3-DIMENSIONAL AUDIO TRACKING SYSTEM Final Report for ECSE-4962 Control Systems Design

Transcription

1 3-DIMENSIONAL AUDIO TRACKING SYSTEM Final Report for ECSE-4962 Control Systems Design Nicholas J. Di Liberto Daniel Fleiner Andrew LeBlanc Edward Tang April 28, 2004 Rensselaer Polytechnic Institute

2 Abstract The primary purpose of this project is to utilize a pan and tilt device to maintain visual contact of an audio sound source as it moves around a room. We developed our system through a series of design procedures which concluded with a finished working product. We first developed a physical model of our pan-tilt system incorporating the properties of mechanics that define the motion of the system. After the model was complete we validated the model and tuned it, allowing us to develop a simulated plant model. From the plant model we developed a closed-loop controller for both the pan and tilt axes to meet our specifications. Once the controllers were built we tuned them to achieve maximum performance. We made our controllers aggressive enough that we beat our specifications and still have desirable performance. Overall we succeeded in designing a new cost-effective solution for all industries that require video tracking during teleconferencing, lectures, meetings, and other audio and speech triggered motion.

3 Contents 1 Introduction 4 2 Professional and Societal Considerations 5 3 Model Development Friction Identification Model Validation Controller Design 11 5 Subsystem Development Sound Localization Microphones Cost and Schedule Cost Analysis Schedule Conclusion 26 8 Statement of Contribution 28 A Modelvalidinit.m 30 B Frictionidtest.m 32 C Curvefitting.m 34 D Closedloopinit.m 36 1

4 List of Figures 3.1 Friction Identification Simulink Motor Frictions Model Validation Simulink Pan Velocity vs. Time Controller Root Locus Plots Closed Loop Simulation Simulated Sine Wave Input MATLAB Physical Controller Physical Controller Results Faster Controller Results Filter Frequency Response Geometry of Microphones Time Delay Method Peak Detection Time Delay Flow Chart Simulink Diagram of the Time Delay Block Final Microphone and Amplifier Circuit

5 List of Tables 1.1 Performance Specifications Friction Identification Capacitor vs. Microphone Response List of parts Schedule

6 Chapter 1 Introduction Teleconferencing in the digital age is increasing in popularity due to the advancement of the internet and audio/video compression technology. Teleconferencing situations such as distance learning in the classroom and board room meetings often involves multiple speakers and/or moving lecturers that often need to stay in focus of camera broadcasting to remote sites participating in the conference. Our design incorporates a pan-and-tilt system to enable a video camera to track a speaking target or targets and follow the speaking subject if it moves or changes speakers. Mounted microphones and integrated filters ensure that only human voice is tracked and the camera accurately points to the location of the speaker. Video-conferencing is a cost efficient and convenient method to allow meetings to happen. Three-Dimension Audio Tracking (3DAT) could provide a cost effective way to exchange information. Since our design is developed to track a moving human and present the subject on camera, smooth fluid motion with minimum overshoot is mandatory. Jerky or quick motions would cause a viewer discomfort so we designed to ensure a quick rise time to track a moving subject moving at a slow rate. The performance specifications are listed in TABLE 1.1. Pan Motor Tilt Motor Voice Filter 180 rotation ±45 rotation Bandpass filter ±5% error 2% error 500Hz to 2kHz π rad/sec π/2 rad/sec 10Hz noise margin Track 1Hz: Track 1Hz: 5% over shoot 5% over shoot 0.5 sec rise time 0.5 sec rise time 0.1 sec settling time 0.1 sec settling time < 5% error < 10% error Table 1.1: Performance Specifications Our project was divided up into several sub-projects to ensure completion on time. Initially we split the project into model identification and validation, control design, and subsystem design. Later the sub-projects were expanded to include microphone development, tracking algorithm development, and fabrication. 4

7 Chapter 2 Professional and Societal Considerations While researching existing products that do similar functions to our proposed design, we only found similar products that offered functionality that we proposed. The cost of these devices were very high and as such, we found that it would not be economical for most institutions and corporations to buy in bulk quantities. Our design allows such institutions and corporations to deploy an easy-to-use and cost-efficient solution to aid teleconferencing and allow the speaker to always be seen on camera. The result is that the organizations can greatly increase their productivity due to enhanced teleconferencing capabilities with minimal effect on their economic standing. Corporations will see ease of video conferencing with less manpower necessary. Institutions will see greater opportunities, learning, and more positive feedback from distance learning offerings. 5

8 Chapter 3 Model Development 3.1 Friction Identification In order to model our system accurately to design our controller, we had to first identify all of the frictional forces that act on our physical system. We identified friction on both the pan and tilt axes separately using a set of 400 data points on each axis. The script runs 200 tests on positive voltages and 200 tests on negative voltages, with a total range of -2V to +2V. We identified the friction constants by plotting the average steady state velocity of the axis at each voltage and plotting a best fit line to the data. The slope of the best-fit line generated for the data points acquired during the friction identification experiments is an accurate representation of the viscous friction for the individual axis. The point at which the best fit line ends and meets the vertical no-torque line represents the Coulomb friction constant. Figure 3.1: Friction Identification Simulink 6

9 The Simulink block diagram as shown by FIGURE 3.1 we used to run the friction identification experiments is listed in TABLE 3.1. Since we are only interested in recording the steady state velocity of the system at any voltage, we have to ensure that at low torques we excite the motor past the point of stiction. To achieve this we used a unit step pulse to excite the motor to maximum torque (+10V). The unit step is also subtracted from the desired steady state voltage and passed through a unit delay with sampling time 0.25s and added to the unit step. This in effect allows the system to pulse at +10V or -10V for 0.25s and then let the steady state voltage take over for the remainder of the test. The output to the motor amplifier must pulse at 10V to excite the motor beyond stiction, negate the pulse after 0.25s and output V ss to the motor amplifier for duration of simulation. The velocity of the system was determined through a separate block diagram that simply reads the output from the encoder and differentiates the position of the encoder each sample period. The unit delay takes the discrete time derivative of the closed loop system and outputs the change in position to the velocity vector. In the MATLAB script that runs the experiment, we use a gain of 100 since our sampling time is 0.01s. Midway through the design of our system we observed a dramatic change in our system performance. Our identified model was no longer behaving similar to the observed system. We had to re-run the friction analysis and determined that the friction values had changed. The final friction values are listed in TABLE?? Motor Viscous Friction Coulomb Friction Pan Positive Nm s/rad Nm Negative Nm s/rad Nm Tilt Positive Nm s/rad Nm Negative Nm s/rad Nm Table 3.1: Friction Identification Since the velocity saturates at a relatively low torque, we only needed to use a small range of voltages to efficiently and accurately identify the friction in our dynamic system. We found that the torque saturates at approximately -1.1V and +1.1V. Below -1.1V and above +1.1V the steady state velocity does not increase above radians per second. Since saturation adversely affects the friction identification, we only tested the steady state velocities between -1.1V and +1.1V. Using a MATLAB script we generated a process that iterates the friction identification Simulink model through voltages between -1.1 volts and +1.1V in increments of 0.01V. The physical system runs for 10 seconds after which an array of velocities is output from the target computer. Each value in this array is the velocity calculated at each sample time of 0.01s. We then averaged the velocity matrix to determine the average steady state velocity at that voltage and stored it into an array of average velocities. Once all velocities were acquired, we plotted velocity versus torque to determine the friction constants. The torque was determined by finding the product of the voltage matrix, amplifier gain, motor torque constant and overall gear ratio. This is expressed in the following equations: τ M = V (t)k A K M Nτ M = V (t) 0.01A/V 4.36E( 2)Nm/A (3.1) The plots of velocity vs. torque for both pan and tilt axes are in FIGURE 3.2. We used the MATLAB function polyfit to generate a best fit line to the data points generated by our MATLAB script. 7

10 (a) Pan Axis Friction (b) Tilt Axis Friction Figure 3.2: Motor Frictions The results that we determined from the friction identification experiments are listed in TABLE Model Validation A physics-based model for the system was implemented in MATLAB s Simulink program as figure 3.3. The equation for the model is θ + B v J θ + B c J sgn θ = K J V (3.2) Where θ is velocity, V is input voltage, B v is viscous friction, B c is coulomb friction, K is a torque constant and J is inertia. The friction values were measured experimentally. The torque constant K converts the voltage into the motor into the torque produced by the motor. This value is comprised of the motor torque constant, K t = 4.36E-2, and gear ratio, N = 6.3, from the motor data sheet, as well as the amplifier gain,.1 Amps/Volt, and the pulley gear ratio, N p = 2.7. The inertia value is calculated with the load inertia, which comes from the CAD file of the system, the gear ratio of the motor and the motor inertia, both of which are on the motor data sheet. All variables were hard coded into an initialize file modelvalidinit.m in the appendix. In that file we also stored all the different friction values for the two axes, pan and tilt, and the applied voltage, positive or negative, which allowed us to simply uncomment the corresponding line of code for the axis being worked with. We ran tests at several input voltages and plotted the transient response of the motor at each velocity. The same response of the model was then plotted on top of the actual response. The parameters were tuned until the model output matched the actual experiments. The final validated model response for the pan axis is listed in FIGURE 3.4. One can deduce from our experiments that our validated model is extremely close to the actual response of the motor system. Therefore we can assume safely that the plant transfer function we derive from this identified model will be accurate for control design. 8

11 Figure 3.3: Model Validation Simulink Figure 3.4: Pan Velocity vs. Time 9

12 The motor saturated at rad/s, determined experimentally, and was modeled in Simulink with a saturation block that clipped the velocity at this value when the model tried to increase the velocity beyond the saturation speed. The model retains a constant rise time which is independent of the input, which is not the case physically. By saturating the output velocity on the model, the rise time to saturation is decreased with increasing input voltage once the input was sufficient to saturate the output. Another saturation block was used to model the amplifier, which outputs between -10V and 10V. Initially, the step response of the model did not exactly match that of the experimental data. By experimenting with the load inertia value slightly, we were able to obtain near-exact step response plots as illustrated in FIGURE 3.4. This is acceptable because the load inertia value, although calculated from the CAD model, was estimated. This was not the first model we implemented. Before we used this model, we used a much more complex one that included the back EMF of the motor and load torque. It also included constants from the motor data sheet such as viscous and coulomb friction, resistance, and the back EMF constant. The model had to be corrected by entering a significantly higher load inertia value than actual to make the step response curves match the measured curves. This correction was due to the fact that all of these constants were accounted for in the measured Coulomb and viscous friction values already. 10

13 Chapter 4 Controller Design Controller design required linearizing the non-linear model we developed. The only non-linear term was the Coulomb friction term due to the signum function. To linearize the model, this term was set to zero, then a transfer function was derived. The general transfer function is G p (s) = K I s 2 + Bv I s b 2 where K = torque constant, I = inertia, B v = viscous friction and b 2 is the gravity term, which is zero for the pan axis. Using the actual values calculated and verified from the simulation, we found the actual transfer functions of each axis to be: G ptilt (s) = s 2 (4.2) s and 25.9 G ppan (s) = s 2 (4.3) s for the tilt and pan axes, respectively. One at a time, the transfer functions were entered into MATLABs SISOtool and a discrete controller was developed by placing poles and zeros on the closed loop root locus plot. This method allows the controller to be designed for certain constraints such as rise time, settling time, steady state error and overshoot. There are other ways to design a controller, such as with state space matrices, but they are more involved. For our purposes, design with SISOtool is sufficient. The gains of the controller must lie inside the unit circle in order for the system to be stable. At first, a second order controller was designed, but did not perform as well as intended. The second order controller was not fast enough to meet our specifications and, more importantly, was not smooth in the control of the system, which is important for the camera to record decent images and not cause headaches for the viewer. So a new controller was developed - this time a first order, lead controller, in which the pole is to the left of the zero. Lead controllers are used to minimize steady state error, which is important in this project so the speaker will be in the middle of the screen. The controller was also designed such that high frequencies were attenuated, since only low frequencies would be input and, again, to keep motion smooth. The final controllers were: G ctilt (z) = 141 z (4.4) z (4.1)

14 and G cpan (z) = z z for tilt and pan axes, respectively. The pan controller requires a larger gain due to the larger inertia of the pan axis. The closed loop root locus plots are illustrated in FIGURE 4.1(a) and FIGURE 4.1(b). The bode plots show the gain falling below zero before 100 rad/sec for each closed loop system. The gain margins are both around 50 which means the controllers are very stable. The phase margins are 9.5 and 7.3, which are not as robust as the gain margin, but are still better than zero. Once the controllers were designed, they were each implemented in a closed loop simulation with a sine wave input. See FIGURE 4.2. A sine wave was used, as opposed to a step input, because tracking a person walking around a room is gradual, like a sine wave, not instantaneous, like a step. The process of designing a controller in SISOtool, exporting to MATLAB and simulating was repeated several times until an acceptable simulated response was obtained. Simulated results of the final controllers tracking a 2 rad/sec sine wave are illustrated in FIGURE 4.3. Once the results were acceptable in terms of our design specifications, the controller was implemented on the physical system. See FIGURE 4.4. The actual versus desired position of the physical system tracking a sine wave is illustrated in FIGURE 4.5. The plot shows the curve flattened out at the peaks and troughs of the sine wave. This is due to the phase shift of the actual position. The actual curve flattens out when the desired curve is at its peak. A faster controller would alleviate this problem. More detailed analysis of the plot, FIGURE 4.6 reveals the position error in the peaks is about 4% for the pan axis and about 10% for the tilt axis, both of which are within the design specifications. Friction cancellation was not used in the physical system because it made the actual response very jerky. Friction cancellation relies on the velocity. Originally, when friction cancellation was in the simulation, velocity was calculated from the output position by derivation. This was different from the actual, simulated velocity in the model due to the quantizer. In the simulation, we added a velocity output from the model, which cleaned up friction cancellation and cleaned up the output position. FIGURE 4.2 is the Simulink block diagram of the controller with friction cancellation. Friction cancellation on the physical system made the response worse for the same reason - that the calculated velocity is not exact and the cancellation is off. (4.5) 12

15 (a) Pan Controller 13 (b) Tilt Controller Figure 4.1: Controller Root Locus Plots

16 Figure 4.2: Closed Loop Simulation Figure 4.3: Simulated Sine Wave Input 14

17 Figure 4.4: MATLAB Physical Controller Figure 4.5: Physical Controller Results 15

18 Figure 4.6: Faster Controller Results 16

19 Chapter 5 Subsystem Development 5.1 Sound Localization Before we even started to figure out exactly where the sound we coming from, we needed to first filter out as much noise that we could. To filter out high frequency and low frequency noise we places a bandpass filter on all of the microphone inputs. This filter would only allow the human vocal range, 500 Hz to 2000 Hz to pass through. With this filter in place we were able to limit the amount of noise on the microphones. To create this filter we used a IIR elliptical filter based off a low pass analog design. FIGURE 5.1 is the frequency respond of this filter. Once the signals have been filtered, we then were able to focus on ways to get our system to respond properly. In order to tell our system how to respond to the sound inputs it was getting, we need to figure out the location of the sound source. To locate the source all we needed were two angles, one for the pan axis and another one for the tilt axis. To figure out the angle all we needed was an approximation. After looking at the geometry of our system, FIGURE 5.2, and reading through Steven George Goodridge s Multimedia Sensor Fusion for Intelligent Camera Control and Human-Computer Interaction, we were able to find equations relating our two microphones to an angle. The equations for this can be seen below. θ = arcsin d L d R d LR (5.1) d L d R = (t L t R )v sound (5.2) θ = arcsin (t L t R )v sound d LR (5.3) These equations have one major assumption; the speaker must be at farther away from the system than the distance between the two microphones. These formulas can be used for both the pan and the tilt axis because the set up is exactly the same. 17

20 Figure 5.1: Filter Frequency Response Now that we had the equations we needed to figure out how to relate out input signals to the equations. Our first approach was to directly relate the amplitude of the microphones to a distance. This method, however, was very flawed. Human voice varies drastically in amplitude, because of that we realized that this method could not be used. If we were using a constant tone this method could work, because the amplitude would decrease exponentially as the sound moves farther from the device. The second method we attempted, and ultimately ended up using, was a time delay approach. Here we could find the delay of similar signals between the two microphones and relate that to distance by estimating the speed of sound. This method does not rely on the amplitudes of the signals, so the fact they are varying does not affect the system. This method can be implemented easily in MATLAB as seen in FIGURE 5.3. To implement it first we applied EQUATION 5.3, and then we added onto that the last angle from the encoder, since this time delay method calculates the angle from the current position. The main issue with this method was actually figuring out how to find the time delay method in real time. We did not want to there to be a delay when 3DAT was trying to find the target. To find the time delay between the two signals, we used a peak detection method. This method is outlined in the flow chart shown in FIGURE 5.4. This method was then implemented in Simulink. As seen in FIGURE 5.5, various parts of the Simulink file have been outlined in different colors to match the previous flow chart. The red and green parts of the diagram are exactly the same; they just represent the two different signals that are being compared. To determine whether or not there is a peak we take the difference between to samples. As seen in the red 18

21 Figure 5.2: Geometry of Microphones Figure 5.3: Time Delay Method 19

22 Figure 5.4: Peak Detection Time Delay Flow Chart Figure 5.5: Simulink Diagram of the Time Delay Block 20

23 and green parts of FIGURE 5.5 to find the difference between two samples we take the input signal and give it a forced delay. We then subtract the delayed value from the current sample and we get a difference. We then compare this difference to a threshold value. If it is greater than the threshold we store the time of the peak as well as increment the peak count. In the blue section of the diagram we compare the peak counts of the two signals, when they match we subtract the two and output that answer. To verify that this method would give us the correct delay time we tested it in MATLAB before implementing it on out system. The test of this algorithm was rather simple. We took a voice sample that we gathered from one of our microphones and fed it into one of the inputs of the diagram. We then forced a delay in the signal and fed it into the other input. The output of that test verified that the algorithm worked because no mater what delay we forced on the input the output caught it each time. The output from the microphones, although filtered, was still erratic, as any sound signal is. Finding the peaks on this type of signal is difficult and inaccurate with the algorithm used by the program. To make more pronounced peaks, several different methods were tried. One method was a low pass filter, but this did not clean up the signal enough. The other main idea we had was to use an envelope detector to smooth out the signal. However we found that the computation for this caused our program to crash a majority of the time. Finally, the RMS was calculated, which changes gradually over time with the signal power, so the peaks were very pronounced. A new problem arose, however, in that the RMS recovered from the peaks slowly. To alleviate this problem, the RMS block was reset to zero every 500ms. Using this method we were able to our peak detection block to work a majority of the time. Other methods to smooth out the signal were discussed, but none of them could have been implements in real time as easily as the running RMS. Using the running RMS along with the peak detection method for figuring out time delay worked for a majority of the time. It seemed to have problems locating the strongest sound in a crowed room, so we were limited as to when we could test the algorithm since we needed relative silence around 3DAT. We also attempted a third method, to try and get a smooth result. This method was called the Laboratory Introduction To Embedded Control (LITEC) approach because it was similar to the approach students are forced to take in LITEC with the smart cars. Basically all we would do is to tell the system to move a set angle in a certain direction based on the difference of amplitude between the two signals. If the left microphone had a stronger signal, tell the system to move 0.01 radians more to the left. This was a simple approach to getting a quick result We moved away from the method for various reasons. One reason was that it was just not a smart approach. What we mean by that is that the time delay method pinpoints exactly in space where the sound is coming from. This method doesn t. Also the LITEC method also has the potential to cause ringing in the steady state because the set angle you have it rotate is not small enough you could easily overshoot your target and start bouncing back and forth around it, if the target is not moving. 5.2 Microphones The microphone that we had chosen for this project is the Horn model EM9752U. We chose this model microphone because it is a cost effective directional microphone. It will attenuate signals coming in from the sides and behind the unit. It is also relatively light weight and small. These microphones also showed 21

24 typical response in the range that we desired according to the manufacturer data sheet. For the initial implementation of the microphone circuit, a 680Ω resistor was placed in series with the 1.5V voltage source. A capacitor size had to be chosen to maximize the response and range of the microphones. TABLE 5.1 illustrates the values of capacitors used to find the optimal response of the microphones. Size 0.01µF 0.1µF 1.0µF Response at 2ft 1mV 5mV 5mV Table 5.1: Capacitor vs. Microphone Response We chose to implement the 1.0nF capacitor since it showed the best response on the oscilloscope. The millivolt range is too fine to quantize with the analog to digital converter. The differences between noise and signal was not readily determinable. An amplifier was implemented to boost the signal as we had a filter to eliminate the unwanted noise that would also be amplified and that we wanted to utilize the entire range of the A/D converters. The first of the amplifiers that we implemented was the Motorola MC1741C operational amplifier. This amplifier was chosen because of it characteristically attenuated frequencies greater than 3000 Hz. This was desirable in helping to keep the noise factor down. With the responses of the microphones being in the millivolt range, a gain of 200 times was chosen. The amplifier did not work with this setting. The output signal of the response was undesirable. The response was still not strong enough for an effective analysis. At this point, the gain was boosted to 500 times. The signal was still undesirable. The response was still not effective. It was still only picking up on the strongest sounds such as claps at close range. The second of the amplifiers was a suggestion by TA Ben Potsaid. He had suggested using a National Semiconductor LM386N audio amplifier. One was purchased and the circuit was rebuilt using the new amplifier. The amplifier has an internal gain of 20 times, but with some extra hardware modification a gain of 200 times could be utilized. Steps were taken to use the 200 times gain. This proved also to be futile. The response was still not effective enough to provide for accurate analysis. Again the only response is from claps at close range which would not be useful in our application. It was determined that another amplifier was required for our application. The final amplifier was suggested by a FLITEC student, Chris Durham. The suggested amplifier was the National Semiconductor TL082 operational amplifier. The major advantage of this amplifier was that it was a dual channel amplifier. We were able to utilize two microphones per integrated circuit. The other major advantage was that we were able to implement much greater gains. The gain that we had used was a 10,000 times gain. With these settings, we were finally able to accomplish the clean responses necessary to be able to use the microphones in MATLAB. The finalized microphone circuit is shown in FIGURE 5.6. As part of uncertainty analysis, it was determined that much of our uncertainty comes from the microphones themselves. Each individual microphone is slightly different. With the type of gain in the amplifier that we are using these slight differences are emphasized. This could have been solved using potentiometers to fine tune the output signals of the amplifiers so that all the microphones showed a uniform response. This could also have been solved with modifying the individual gains of the output from the analog to digital converters such that the response there was uniform. Both of these options are viable given more time. 22

25 Figure 5.6: Final Microphone and Amplifier Circuit 23

26 Chapter 6 Cost and Schedule 6.1 Cost Analysis The cost for developing the system can be broken down into the TABLE 6.1. Table 6.1: List of parts Part Qty Cost Each Part Number Pan Motor 1 $89.80 Pittman: GM8724S010 Tilt Motor 1 $89.80 Pittman: GM8724S010 Pan Pulley 2 $4.35 SDP/SI: A 6Z 6-34DF02506 Tilt Pulley 2 $17.69 SDP/SI: A 6A 6-96NF01812 Timing Belt 2 $2.92 SDP/SI: A 6B Microphone 10 $1.99 Horn: EM9752U Total $ There are additional costs from the the mountings of the circuits use and the mountings on the pan and tilt system. The cost of the mountings on the pan and tilt system was not identified as they were donated by another group. Also the all of the wire, components and circuit boards were donated by the FLITEC group. As for the cost of labor, we had estimated the salary of an engineering working on this project to be roughly $37.50 per hour. We have worked roughly 150 hours per person over the course of the 15 week semester. The cost of labor totals $22, 500 for the whole project. 6.2 Schedule Shown in TABLE 6.2 is our original schedule from the proposal. The schedule has changed slightly since we first created this schedule. After the progress report, less emphasis was now on the subsystems portions. More effort was allotted for the control design portion and less time was devoted to fabrication. 24

27 We had found the initial schedule to be too aggressive in developing the controller. Not enough time was given to developing and verifying the model. We had to redistribute the time line to accommodate for the fluctuations seen in the friction identification portions. This also led to redeveloping the model and gaining a slightly different plant. The start times of some of the actions had to be pushed back significantly while others could have been pushed up. The duration of some of the activities could have used some extra time to more thoroughly verify validity. Table 6.2: Schedule Task Name Duration Start Finish 3D Audio Tracking 58 Days Wed 2/11/04 Wed 4/28/04 Testing/Simulation 44 Days Thu 2/12/04 Fri 4/9/04 Filters 29 Days Thu 2/12/04 Sun 3/21/04 Design 13 Days Thu 2/12/04 Sun 2/29/04 Implement/Test 16 Days Mon 3/1/04 Sun 3/21/04 Microphones 29 Days Thu 2/12/04 Sun 3/21/04 Research 13 Days Thu 2/12/04 Sun 3/29/04 Implement/Test 16 Days Mon 3/1/04 Sun 3/21/04 Complete System 15 Days Mon 3/22/04 Fri 4/9/04 Fabrication 21 Days Mon 2/23/04 Fri 3/19/04 Create Mount 11 Days Mon 2/23/04 Fri 3/5/04 Attach Peripherals 5 Days Mon 3/15/04 Fri 3/19/04 Control Design 40 Days Wed 2/11/04 Fri 4/2/04 Physical Analysis 19 Days Wed 2/11/04 Fri 3/5/04 Pan Algorithm 26 Days Mon 2/23/04 Fri 3/26/02 Tilt Algorithm 26 Days Mon 3/1/04 Fri 4/2/02 Reports 58 Days Wed 2/11/04 Wed 4/28/04 Project Proposal 6 Days Wed 2/11/04 Wed 2/18/04 Progress Report 11 Days Wed 3/3/04 Wed 3/17/04 Final Report 20 Days Thu 4/1/04 Wed 4/28/04 Project Demo 0 Days Wed 4/14/04 Wed 4/14/04 Final Presentation 0 Days Wed 4/21/04 Wed 4/21/04 25

28 Chapter 7 Conclusion As an increasing importance in our daily personal and professional lives, we have made headway into developing the next breakthrough in telecommunications technology. We designed a way to use a pan-tilt system to control a camera to focus on a speaking target which may be stationary or moving around a room. The target will stay on camera regardless of where the target is in a 180 range around the pan-tilt system. We have derived a complete non-linear model to simulate the dynamics of the physical system and have validated the dynamic model with the physical response of the system. We verified that our simulated model responds nearly identically with the physical system. After much analysis of performance, it was determined that we had achieved the specifications that we had desired to accomplish at the beginning of the semester. We were able to achieve a controller that met the specifications. We were able to achieve a system that tracked an audio source. Finally we were able to achieve integration such that both were able to work synergistically. Though the system was working in the end, if given more time we would be able to improve the overall performance of the system. The amount of error on the controller could be improved. The microphones could be more finely tuned. And, the sound localization algorithm could be perfected. 26

29 Bibliography 1.Course Website Tretter, Steven A. Communication System Design Using DSP Algorithms. Kluwer Academic/Plenum Publishers, New York, New York 4.Visual Target Tracking System Final Report, Rensselaer Polytechnic Institute, Control Systems Design, Spring

30 Chapter 8 Statement of Contribution For the project proposal document: Nick completed the following sections: Controller Design Sound Localization Schedule Presentation Dan completed the following sections: Abstract Introduction Professional and Societal Considerations Friction Identification Model Validation Presentation Andrew completed the following sections: Abstract Introduction Friction Identification Model Validation Controller Design Microphones 28

31 Ed completed the following sections: Abstract Introduction Friction Identification Model Validation Controller Design Microphones Cost Analysis Schedule Conclusion Nicholas J. Di Liberto Daniel Fleiner Andrew LeBlanc Edward Tang 29

32 Appendix A Modelvalidinit.m %%%%% Group DAT %%%%% % initiate variables for the MODELvalid.mdl simulink model %%%%%%%% Motor Constants %%%%%%%%%%%%%% %%% Torque Constant Kt = 4.36E-2; %% Units (N*m/A) %%% Motor gear ratio N = 6.3; %% Dimensionless %%% Motor inertia Jm = 1.6E-6; %% Units (Kg * m^2) %%% Peak Torque Tp =.3; %%% Pulley Gear Ratio Np = 2.7; %%% Load inertia Jl = ; %Jl =.047; %% Dimensionless %% Units (Kg * m^2) Tilt Axis %% Units (Kg * m^2) Pan axis %%% Load Viscous Friction Blv = 4.18E-4; %% Units (N*m*S/Rad) Tilt pos %Blv = 3.8E-4; %% Units (N*m*S/Rad) Tilt neg %Blv =.0011; %% Units (N*m*S/Rad) Pan pos %Blv =.0013; %% Units (N*m*S/Rad) Pan neg 30

33 %%% Load Coulomb Friction Blc =.0605; %% Units (N*m) Tilt pos %Blc =.0625; %% Units (N*m) Tilt neg %Blc =.0417; %% Units (N*m) Pan pos %Blc =.0466; %% Units (N*m) Pan neg %%% Inertia Value for the model I = (Jl + N^2 * Jm); %%% K gain for voltage K = N*Np*Kt*.1; 31

34 Appendix B Frictionidtest.m % friction ID script February 28, 2004 disp( Starting execution of the real time code. ); disp( Setting voltage to -1.1 ); tg.p10 = -10; tg.p21 = -2.01; for i = 1 : 201 pause(2); disp( Increasing voltage by.01 to ); tg.p21 = tg.p ; disp(tg.p21); start(tg); disp( Capturing the response ); pause(10.0); stop(tg); %pause(5.0); %time = tg.timelog; outputlog = tg.outputlog; velocity = outputlog(:,1); for j = 5000 : velocitya(j-4999) = velocity(j); end 32

35 end average_velocity(i) = mean(velocitya); disp( average velocity was ); disp(average_velocity(i)); tg.p10 = 10; for i = 202 : 401 disp( Increasing voltage by.01 to ); pause(2); tg.p21 = tg.p ; disp(tg.p21); end start(tg); disp( Capturing the response ); pause(10.0); stop(tg); outputlog = tg.outputlog; velocity = outputlog(:,1); for j = 5000 : velocitya(j-4999) = velocity(j); end average_velocity(i) = mean(velocitya); disp( average velocity was ); disp(average_velocity(i)); 33

36 Appendix C Curvefitting.m %poly fit figure(1); new_torque_pan = torque(90:299); new_pan_velocity = pan_velocity(90:299); plot(new_pan_velocity,new_torque_pan, x ) %[P,S] = polyfit(new_pan_velocity,new_torque_pan,1) %viscous_slope_positive = P(1); [P,S] = polyfit(new_pan_velocity(1:60),new_torque_pan(1:60),1); viscous_slope_negative_pan = P(1); negative_offset = P(2); negative_x = new_pan_velocity(1:60); negative_y = viscous_slope_negative_pan*negative_x+negative_offset; hold on plot(negative_x,negative_y, r ); [P,S] = polyfit(new_pan_velocity(157:210),new_torque_pan(157:210),1); viscous_slope_positive_pan = P(1); positive_offset = P(2); positive_x = new_pan_velocity(157:210); positive_y = viscous_slope_positive_pan * positive_x+positive_offset; plot(positive_x,positive_y, g ); hold off; xlabel( velocity (rad/s) ); ylabel( Torque (N-m) ); title( Pan Axis Friction ); figure(2); new_torque_tilt = torque(92:310); new_tilt_velocity = tilt_velocity(92:310); plot(new_tilt_velocity,new_torque_tilt, x ) hold on; %[P,S] = polyfit(new_tilt_velocity,new_torque_tilt,1) %viscous_slope_positive = P(1); [P,S] = polyfit(new_tilt_velocity(1:27),new_torque_tilt(1:27),1); 34

37 viscous_slope_negative_tilt = P(1); negative_offset = P(2); negative_x = new_tilt_velocity(1:27); negative_y = viscous_slope_negative_tilt*negative_x+negative_offset; hold on plot(negative_x,negative_y, r ); [P,S] = polyfit(new_tilt_velocity(193:219),new_torque_tilt(193:219),1); viscous_slope_positive_tilt = P(1); positive_offset = P(2); positive_x = new_tilt_velocity(193:219); positive_y = viscous_slope_positive_tilt * positive_x+positive_offset; plot(positive_x,positive_y, g ); hold off; viscous_slope_negative_pan viscous_slope_positive_pan viscous_slope_negative_tilt viscous_slope_positive_tilt xlabel( velocity (rad/s) ); ylabel( Torque (N-m) ); title( Tilt Axis Friction ); 35

38 Appendix D Closedloopinit.m %%%%% Group DAT %%%%% % initiate variables for the closedloop1.mdl simulink model % and physicalcontroller.mdl %%%%%%%%% Sampling Time %%%%%%%%%%%%%%% Ts =.001; %%%%%%%% Motor Constants %%%%%%%%%%%%%% %%% Torque Constant Kt = 4.36E-2; %% Units (N*m/A) %%% Motor gear ratio N = 6.3; %% Dimensionless %%% Motor inertia Jm = 1.6E-6; %% Units (Kg * m^2) %%% Peak Torque Tp =.3; %%%%%%%%%%% Amplifier Constant %%%%%%%%%% Ka =.1; %% Units (A/V) %%% Pulley Gear Ratio Np = 2.7; %%% Load inertia Jltilt = ; Jlpan =.0028; %% Dimensionless %% Units (Kg * m^2) Tilt Axis %% Units (Kg * m^2) Pan axis 36

39 %%% Load Viscous Friction Blvtilt = 4.18E-4; %% Units (N*m*S/Rad) Tilt Blvpan = 8.5E-4; %% Units (N*m*S/Rad) Pan %%% Load Coulomb Friction Blctilt =.0605; %% Units (N*m) Tilt Blcpan =.052; %% Units (N*m) Pan %%% Inertia Value for each model Itilt = (Jltilt + N^2 * Jm); Ipan = (Jlpan + N^2 * Jm); %%% K gain for voltage K = N*Np*Kt*Ka; %%%% Make plant transfer functions for both axes Gpstilt = tf(k/itilt,[1 Blvtilt/Itilt 0]); Gpztilt = c2d(gpstilt, Ts); Gpspan = tf(k/ipan,[1 Blvpan/Ipan 0]); Gpzpan = c2d(gpspan, Ts); %%%% tilt controller znumtilt = [ ]; zdentilt = [1.9]; %%%% pan controller znumpan = [ ]; zdenpan = [1.87]; %%%%% Voice Filter %%%%%%%%%%%% fs = 8000; fo = fs/2; T = 1/fs; Wp = [ ]/fo; % Passband Ws = [ ]/fo; % Stopbands Rp =.3; % Passband Attenuation Rs = 40; % Stopband Attenuation % Creating the IIR Passband Filter based on an ellipitcal % analog lowpass filter [n,wn] = ellipord(wp,ws,rp,rs); [iirb,iira] = ellip(n,rp,rs,wn, bandpass ); iirsys = tf(iirb,iira,t); 37