out(+) 7 Green Accelerometer Out(-) 6 Solid Color Wire Solenoid Valve Control Green Quadrature Channel Z 4 White Quadrature Channel A 3 Blue Quadrature Channel B 2 Red/Blue +V 1 White/Black Common The thrust of the rocket is dependent on time. A free body diagram of the forces on the rocket are shown in Fig. 2. The point O is fixed with a bearing and an incremental optical encoder measures the angle θ. We can determine a value for the thrust F by summing the moments about point

5 O. MO = I O θ = F LF wl cg sin θ (1) where I is the mass moment of inertia about the center of rotation. The angle, measured in radians from vertical, is θ and θ(t) the angular acceleration in radians per second per second. Friction and damping are neglected in this experiment. Dividing through by I O and rearranging gives a second order differential equation: θ + wl cg I O sin θ = F L F I O. (2) By making a small angle assumption (which is actually violated during the firing of the rocket), we can let sin θ θ, thus making a linear differential equation. The well-known solution to this differential equation gives the frequency of oscillation (in radians per second) as wlcg ω n = (3) I O Students can obtain the natural frequency by timing multiple oscillations. Since point O is assumed to be fixed, the angular acceleration is the quotient of linear acceleration to the radius, or θ = a (4) L accel The students could then use this equation to derive angular acceleration from the acquired acceleration data, but the accelerometer used on the lab is influenced by gravity. Therefore, the actual angular acceleration when measured by a DC coupled accelerometer is Substituting Eq. into Eq. 1 and solving for thrust yields θ = a g sin θ L accel () F = I O(a g sin θ) L F L accel The impulse can be determined by integrating with respect to time Impulse = t + wl cg sin θ L F (6) F (s) ds (7) where s is a dummy variable of integration. This cumulative integral is estimated numerically using the trapezoidal rule in excel or Matlab. Since the thrust is always positive, the impulse function will always increase with respect to time. Therefore, the value of the overall impulse is the maximum value of the impulse function. Determining Acceleration from the Encoder Data Two methods for determining the angular acceleration of the rocket are used during the analysis. The calculation of the angular acceleration is performed using Eqn. and the data gathered from the accelerometer. Angular acceleration is also calculated by numeric differentiation of the

6 O L cg +θ(t) Laccel L F Accel w F Figure 2: Free body diagram of the rocket for thrust calculation.the following values are known: m = g, L cg = 8.1 mm, L accel = 762. mm, and L F = 98.9 mm.

7 position data from the encoder. Encoder counts are directly translated to an angular measurement with the LabVIEW software. However, the data acquisition rate is typically fast enough to acquire data points which represent pendulum motions smaller than ther resolution of the encoder. While a typical plot of the encoder data, shown in Fig. 3, look superficially smooth, the actual data is stair-stepped. Taking numerical derivatives of the smooth looking data in Fig. 3 can be difficult because the stair-stepped nature of the data acts as noise and is amplified by differentiation. Most students have not differentiated numeric data from an experiment before and are introduced to moving average filtering in order to successfully produce an acceleration curve from the position data. In addition to the use of numeric differentiation techniques, the position vs. time plot can provide a graphic reinforcement of the effect of the rocket impulse on position. The initial displacement has a noticeably greater amplitude than the subsequent pendulum oscillation after the pressurized air is exhausted during the first 1 to 2 seconds. 4 Raw Encoder data from firing the rocket 3 2 Angle θ (degrees) Time (sec) Figure 3: Typical angle measurement from the quadrature incremental encoder (496 counts per turn). Uncertainty Analysis The uncertainty analysis of the experiment is guided by the given uncertainties shown below. m = 6167 ± 1 g L cg = 8 ± 1 mm L accel = 762 ± 1 mm L F = 99 ± 1 mm u a = ±.3 m s 2

8 u θ = ±. u T = ±. s We allow the students to assume the following uncertainty relationship U thrust U impulse, (8) which eliminates the need for numerical integration of the uncertainties. Students assume average values for the values of the variables when calculating the weighting factors θ i. Therefore the uncertainty in the experiment is [ ( F u F = + ) 2 ( ) 2 ( F F J u J + u LF + L F a u a ( ) 2 ( ) 2 F F m u m + u Lcg + L cg ) 2 ( F θ u θ ) 2 ] 1/2 The weighting factors are calculated from the thrust relationship in Eqn. 6. Control System This course precedes the formal controls system course by at least two semesters for an average student. A typical ME student will not have had a formal course in boolean logic or digital electronics at any point in their curriculum. The task set to the students is to develop a control system using one or more of the sensors as input that will govern the timing and duration of the rocket fire in order to achieve the highest angle. Since students are not expected to have a deep understanding of the theory or practical aspects of designing and implementing a control system, the grading bar for success is relatively low for this particular portion of the lab. Demonstration of adequate control, i.e. response of the system to some input, is enough to be considered success. To date, only one group (four students) out of 24 groups has been content with the bare minimum. Most spend at least one full lab period (3 hours) and several spent further outside time attempting to develop the best firing algorithm. A small extra credit reward, points on the final lab grade, is provided to the group that has the highest recorded angle for a given initial pressure as an incentive for students to take the challenge seriously. Instructor and teaching assistant interaction is vital during this portion of the lab. Students typically have no basis to consider where to begin. As a starting point, the instructor encourages the students to spend time investigating what firing timings produce the highest angles using the manual fire control. After the students determine the appropriate firing times, they are encouraged to write down a mathematical condition for firing. Nearly all the groups picked a position-based fire control approach. An example of the fire condition generated by the students is: if θ and dθ dt then fire. (9) This fire condition allows for an initial at-rest fire (θ ) and fires the rocket on the down swing, assuming that the increasing θ direction is defined as the upswing. This conditional statement is arrived at by drawing pictures of the position of the rocket as a function of time and asking students where they are trying to fire the rocket. The students provide the derivative statements

9 Figure 4: Example of a student programed Data Acquisition Program in LabVIEW. with only a small amount of guided questioning. Since the solenoid valve used on the rocket is not proportioning, the students can only open or close the valve. The control system typically requires significant troubleshooting, usually because of incorrect boolean logic. In order to troubleshoot the control system, students are introduced to a truth table as a method of developing appropriate boolean logic. An example of a truth table based on the fire condition fire condition in equation 9 is shown in Table 3. The simple request to state the requirements that both conditions be true is enough to prompt the students to realize the need for an and statement. The conditions are then implemented in LabVIEW. Example Student LabVIEW Programs We allow the students to discuss their progress with each other, which has a tendency to drive the resulting LabVIEW program to a consistent implementation. Specific sampling rates differ and

10 Table 3: An example truth table for constructing the boolean fire logic Condition θ θ < dθ/dt > dθ/dt < Fire T F T F Figure : Example of a student programed control Program in LabVIEW. the final visual representation of each groups LabVIEW program are unique, but the basic program flow tends to be identical. A representative data acquisition program for the first part of the lab is shown in Fig. 4. The trick of using an empty while loop to provide a start and wait was given to the students in a previous lab. The DAQ programs were used as starting points for the

11 control systems. Students typically removed the unnecessary acquisition tasks and then implemented the control system. Boolean logic blocks were used to test the position constraints, with the differential constraint being implemented through a simple shift register. Students were given help as required with specific implementation questions (i.e. where is the shift register found?) if needed. An example of a student implemented control program is shown in Fig. 6. Figure 6: Example of a student programed control Program in LabVIEW. Student Assessment Students were given a 9 question survey to assess the effectiveness of the educational objectives of the lab. Questions pertaining to the instrumentation and experimental analysis objective and the introduction to control systems objective were included in the survey. The questionnaire was a point Likert-type survey asking each student to indicate if they strongly disagree, disagree, neither agree nor disagree, agree, or strongly agree. The last question was an open response

12 asking for comments about the lab either in criticism or appreciation. The Likert scaled questions and average value of the responses are listed in Table 4. Histograms of the response for each question are shown in Figure 7. Question Table 4: Likert Scale survey question Average Response 1. The experiment did a good job of familiarizing me with typical instrument 3.72 calibration procedures. 2. The laboratory did a good job of familiarizing me with computerized data 3.64 acquisition. 3. The laboratory did a good job of familiarizing me with the operation of a 3.72 rotary encoder, strain gages, accelerometer, and pressure transducer. 4. Detailed uncertainty analysis became clearer as a result of the experiment 3.16 and lab write-up.. The lab and subsequent lab report caused me to think critically about 3.8 sources of experimental error that contribute to uncertainty in the rocket engine thrust. 6. The lab did a good job introducing me to the concepts of control systems My understanding of how data acquisition and control systems work together was improved Overall the lab was a positive experience Overall the lab helped me learn and understand experiments Overall the lab write-up was a positive experience In general, the students felt that the lab was a good introduction to control systems as indicated by the results of question 6. The students also generally agreed that the lab was a good introduction to calibration and computer-based data acquisition. Only limited responses were collected from the open-ended question. The control system portion of the lab was generally considered a good introduction to feedback control systems. The students also felt that the lab successfully demonstrated the relationship between data acquisition systems and control systems. Conclusions A lab was designed that enabled an open ended experience with the implementation and analysis of an experiment. This lab was the culmination of a series of directed experiments and gave students an experience in constructing and implementing an experiment from start to finish. The requirement to develop a basic control system also introduced the students to the design and implementation of a feedback control system. Students successfully implemented a condition-based firing scheme that took feedback from sensors and determined a firing time. In general, the students responded that the lab was a good introduction to control systems based on a post-lab survey. Future Plans This lab is under continuous improvement. The results in this paper represent the first complete implementation of the full data acquisition lab and the control system lab. Since our curriculum

13 Question 1 Question 2 Question 3 Question 4 Question Question 6 Question 7 Question 8 Question 9 Question Figure 7: Histogram results for the survey based on a Likert scale where strongly disagree = 1 and strongly agree =. does not currently include a lab class complementing a the senior controls class, this lab represents one of the only practical experiences with the design and implementation of a control system that many of our students will receive. We are actively updating this lab and are exchanging the currently implemented single-axis, strain-gage-based accelerometer with a dual-axis MEMS-based accelerometer. One of the significant barriers to allowing students to implement an accelerometer-based control system was accelerometer noise. The MEMS sensor is expected to reduce this issue. Furthermore, the MEMS accelerometer is two axis and the calibration procedure can account for any initial tilt of the sensing element. This is a nonlinear phenomena; however, starting with an assumed tilt, the Solver Add-in for Excel can be used to determine the initial tilt angle that maximizes the coefficient of determination (R 2 value) for the calibration curvefit. [1] Catherine H. Crouch, Adam P. Fagen, J. Paul Callan, and Eric Mazur. Classroom demonstrations: Learning tools or entertainment? American Journal of Physics, 72(6):83 838, 24. [2] Michael R. Kessler. Air rocket thrust experiment involving computerized data acquisition, calibration, and uncertainty analysis. In Proceedings of the 2 ASEE Annual Conference and Exposition, 2. [3] Denis J. Zigrang. Elements of Engineering Measurements. University of Tulsa, 6 edition, 1989.