<center> <h2>Mesicopter Progress Report<br> March 2001</h2> </center> <p><br> <h3>Summary</h3> <p>See the <a href="http://adg.stanford.edu/mesicopter/ProgressReports/MesicopterProgressFeb01.html"> February report</a> for the previous update. See also the <a href="http://adg.stanford.edu/mesicopter/ProgressReports/gifupload.html">Instructions for uploading images</a> and be sure to include all of the referenced figures.</p> <p> <h3>Aerodynamics</h3> <p> Two significant modifications have been made to the design and analysis codes. The viscous swirl model has been changed to a model based on the conservation of angular momentum in the wake. The viscous drag power generated by a blade element in one revolution is equated to the angular momentum of the corresponding annulus of fluid in the wake. This model is described in many introductory texts on rotorcraft aerodynamics and reduces to a factor inversely proportional to the local sectional lift to drag ratio. At typical Reynolds numbers above 1.0e5, the sectional lift to drag ratio commonly ranges from 50 to 100 and the viscous swirl term is small and often neglected. At the Reynolds numbers considered here, generally less than 10,000, the sectional lift to drag ratios drop into single digits. The viscous swirl velocity increases significantly and the effect on performance is large. <p> In addition to the modifications to the swirl model, a wake contraction model has been added to the program. The wake is modeled as a series of coaxial vortex rings using an axis-symmetric streamline formulation. The initial radii of the rings are set equal to the tip radius. The spacing and strength represent a helical wake generated by an idealized constant downwash rotor with equivalent thrust to the current design iteration. The contracted wake is obtained by iteratively resizing the rings to obtain a constant mass flux through the stream-tube equal to the flux through the rotor disk. The initial cylindrical wake approximates the Prandtl tip loss correction. The contracted wake yields a non-uniform inflow distribution that captures much of the effect of the blade/ tip vortex interaction. Cutting planes through the initial and final wake geometries are shown in the first figure below with streamlines superimposed. The rotor disk is at x=0 and the black circles represent the location of each ring. The second figure compares the radial thrust distribution for the 2.5cm 4-blade rotor calculated several different ways, including OVERFLOW-D results. The presence of the tip model significantly improves the accuracy of the thrust distribution in the tip region. Comparing with the OVERFLOW-D calculation, these two improvements reduce the discrepancy in predicted power required from 17% with the old models to below 10% with the current version. Thrust continues to agree within 5%. </p> <br><img src="images/ringwake.gif" width="600" height="559"><br> </p> <br><img src="images/radthrustwake.gif" width="600" height="463"><br> </p> <H3> Rotor Fabrication</H3> <!-- Shelly --> As shown in the October report, the incidence distributions of the aluminum rotor from laser-scanned data were closer to the design values than those of epoxy rotors were. However, the data points were fluctuated with the maximum variations of around 2 degrees (except the tips) from the design values. We suspect the resolution of laser scanning is not sufficient, as the incidence variations get smaller. Therefore, we tried to gather incidence data of the aluminum rotor from the cross sections. </P> The basic idea is to embed the aluminum rotor in a transparent epoxy block and cut cross sections gradually. Each cross section was polished and observed under the optical microscope. Three major issues should be considered and planned before embedding the rotor: (1) how to ensure the cutting planes are perpendicular to the blades; (2) how to define the horizontal plane for incidence measurement; and (3) how to measure the radial locations correctly. To solve the first problem, a square pocket was machined in the center of the rotor hub, and the same size of square post was located at the center of the substrate. Fitting the rotor into the post of the substrate can ensure the blades are placed at 0, 90, 180, and 270 degrees. Polyurethane was cast and machined flatly to provide horizontal reference to solve the second issue. Moreover, the cast transparent epoxy block was cut into a square before detached from the substrate. The center of the block can be determined by measuring the distance between the two opposite sides. When cutting the cross sections, we only cut two adjacent sides and left the other two as reference. At every cross section, the width of the block was measured and could be converted to the radial location of the blade. After two adjacent sides were gradually cut down close to the hub, they were then performed as reference sides for the other two blades. </P> All photos taken from the optical microscope were analyzed in the CorelDRAW. Lines were drawn from the leading edge to the trailing edge and on the reference plane. By reading out the coordinates of the start and end points of lines, the angle between the chord and the reference plane can be calculated. The incidence distributions of four blades analyzed through this approach are shown in the following figure. The results are less noisy and less deviated than those from the laser scanning data. The maximum incidence deviation (except at tips) is less than 1 degree. </P> <br><img src="images/incidence_al_rotor.gif" width="488" height="316"><br> <H3>Electronics, Power</H3> <P> We continue in search for commercially available, high power and energy density batteries and light and efficient micro-motors. Samples of Lithium-Ion polymer batteries from company called Polystor have been ordered for evaluation. (The lightest sample PSC322933 weighs 5g at rated capacity of 175 mAh. The maximum continuous discharge current is specified at 525 mA). A similar prismatic cell with following parameters: weight 3.5g, rated capacity 125 mAh will be also tested. This cell is made by Valence Technology, Inc. <P> Micro motors from Mabuchi Motor will be tested. Samples of 1.6g micro motors have been ordered. <p> <H3> Flight Control Test Bed </H3> <!-- Gary --> <p> The second version of the flight control test bed vehicle has been completed and is ready for it's maiden flight. Testing of the first prototype indicated that some bracing was needed to protect the circuit boards from flexing due to large torques being applied by the motors on the ends of the vehicle arms. This caused extremely high stress concentrations at the central joint, but this joint was also the solder joint connecting the circuit boards. The large stresses caused intermittent electrical contact resulting in malfunctioning electronics after only a brief period of usage. To alleviate this problem in the second vehicle, the braces were used to form a rigid box around the circuit boards to carry all the stress. Photos of the new vehicle show the bracing. The braces are manufactured using a hollow carbon fiber and glass composite lay up adding only 5 grams total extra weight to the vehicle. The total vehicle weight including the battery pack is approximately 185 grams. The rotors are capable of producing more than 200 grams of lift. <p> <br><img src="images/testbed.gif" width="817" height="582"><br> Photo of completed flight control test bed vehicle. <p> Also shown in the photos is the transmitter used to fly the vehicle. The microcontroller on board the vehicle is hard-coded with the flight control software. The original designer incorporated a PID controller into the code utilizing feedback from the rate gyros. The gains for the controller are set in the microcontroller of the transmitter and sent using a 418 MHz radio. The microcontroller for the transmitter can be reprogrammed with new gains so that stability experiments can be performed. Vehicle motion is controlled by independently varying the rotor speeds. Roll, pitch, yaw, and vertical velocity can be controlled in this manner. Vertical velocity is commanded by raising and lowering the speeds of all the rotors simultaneously. By respectively speeding up and slowing down the front and rear rotor, pitch commands can be given. Roll commands can be given using the left and right rotors in a similar manner. Finally, by speeding up the clockwise rotating blades and slowing down the counter-clockwise rotating blades, an overall torque can be imposed on the vehicle causing yaw commands to be issued. The two joysticks on the controller control all four of these operations. <p> Power is supplied by four AA sized Tadarin lithium metal batteries shown attached under the vehicle. Before actual free flights take place, an endurance test was performed with the vehicle rigidly attached to the ground and with the throttle set at an operating speed of approximately 1800 RPM. The rotors maintained their speed for approximately 10 minutes. After this time, higher throttle commands needed to be given by the controller to maintain operating RPM. After 14 minutes, the throttle needed to be at its maximum setting to maintain operation RPM. With the throttle set in this position, the rotors continued to slowly decrease in speed according to the following table: <p> 16.0 min. ......... ~1700 RPM<br> 17.5 min. ......... ~1600 RPM<br> 19.5 min. ......... ~1500 RPM<br> 22.0 min. ......... ~1400 RPM<p> This indicates that we should get about 14 minutes of free flight using this battery pack, after which there should be enough power to gently land the vehicle. <p> Free flight tests are scheduled for later this month following restrained flight tests. The vehicle will be suspended by a string attached to the top of the carbon rods sticking up above the vehicle (see photo). If something goes wrong, the throttle can be cut and someone the string will keep the vehicle from crashing into the ground. Also, some studies will be done on choosing appropriate control gains. The three-dimensional simulation with feedback will be modified to incorporate a PID controller instead of LQR so that these gains can be chosen theoretically first. <p> <H3> Systems Integration Testbed</H3> <!-- Mike --> <P> </P> <H3> Control Issues</H3> <P> After various discussions, we determined that we were not fully satisfied with the response of the 2 degree of freedom system (wire restricted mesicopter). In February we had presented results from our system which showed a smooth vertical response but had an oscillitory yaw response. After further analysis, we found that by removing the tethered power wire, the mesicopter was limit cycling with a high amplitude. This response did not match our expected Matlab response (from which we choose our control gains). Unsatisfied, we decided to revisit the 2 degree of freedom sensing strategy to diagnose the cause of the oscillitory yaw response. We found interesting results that will affect our 6 degree of freedom controller design. <P> Our questions led us to exploring why our vertical control was acceptable while our yaw control was not, especially when we were using the same vision sensor for both. An explanation follows: <P> On our external camera that tracks yaw and height, we have roughly 480 pixels vertical and 640 pixels horizonatal. With transformations based on our camera position, each pixel reflects roughly 1 mm^2 in the mesicopter coordinate system. At a minimum, our control is quantized to 1 mm minimum accuracy in any direction. <P> For our vertical control, a motion of 1 pixel does not have a significant affect on control. We can assume that for our position gains, our motor control changed a minumum of about 0.001*0.005 (distance*vertical gain) = 5*10^-6 N*m. Since the motors max torque is 0.0015 N*m, a one pixel motion is 0.3% of the torque command range. This is acceptable resolution. <P> At 15Hz, with a first difference, the vertical velocity estimate is quantized at roughly 15 mm/sec or 1.5 cm/sec. When the mesicopter moves about 1 m/sec maximum, 1.5 cm/sec is about 1.5% of the maximum response. Even quantized at these levels, we can still feed this velocity estimate into a discrete controller to produce adequate control. We can do even better by introducing a small lag, which smooths the velocity estimate. <P> Vertical control isn't a problem as we've shown, but by similar analysis we can show our yaw signal is problematic. To get yaw, we are using simple trigonometry. By tracking the midpoint between the two LEDs, knowing horizontally how far that is away from the shaft, and knowing the radius of the midpoint from the center of the mesicopter, we can find yaw that has the best resolution near 0. The distance from mesicopter to the shaft is roughly 4 cm. Around 0, asin((x + 0.001)/0.04) - asin(x/0.04) is about 1.5 degrees or 0.025 radians. We can assume that for yaw position gains, our motor control transitions about 0.025*0.001 (distance*vertical gain) = 2.5*10^-5 N*m per pixel. Since the motors max torque is 0.0015 N*m, a one pixel movement is 1.6% of the torque command range. To provide a good response, I wanted to use a gain of 0.005, but that was not possible as a 1 pixel motion accounted for a 8% torque transition between pixels. <P> With a first difference on this yaw calculation, we get little more than noise (doesn't even represent velocity). At 15 Hz, the rotational velocity calculation shifts 1.5*15 = 22.5 degrees/sec or 0.39 radians/sec between pixels. Even when the mesicopter is stationary, my system estimates that it is spinning wildly. When using this signal at a high gain, the system goes out of control, but at a low gain, we get the oscillitory behavior we expect (no dampening). <P> The low resolution on our yaw (at higher gains) and rotational velocity measurements is unacceptable for controlling the mesicopter. We can use the vision system for estimating yaw (especially when coupled with other vision position sensors), but using this system as is to estimate rotational velocities is out of the question. <P> We have two solutions for this problem assuming we can tolerate the yaw estimate. We can create a completely different filter (instead of the first difference) that will be more effective with the current yaw calculation. We can also better utilize an estimator to produce the rotational velocity estimate, and then use our filtered estimate to stablize this estimator. <P> The other solution is to incorportate a gyro-like sensor on board which will sense the angular acceleration or even rotational velocity. We could integrate to get velocity if necessary, and then use the position measurement to eliminate the drift that might accumulate during integration. <P> We are going to finalize a solution and incorportate it directly into our 6 degree of freedom controller design. <P> <H3> Systems, Applications, and Other Items</H3> <P> <!-- Ilan -->