Self-Correcting Projectile Launcher: Proposal for ECSE-4460 Control Systems Design

Transcription

1 Self-Correcting Projectile Launcher: Proposal for ECSE-4460 Control Systems Design Josh Schuster Yena Park Diana Mirabello Ryan Kindle March 1, 2005 Rensselaer Polytechnic Institute

2 ABSTRACT The design of a Self-Correcting Projectile Launcher was motivated by the desire to improve the accuracy existing launchers without the use of extensive sensor networks, and to demonstrate the viability of an iterative learning algorithm for disturbance rejection. The goal is to fire a disc from a commercially available toy gun at a target, and have its accuracy improve with each subsequent shot until the target is struck precisely. To accomplish this task, an IR beacon will be used to approximate the direction to the target, which will be mounted on a touchscreen sensor. As the disc strikes the touchscreen, the error in the trajectory will be calculated based on the difference between the target and impact site, and the orientation of the launcher will be adjusted to compensate using a pan and tilt mechanism. i

3 TABLE OF CONTENTS 1. Introduction 1 2. Objectives 4 3. Design Strategy Simulation & Modeling Mechanical Design Control Design Plan of Action Verification Launcher Verification Friction Identification Cost & Schedule 6.1. Cost Analysis Schedule Bibliography Statement of Contribution 27 A. Appendix 28 ii

4 LIST OF FIGURES 3.1 Control Flowchart Initial Orientation Calculator Vertical Drop vs. Distance Traveled Friction Identification Simulink Model File Velocity Diagram Without Filter Velocity Diagram With Filter Velocity Diagram After Implementation of Third Filter for Tilt Axis Velocity Diagram After Implementation of Third Filter for Pan Axis Diagram of Torque vs. Steady State Velocity of Tilt Axis Diagram of Torque vs. Steady State Velocity of Pan Axis iii

5 LIST OF TABLES 1.1 System Specifications Division of Tasks Disc Shooter Accuracy Preliminary Trajectory Results Short Range Trajectory Results Average Short Range Trajectory Coulomb & Viscous Friction for Both Axes Pan and Tilt Mechanism Cost Additional Parts Needed for System Labor Costs Lab Usage Total System Costs Actual System Cost iv

6 1. INTRODUCTION The world is an unpredictable place, and when it comes to projectile motion the unknowns one must take into account are numerous and complex. A trajectory may be altered by the varying currents, density, and stresses found in any given medium. While some of these may be measured and accounted for in advance, the variable nature of the environment dictates that no disturbance will be completely rejected. The measurements and computations to achieve such an incomplete error reduction would also require a significant investment in equipment. If an iterative learning approach were utilized instead, all that would be required to reject an error is the ability to sense to actual impact s location relative to the target and extra projectiles. The purpose of the project proposed in this memo is to create a prototype Self-Correcting Projectile Launcher. Instead of rejecting disturbances in advance to improve the chance of striking a target in a single shot, the system will fire repeatedly at a target and learn from its errors to strike more accurately with subsequent shots. The motivation for the project was to create a launcher that was capable of high accuracy but without the extensive sensor setup required to predict disturbances. The creation of such a system would be an economical solution for any number of applications, as well as a significantly more portable system. The design of projectile launchers is hardly a new endeavor; everything from batting cages to artillery has attempted to accurately hit a target. While small consumer systems such as a ping pong machine or batting cage lack sensory capabilities and rely instead on calibration, military applications are usually far more sophisticated. However, while guided artillery batteries are capable of rejecting disturbances through sensors and computers, smaller launchers such as mortars are not. The same desire for compactness and economy is what drives commercial applications to rely simply on calibration to ensure accuracy. Both commercial 1

7 enterprises that market projectile launchers requiring accuracy as well as the military would benefit from a small cost-effective trajectory correction system. Since the purpose of the prototype is simply to demonstrate the viability of such a system, the most significant functional requirement is accuracy. The firing system must be above all be capable of consistently striking the same location when locked into a position, else the iterative learning algorithm will be unable to calculate corrections. Also, the pan and tilt mechanism used to aim the launcher must be able to accurately adjust and detect its orientation, and the controller must ensure that steady-state error is near zero and that noise tolerance is high. To ensure that any error in the orientation is insignificant, the rise time, fall time and settling time of the control system should be low; the percent overshoot should be low but this is not a critical factor. Beyond the control system, the rotational velocity of the launcher is not a significant factor and as such will likely be kept low to allow for increased accuracy. The range of motion for the launcher will be sufficient to strike any target within range. The payload for the pan and tilt mechanism, specifically the launcher and its mounting apparatus, will be made of plastic and aluminum and hence lightweight. The cost of the system will be low enough to allow for its widespread adaptation to the various low-cost applications discussed previously. Quantitative specifications are described in Table 1.1. The scope of effort required to realize the project proposed here is significant and diverse. The initial design and control of the pan and tilt mechanism require knowledge of control theory and modeling. Once that is accomplished, the implementation of the disturbance rejection system will integrate algorithm design skills, sensor development and trajectory planning. Beyond the control design, mechanical design skills will be used to create the 2

8 mounting apparatus for the launcher, as well as to automate the firing of a projectile. Nonetheless, the project goal is attainable within the allocated timeframe. Range of Motion (Pan) -180 to +180 Range of Motion (Tilt) -45 to +45 Rotational Accuracy ±0.1 Rotational Velocity 30 / s Steady State Error 0% Noise Tolerance 98% Rise Time / Fall Time < 0.1 s Settling Time < 0.1 s Percent Overshoot < 15% Payload < 2 lbs Table 1.1: System Specifications 3

9 2. OBJECTIVES The goal of the project is to fire a projectile in the rough direction of a given target, and automatically compensate for any disturbance that causes the projectile to miss its target using feedback. The important features of the project are the pan and tilt mechanism responsible for orienting the launcher, the launcher itself, the infrared sensor responsible for indicating the approximate direction of the target, and the touchscreen responsible for determining the exact point of impact. These will be tied together by a computer system responsible for controlling the pan and tilt mechanism and computing the data from the sensors to allow for proper trajectory corrections. The scope of the project has narrowed slightly since the original concept. Due to the launcher selected, which fires circular discs, a horizontally mounted touchscreen is no longer feasible due to the trajectory of the discs. Though it is believed that the time and resources will be sufficient, the infrared sensor will be the last feature added as it is not a pivotal factor in achieving the project s goals. The most critical design parameter for the project will be the accuracy and consistency of the shots. In addition to a steady-state error of zero, the rise and fall times of the control system must be minimized to ensure that the actual orientation of the launcher precisely matches the desired orientation. The greatest challenge in the design of the system will be the creation of the iterative learning algorithm responsible for orienting the launcher to strike the targeted point directly. It must take into account not only the disturbances due to the environment, but the possibility that the launcher will not be perfectly consistent. Another significant challenge will be the integration of the touchscreen itself, as the group has no experience with this sensor type, and it may be difficult to ensure that an impact to the screen registers a location. 4

10 The prototype model will not suffer from any constraints due to economics, environment, sustainability, manufacturing, ethics, health and safety, or sociopolitical impact. Although some of the potential applications of the concept, specifically those involving weaponry, may generate concerns based upon ethics, environment, and sociopolitical impacts, it is believed that those concerns are due to existing technology and will not be significantly amplified by the project. Improved accuracy of small artillery may in fact improve a number of factors such as safety and economics due to the more contained nature of the destruction. A possible manufacturing concern will be that each application will likely need to modify the project to utilize a different sensor depending on how it is to be used: a glass touchscreen is not quite up to the task of determining the error in an 80 mpg fastball s trajectory. Beyond that however, the project is an exercise in theory that by itself, carries no inherent moral quandaries. 5

11 3. DESIGN STRATEGY 3.1 Simulation & Modeling The objective of the simulation and modeling phase is to develop a complete model of the behavior of the pan and tilt system. To model the system correctly, the mass properties and friction parameters had to be identified. These, as well as the physical dimensions of the motors, gears, mounts and belts are needed to model the behavior of the system. With a model of the system, we can send inputs to the system so that we can simulate the expected response. Modeling is very useful in verifying that the two GM8724S017 motors are sufficient for our design requirements. In order for the pan-tilt system to be properly modeled, various parameters have to be identified. In order to identify the mass properties such as inertia tensors and center of mass, the existing SolidWorks model of the pan and tilt system was modified to match our system with the estimated payload. Then the mass properties dialogue built into SolidWorks was used to obtain the inertia tensors and center of gravity. The mass properties are given in the Appendix, pages 28 & 29. Once we have decided exactly how to mount the projectile launcher onto our pan and tilt device, a more accurate SolidWorks model will be built. Parameters for coulomb and viscous friction in both the pan and the tilt portions also had to be identified. Friction identification is important because it can be compensated for later. A constant voltage is output to the motor to apply a constant torque and then data from the encoders is obtained and used to calculate the steady-state velocity. The test was run using a variety of different input constant voltages and it was found that, for both the pan and the tilt parts, the system began to saturate at 0.9 volts, in that anything above that would reach the same steady-state velocity. Therefore, it was necessary to test both the pan and tilt axis over a range of 6

12 -1V to 1V in increments of 0.1V. It takes less torque to keep the device in motion then it does to start it moving in the first place. In order to overcome that effect, we applied a 0.01s impulse of positive 10V for the positive voltages and -10V for the negative voltages. Upon running the initial test, it was found that there was much noise present in the output. In order to filter out some of the noise, the test was run five times at each constant voltage and then those five tests were averaged. The data obtained from the averaging of the five tests was better, but it still had much noise. The noise could be further dealt with by averaging the each value with the 25 values after it in the steady-state portion of the plot. A MATLAB script was written to automate the process and is shown in the Appendix. The velocities vs. time curves for the tilt and pan axes were plotted and these plots can be found in Figures 5.5 and 5.6 respectively. In order to obtain the coulomb and viscous friction, a plot was made of the steady-state velocities vs. the constant torque and then obtaining the best-fit line. Both the coulomb and viscous friction can be obtained from Figures 5.7 and 5.8. Friction identification will be discussed further in the verification section of the report. 3.2 Mechanical Design When the mechanical design is complete, the pan and tilt motor system will be fully functional and will have the ability to aim at a target and fire the disc. It will also have the ability to correct any error that occurs so that it can get closer to the target. Our design involves a disc launching mechanism that was purchased at Wal-Mart. The disc launcher needs to be mounted onto the pan and tilt system, but before this can be done the disc launcher needs to be modified. As purchased, the launcher runs on battery power. The problem with it running on battery power is that the amount of power supplied to the system 7

13 would dissipate over time as the battery drains. In order to overcome this difficulty, the launcher needs to be powered by a DC power supply so that the amount of power supplied to the system will remain constant. After the modification is made, the launcher will be mounted onto the system. 3.3 Control Design The objective of the control design is to develop a control system that is capable of aiming at the target by correctly and accurately positioning the disc launcher properly. The target is on a touchscreen and an infrared sensor will be used to detect the position of the touchscreen and the target so that the mechanism can aim near the target. In order to successfully complete the initial aiming, the control system will receive input from the sensor regarding the position of the touchscreen and then orient the pan and tilt system at the angles required to target the touchscreen. The touchscreen itself is also a sensor. When the disc hits the touchscreen, it may not hit the actual target on the first try. The touchscreen will give Cartesian coordinates of the point of impact, as well as Cartesian coordinates of the location of the target. In order to correct the error, a transformation between the Cartesian coordinates and the states of the pan and tilt joints has to be developed. The error from the touchscreen must be transformed into a desired pan or tilt angle. The output from the transformation will be input to the controller and the control system. The disc launcher will then be positioned appropriately. Figure 3.1 illustrates the control flow of the proposed system. A Cartesian coordinates of the target and the point where the disc hits the touchpad. The coordinates are used to calculate the error. B Desired Pan and Tilt joint angles 8

14 C If the coordinates of the target on the touchpad and the coordinates of the point where the disc hit the touchpad are equal, then it has hit the target and completed the objective. Signal from sensors Control System Pan and Tilt Motors Projectile Launcher Pan and Tilt Motors Control System B A Data from Inverse Kinematics Touchpad C Projectile Launcher Figure 3.1: Control Flowchart Complete The pan and tilt mechanism requires input to be in radians whereas the project will be dealing with distances. Figure 3.2 shows a part of the Simulink model file where it converts the distances to desired angles. Since the target cannot be sensed yet, the distance between the firing mechanism and the target needs to be input manually. After the shot is fired, the distance between the target location and impact location on target must be input manually until the touchscreen is installed. Once the screen is installed, the error will be fed back automatically. Figure 3.2: Initial Orientation Calculator 9

15 4. PLAN OF ACTION The plan of action is to streamline the process of designing and creating the system, so we begin by breaking the entire project into four major categories: Simulation and Modeling, Mechanical Design, Control, and Testing each led by a separate group member. We then further divided these down into minor categories completed by different group members. Table 4.1 lists each category, the leader of that section, and the parts that make up that category listed in the column underneath. The rows separate different parts of the development of our entire system. Simulation and Modeling - Yena Park Mechanical Design - Josh Schuster Control - Diana Mirabello Testing - Ryan Kindle - Friction Identification - Inertia of Pan and Tilt Mechanism (Diana and Yena) - Trajectory of Disc after Launch (Josh) - Mounting of Gun on System - Design and Mounting of Firing Mechanism (Ryan and Josh) - Automated Firing of Disc Launcher (Diana and Yena) - Test of Mounted System and Automated Firing (Ryan and Josh) - Develop Model of System with Touchpad - Simulate System with Touchpad (Yena and Diana) - Integration of System with Touchpad (Yena and Ryan) - Programming of System with Touchpad (Diana and Josh) - Learn to use and calibrate touchpad (Yena and Ryan) - Test integration of touchpad with System (All) - Develop Model of System with IR sensor - Simulate System with IR sensor (Ryan and Josh) - IR Integration and calibration (Josh and Diana) - Program System to respond to IR sensor (Yena and Ryan) - Test IR System (Josh and Ryan) 10

16 - Advanced Trajectory model (Josh) - Adjust Mounting of Gun to fit with new Advanced Trajectory Model (if necessary) (Ryan and Josh) -Adjust Firing Control of Gun to fit with new Advanced Trajectory (if necessary) (Yena and Diana) - Test new Trajectory and any changes made (Josh and Yena) -Develop Complete Model (Ryan, Diana, Yena) - Develop learning algorithm - Programming (Diana and Josh) - Test algorithm and debug programming (Yena and Josh) - Test Complete System (All) - Re-evaluate Simulations and Models that fail Testing (Yena) - Adjust and Repair Physical System as needed during Testing (Josh) - Continue to develop and debug code as needed (Diana) - Continual Testing of System. (All) Table 4.1: Division of Tasks 11

17 5. VERIFICATION 5.1 Launcher Verification To verify that the toy disc shooter obtained would be consistent and accurate enough to be viable for use in our system a few tests were run. The first test was a simple test to determine consistency. Holding the gun on a level surface and aiming it at a pint glass on the same level surface, the gun was fired 5 times at a set distance. This was repeated for three trials for each distance. The number of times the disc hit the glass was recorded and the percent of that number out of 5 was put in the table. The Total Accuracy of the disc shooter at that set distance was then averaged from the averages obtained from the three trials. The results of this experiment are listed in Table 5.1. Distance Try 1 Try 2 Try 3 Total Accuracy 3ft 0.9m 100% 100% 100% 100% 5ft 1.5m 80% 100% 100% 93.33% 7ft 2.1m 80% 80% 80% 80% 9ft 2.75m 80% 60% 80% 73.33% 11ft 3.35m 80% 100% 80% 86.67% 13ft 4m 60% 60% 40% 53% Table 5.1: Disc Shooter Accuracy Finding the results of this first experiment satisfactory, it was decided that the disc shooter would be used. To obtain a more accurate understanding of how the disc is fired and how it travels a second test was designed to determine the trajectory of the disc after being launched from the toy gun. This experiment was set up very similarly to the previous one. The gun was held on a level surface and now aimed at a piece of paper with a graph drawn on it. This graph had marks for each centimeter vertically and horizontally away from the origin and 12

18 was taped to the wall so that the origin was on the same level surface as that of the barrel of the toy gun. The gun was fired 10 times at a set distance and the x and y coordinates where the disc hit were recorded for each shot. The gun was then moved to another set distance and the experiment was repeated. The results of this experiment are listed in Table 5.2. Shot # 0.5 m (x 0.5 m (y 1.0 m (x 1.0 m (y 1.5 m (x 1.5 m (y 2.0 m (x 2.0 m (y x x x x x x x x x x x x x x x x x x x means the disc hit lower than -14cm and could not be recorded Table 5.2: Preliminary Trajectory Results The conclusion drawn from this experiment was that the trajectory should be determined from data collected between 0.5 and 1.5 meters. Anything before 0.5 meters will be fired at a negative angle and anything after 1.5 meters will be fired at a positive angle relative to the horizon. This led to the next experiment that was done in the exact same matter as above. The result of the trajectory experiment with data from 0.5 to 1.5 meters is shown in Table 5.3. Shot # 0.5 m (x 0.5 m (y 0.7 m (x 0.7 m (y 0.9 m (x 0.9 m (y

19 1.0 m (x 1.0 m (y 1.1 m (x 1.1 m (y 1.3 m (x 1.3 m (y 1.5 m (x Table 5.3: Short Range Trajectory Results 1.5 m (y A summary of this experiment can be seen in the Table 5.4, which shows the average x and y positions at each distance. 0.5 m (x 0.5 m (y 0.7 m (x 0.7 m (y 0.9 m (x 0.9 m (y m (x 1.0 m (y 1.1 m (x 1.1 m (y 1.3 m (x 1.3 m (y 1.5 m (x 1.5 m (y Table 5.4: Average Short Range Trajectory From this data, it can be concluded that the horizontal position of the disc stays relatively close to straight with a maximum of 1 cm average deviation from the origin. It can also be seen that as the distance from the target increases, the vertical position that the disc strikes the target also decreases. A plot of distance from target (in meters) vs. vertical position relative to the horizontal (in centimeters) is shown in Figure

20 Figure 5.1: Vertical Drop vs Distance Traveled Fitting a best-fit line to this data, the equation is found to be: Y = -9.5X , where X is the distance from the gun barrel to the target and Y would be the vertical displacement where the disc would hit the target. This equation is a good estimation of the trajectory of the disc knowing the distance to the target between 0.5 and 1.5 meters. This will later be expanded to range from zero to three meters after the disc launcher has been mounted and angled tests can be done. 5.2 Friction Identification The purpose of the following Simulink model file (Figure 5.2) is to obtain necessary data for estimating coulomb frictions and viscous frictions for tilt axis. For pan axis, the two inputs to the PCIM-DAS block have to be swapped. PCI-QUAD04 has one output port that needs to be multiplied by 2π/(2048*4) to acquire theta, which is the angle that motor points to after the 15

21 command. Theta1 and thetadot1 corresponds to angle and the speed of tilt motor. Since the amount of torque that is required to start the system moving is greater than the torque required to keep the system moving in motion once it is already moving, an impulse was inputted 0.3 seconds after the simulation started with a pulse width of 0.01 seconds to break the static friction. Input voltage was incremented automatically with the for loop from the script. Figure 5.2: Friction Identification Simulink Model File Some filtering was necessary because the velocity collected from a single simulation was fluctuating up and down. Figure 5.3 shows the raw data before the filter was applied. Filtering was implemented in three steps. First step was taking average from five runs for each voltage steps. During second step, it took the average of the twenty-five adjacent data points from the data set that was calculated from first step. Finally, the impulse spikes were eliminated. The data plot from Figure 5.4 is after second step of the filtering, with Figures 5.5 and 5.6 showing the fully filtered output for the tilt and pan axes respectively. 16

22 For both the pan and tilt axes, all velocities with input voltage greater than -0.5 volts and less than 0.5 volts saturated to zero. Velocities with input voltage greater than 1 Volts or less than -1 volts all saturated to rad/s and rad/s for tilt axis, rad/s and rad/s respectively for pan axis, well above the velocity the specifications require. Figure 5.3: Velocity Diagram Without Filter Figure 5.4: Velocity Diagram After Implementation of Second Filter 17

23 Figure 5.5: Velocity Diagram After Implementation of Third Filter for Tilt Axis Figure 5.6: Velocity Diagram After Implementation of Third Filter for Pan Axis 18

24 Torque was calculated using following equation: Torque = Voltage * N * Nm * Kt*Ka Voltage = Input Voltage (-1~1 Volts) N = External Gear Ratio (2.47) Nm = Internal Gear Ratio (19.5) Kt = Motor Torque Constant (4.36e-2Nm) Ka = Amplifier Gain Constant (.1A) From Figure 5.7 and Figure 5.8, the coulomb frictions and the viscous frictions were obtained (Table 5.5). The coulomb frictions are the two end points of the line where steady state velocity is zero, and the viscous frictions are the velocity of the line where it connects the maximum velocity to zero. For the tilt axis, the negative coulomb friction equals Nm, and the positive coulomb friction equals Nm. The negative viscous friction and positive viscous friction are NmS/rad and NmS/rad respectively. These values were calculated using script attached in the back. For pan axis, negative coulomb friction equals Nm, and positive coulomb friction equals Nm. The negative and positive viscous frictions are NmS/rad and NmS/rad respectively. Axis Coulomb Friction (Nm) Viscous Friction (NmS/rad) negative positive negative positive Tilt Axis Pan Axis Table 5.5: Coulomb & Viscous Friction for Both Axes 19

25 Figure 5.7: Diagram of Torque vs. Steady State Velocity of Tilt Axis Figure 5.8: Diagram of Torque vs. Steady State Velocity for Pan Axis 20

26 The data captured from the above procedure will not be in our project for two reasons. First, because the pan and tilt mechanism was tested without the firing mechanism since mounting the firing mechanism has not been done yet. The second reason is that the testing was done before the pulse width for impulse was given. The testing was done with the pulse width of 0.01 seconds when the given pulse width for impulse is 0.25 seconds. Therefore, more accurate friction testing should be done once the mechanism is complete with the right value of pulse width. 21

27 6. COST & SCHEDULE 6.1 Cost Analysis The cost of the assembled pan and tilt system used as the basis of this project has been itemized and calculated as follows: Item Part Number Price ($) Quantity Total ($) Motor GM8724S Timing Belt A6Z16-C Encoder S1 & S2 Optical Shaft Encoders Gear A6A6-75NF01812 A6A6-25DF Total Table 6.1: Pan and Tilt Mechanism Cost The additional parts and programs needed for our complete system beyond those of the assembled pan and tilt mechanism are as follows: Item Price ($) Quantity Total Toy Disc Shooter and Discs Touchpad Wires (spool) Programs: SolidWorks MATLAB 7 Simulink , , Motor Gears Sensors: Infrared LED

28 Infrared Detector Clamps (for Mounting) TOTAL 18, Table 6.2: Additional Parts Needed for System The labor cost of designing, building, testing and operating the system among the four members of this group project are as follows: Laborer Salary ($/hr) Hours/Week Weeks Total ($) Ryan Kindle ,500 Diana Mirabello ,500 Yena Park ,500 Josh Schuster ,500 Total for 4 Employees ($) 10,000 Table 6.3: Labor Costs The use of different labs to build and test our system has been assumed to cost as follows: Lab Rate ($/day) Use (days) Total ($) Control Systems Lab ,000 Engineering Lab Total 3,200 Table 6.4: Lab Usage Pan and Tilt Mechanism Additional Parts Needed for System Labor Costs Lab Use Total $ $18, $10,000 $3,200 $32, Table 6.5: Total System Costs 23

29 Seeing as many of the components, programs, labs and equipment are provided free of charge, along with the fact that there is no labor cost, the actual cost to our group can be calculated (Table 6.6). Pan and Tilt Mechanism Additional Parts Needed for System Labor Costs Lab Use Total $0 $59.54 $0 $0 $59.54 Table 6.6: Actual Cost of System 24

30 6.2 Schedule Week 1 (2/23 3/2) - Friction Identification - Inertia of Pan and Tilt Mechanism (Diana and Yena) 2 (3/3 3/9) - Mounting of Gun on System (Ryan and Josh) 3 (3/10 3/16) -Develop Complete Model (Ryan, Diana, Yena) 4 (3/17 3/23) - Learn to use and calibrate touchpad (Yena and Ryan) 5 (3/24 3/30) - Integration of System with Touchpad (Yena and Ryan) 6 (3/31 4/6) -IR Integration and calibration (Josh and Diana) 7 (4/7 4/13) -Testing and Adjusting (All Group Members) 8 (4/14 4/20) -More Testing (All Group Members) 9 (4/21 4/27) - Adjust System based on feedback from demonstration (All Group Members) 10 (4/28 5/4) -Work on Final Report (All Group Members) Work to be Completed - Trajectory of Disc (Josh) - Automated Firing of Disc Launcher (Diana and Yena) - Advanced Trajectory model (Josh) - Develop learning algorithm - Programming (Diana and Josh) -Programming of System with Touchpad (Diana and Josh) - Finish Programming (Yena and Ryan) -Prepare for Demonstration (All Group Members) -Prepare for Final Presentation (All Group Members) - Project Proposal and Presentation Due. (All Group Members) - Obtain needed parts (sensors, touchpad) (Ryan) - Work on Progress Report (All Group Members) - Design Progress Report and Presentation Due. (All Group Members) -Begin Testing (All Group Members) Project Demonstration (All Group Members) Final Presentation (All Group Members) Final Report Due (All Group Members) 25

31 7. BIBLIOGRAPHY Strassberg, Dan. Math, simulation updates offer new programming tools, faster development. EDN.com. 6/10/ SolidWorks Student Edition JourneyEd.com DWORKS&GEN3=JEM&T1= FS6 Action Solutions. Action Solutions Wen, John. S1 & S2 Optical Shaft Encoders. Encoder Datasheet. 9/26/02. Bowen, Luke, Cieloszyk, Matt and Gillette, Rob. Team 5 Proposal. Team 5 Proposal. 2/22/ High Power Infrared LEDs. Reynolds Electronics Motors, Servos, Wheels and H-Bridges Section. Hobby Engineering. 2/28/

32 8. STATEMENT OF CONTRIBUTION Abstract Introduction Objectives Design Strategy Plan of Action Verification Cost & Schedule Compilation & Editing Ryan Kindle Ryan Kindle Ryan Kindle Diana Mirabello Yena Park Josh Schuster Yena Park Josh Schuster Diana Mirabello Josh Schuster Ryan Kindle Josh Schuster Yena Park Diana Mirabello Ryan Kindle 27

33 APPENDIX Mass Properties for the Pan Axis Density = kilograms per cubic meter Mass = kilograms Volume = cubic meters Surface area = square meters Center of mass: ( meters ) X = Y = Z = Principal axes of inertia and principal moments of inertia: ( kilograms * square meters ) Taken at the center of mass. Ix = (0.1099, , ) Px = Iy = ( , , ) Py = Iz = (0.9917, , ) Pz = Moments of inertia: ( kilograms * square meters ) Taken at the center of mass and aligned with the output coordinate system. Lxx = Lxy = Lxz = Lyx = Lyy = Lyz = Lzx = Lzy = Lzz = Moments of inertia: ( kilograms * square meters ) Taken at the output coordinate system. Ixx = Ixy = Ixz = Iyx = Iyy = Iyz = Izx = Izy = Izz =

34 Mass Properties for the Tilt Axis The center of mass and the moments of inertia are output in the coordinate system of pan_tilt_mechanism Mass = kilograms Volume = cubic meters Surface area = square meters Center of mass: ( meters ) X = Y = Z = Principal axes of inertia and principal moments of inertia: ( kilograms * square meters ) Taken at the center of mass. Ix = ( , , ) Px = Iy = ( , , ) Py = Iz = ( , , ) Pz = Moments of inertia: ( kilograms * square meters ) Taken at the center of mass and aligned with the output coordinate system. Lxx = Lxy = Lxz = Lyx = Lyy = Lyz = Lzx = Lzy = Lzz = Moments of inertia: ( kilograms * square meters ) Taken at the output coordinate system. Ixx = Ixy = Ixz = Iyx = Iyy = Iyz = Izx = Izy = Izz =

35 MATLAB Scripts %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %friction_param_setup.m %02/26/05 %set the initial values for friction_param.mdl %put the logs on the signals %subsystem under friction_param.mdl needs to be selected before running this file %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% ts = 0.001; %sample time const_voltage = 1; peak_voltage =10; handles = get_param(gcb, 'porthandles'); outputports = handles.outport; for i = 1 :length(outputports) set_param(outputports(i), 'DataLogging', 'on'); set_param(outputports(i), 'TestPoint', 'on'); end set_param(outputports(1), 'Name', 'theta1_log'); set_param(outputports(2), 'Name', 'thetadot1_log'); set_param(outputports(3), 'Name', 'theta2_log'); set_param(outputports(4), 'Name', 'thetadot2_log'); set_param(outputports(5), 'Name', 'voltage_log'); 30

36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %friction_param_save.m %02/26/05 %run friction_param.mdl in a for loop %collect the data and plot it %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% voltage_range = [-1:.05:1]; times = [0:0.001:5]; for k = 1:length(voltage_range) voltage_range(k) for i = 1 : 5 setparam(tg, 28, voltage_range(k)); i if voltage_range(k)==0 else if voltage_range(k)>0 setparam(tg, 27, 10); setparam(tg, 24, 10); else setparam(tg, 27, -10); setparam(tg, 24, -10); end start(tg); pause(5); stop(tg); outputlog = tg.outputlog; theta_1(i, :) = outputlog(:, 1); theta_dot_1(i, :) = outputlog(:, 2); voltage_out(i, :) = outputlog(:, 5); pause(.5); end end %first filtering thetadot_ave_temp(k, :) = (theta_dot_1(1, :)+theta_dot_1(2, :)+theta_dot_1(3, :)+theta_dot_1(4, :)+theta_dot_1(5, :))/5; %second filtering for j = 1 : length(thetadot_ave_temp(k, :)) - 25 sum = 0; for ii = 0 : 24 sum = sum + thetadot_ave_temp(k, j+ii); end thetadot_ave(k,j) = sum/25; 31

37 end end %third filtering for i = 1 : 41 for j = 1 : 4975 if abs(thetadot_ave(i, j) - thetadot_ave(i, j+1))>1 thetadot_ave(i, j +1) = (thetadot_ave(i, j) + thetadot_ave(i, j + 2))/2; end end end for i = 1 : 25 plot(times(1:4976), thetadot_ave(i, :)); hold on; end ylabel('thetadot'); xlabel('second'); title('tilt Axis'); save tilt_axis.mat thetadot_ave_temp thetadot_ave 32

38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %steady_state1.m %2/27/05 %calculate steady state velocity %calculate torque %plot torque vs. velocity %calculate frictions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% voltage = [-1:.05:1]; %calculate Torque N1 = 2.47; %External Gear Ratio Nm1 = 19.5; %Internal Gear Ratio Kt = 4.36e-2; %motor torque constant Ka =.1; %amplifier gain constant torque = voltage.* N1 * Nm1 * Kt * Ka; k = 1; positive = 0; viscous_friction_negative_sum = 0; viscous_friction_positive_sum = 0; negative_count = 0; positive_count = 0; for i = 1 : 22 thetadot1_ss(i) = 0; for j = :4976 thetadot1_ss(i) = thetadot1_ss(i) + thetadot1_ave(i, j)/1000; end if abs(thetadot1_ss(i)) < save_torque(k) = torque(i); k = k + 1; positive = 1; elseif i ~= 1 && abs(thetadot1_ss(i) - thetadot1_ss(i-1))>0.05 if positive ==0 viscous_friction_negative_sum = viscous_friction_negative_sum + (torque(i)-torque(i- 1))/(thetadot1_ss(i)-thetadot1_ss(i-1)); negative_count = negative_count + 1; else viscous_friction_positive_sum = viscous_friction_positive_sum + (torque(i)-torque(i- 1))/(thetadot1_ss(i)-thetadot1_ss(i-1)); positive_count = positive_count + 1; end end end 33

39 coulomb_friction_negative_tilt = save_torque(1); coulomb_friction_positive_tilt = save_torque(k-1); viscous_friction_negative_tilt = viscous_friction_negative_sum/negative_count; viscous_friction_positive_tilt = viscous_friction_positive_sum/positive_count; plot(thetadot1_ss, torque) xlabel('steady state velocity') ylabel('torque'); title('tilt Axis'); 34

40 SolidWorks Model of the Projectile Firing Mechanism 35