See the November report for the previous update.
Four additional rotors, two left-handed and two right-handed, have been fabricated for the 150g vehicle. The initial set of rotors exhibits poor resin retention at the blade tips, possibly caused by excess laminate in the outboard portion of the blade. The two-sided molds are likely forcing the resin out of the tips when clamped. A modified laminate schedule will be implemented for subsequent rotors. The inconsistencies at the tips of the blades result in a 10% variation in mass across the four rotors. There is also an associated variation in aerodynamic performance, but the difference between rotors is small enough that the initial set of four is still usable. At the target thrust of 50g, input power ranges over approximately 9% of the mean, but the variations in voltage and RPM are only 3% and 4% respectively. The figure below compares input power and thrust for all five Stanford 10? diameter rotors and the Wes-Technik 10? diameter rotor.
Additional work has been completed to assess the accuracy of the INS2d computations that are a key component of the rotor design methodology. Validation of the 2-D computational analyses is difficult due to the almost complete absence of experimental data at relevant Reynolds numbers. One of the few examples is provided by Thom and Swart[1], who tested a small R.A.F. 6a airfoil model in an oil channel and water channel at Reynolds numbers below 2000. The Thom and Swart data is based on a 1.24 cm chord airfoil with manufacturing deviations from the R.A.F. 6a. This small test piece was hand filed to shape causing the measured geometry to vary across the span. An exact validation is not possible due to the unknowns in the section geometry, but comparison with computations for the R.A.F. 6 airfoil with a 256 by 64 grid show reasonable agreement with experiment. No coordinates for the R.A.F. 6a could be located, but the R.A.F. 6 appears to be nearly identical. The results are shown in the figure below. The Reynolds number varies from point to point and ranges from Re=650 to Re=810. The computed drag is on average 7.5% lower than experiment, but the trends in Cd with angle of attack agree. Corresponding Cl data is only given for AOA=10.0 degrees. The computational result matches the experimental value of Cl=0.52 within 3.0%.
[1] Thom, A., Swart, P., "The Forces on an Aerofoil at Very Low Speeds," Journal of the Royal Aeronautical Society, Vol. 44, 1940, pp. 761-770.
Shelly has been summarizing all of her work in a thesis. Her defense is in a few weeks and the next update will include more on the fabrication issues.
The bottleneck in the smallest 15g mesicopter project is the battery system. The existing smoovy motors require high voltage levels. Therefore a search for high power density batteries continues in parallel with a search for alternative motors requiring lower voltage levels to operate. ITN Energy Systems spin-off, Infinite Power solutions, offers a new solid-state thin-film rechargeable lithium battery called LiteStar. These batteries are currently available only with small mAh capacities. Research department was contacted to obtain larger samples for feasibility tests.
Progress has been made in the development of the full six degree of freedom three-dimensional model. The improvements include the addition of rotor hub forces and motor torques to the model. The rotor hub force, or rotor drag, is assumed to oppose the horizontal motion of the rotor. Rotor side forces which are perpendicular to the direction of horizontal travel of the rotor are assumed negligible. The hub force is comprised of a induced term due to lift, and a profile term due to the blade drag coefficient which is approximated by a mean value over the entire rotor disk. The motor torque is also divided into an induced torque caused by the rearward tilt of the lift vectors of each blade and a drag torque. A simulation of the dynamics of the vehicle with a small initial tilt offset seem to indicate there is significant damping of the vehicle oscillations compared to the previous three-dimensional model without hub forces. Compare the following plots of the dynamics with previous reports. Unfortunately this is not the behavior exhibited by the actual vehicle. Although inaccurate positioning of the center of gravity, unidentical rotors and motors, and some disturbance and signal noise may explain some differences, the behaviors are still quite different. Some of the fundamental assumptions for the aerodynamic model will be examined. Also the behavior of the model will be studied with varying center of gravity positions, differing rotor/motor performance, and random disturbances to see what affect these variables have on the model. The third plot shows the motion of the mesicopter as observed from above, and indicates that the roll and pitch motions are slightly coupled due to the addition of rotor torques.
Three-dimension simulation showing positions and orientations.
Three-dimension simulation showing velocities and angular rates.
Overhead view clearly shows slight coupling.
Further progress has also been made on producing a simple rate feedback control law for the six degree of freedom model. The roll and pitch motions are assumed to be decoupled. Therefore the control law developed for the two dimensional pitch-only case can be used simultaneously on both the roll and pitch rates of the three-dimensional case. The following plot show the effect of control gain on pitching motion. A reasonable control gain was then selected and applied to both the two-dimensional and three-dimensional models. The two-dimension model behaved as expected. There are still some issues with step size determination and convergence for the three-dimension model. Since the model is now coupled, it might be instructive to return to the decoupled three-dimension model to make sure the control is being applied correctly. Since the motion is decoupled, the results should be identical to the two-dimensional case as demonstrated in previous reports.
Effect of various error weighting in determining the control gain using LQR.
Two-dimensional simulation of the mesicopter under rate control using a reasonable control gain from the plot above.
Three-dimension simulation using under roll and pitch rate control. Positions and orientations are shown.
Three-dimension simulation using under roll and pitch rate control. Velocities and angular rates are shown.
Further analysis of the three-dimensional simulation is required before believable control schemes may be developed and applied to a real world system. In the meantime, a larger prototype is needed as a flight controls testbed. The same analysis used to design the previous prototype will also be used to determine the center of gravity location and cant angle for the larger prototype.
A new set of PC boards has been fabricated and is being combined with the new rotors. More on the status of the testbed next month.
We have made significant progress in producing a 2 degree of freedom flight testbed. In June 2000, we designed a 1 degree of freedom flight testbed on which we regulated the vertical position of our 60 gram, 12cm diameter vehicle on a shaft. Our next goal was to simultaneously regulate the vertical position and the yaw angle of the vehicle. Instead of using our old vision tracking hardware/software for sensor feedback (see the May progress report), we created a new vision system which extended our tracking capabilities. The new tracking system can be used to track the mesicopter in full flight. The base vision system was recently completed (see the latest progress reports), and we've returned to the initial goal of providing automated flight. We will describe the latest components we've designed for the testbed. We are integrating these components and hope to have a complete testbed in the following weeks. We are currenly ridding the system of a few minor errors.
To track multiple LEDs and indirectly height and yaw, we've developed a multi-purpose, multiple point tracking vision component. The component inherits from the state class in our vision package. The component has threshold, minimum pixel radius, points desired, and max points tracked inputs. We use an algorithm that processes each pixel with a value greater than the threshold. If a candidate pixel is a distance greater than the minimum pixel radius from any tracked point, the candidate point is added to the list of tracked points. The component tracks only one of the pixels within the pixel radius. If a point is close to another tracked point, we increment the intensity value for the tracked point. In the end, the component outputs the number of points desired even though it may have identified many unique tracked points (maximum - max tracked points). The selected output points have the highest intensity values (highest number of valid, adjacent pixels). We use the intensity value as a filter to eliminate noise.
The point tracking component tracks two LEDs attached to the vehicle. The pixel coordinates of these LEDs are scaled are passed through simple geometric calculations to yield the height and yaw angles of the mesicopter. With these values and the velocities of these values (calculated using a first order difference), we have a complete set of controller inputs.
We have designed a controller/estimator pair for the mesicopter based on the available sensor feedback. There are 8 significant internal variables essential to regulating the position of the vehicle. We are concerned about the height and yaw position along with their associated velocites. We are also concerned with the angular velocity of each rotor. Based on a rigid body design model, we were able to to design a controller that stablized the height and yaw outputs. The model was not controllable, but the uncontrollable modes are stable so our controller is sufficient. To estimate the rotor velocities we also had to design an estimator. Like the controller, the estimator was not observable, but the the unobservable mode was stable so our estimator was adequate. We've integrated the controller and estimator into our software feedback loop.
In our 1 degree of freedom testbed, we used a PIC processor to drive an 8 channel PWM signal which commands the onboard motor controllers of the mesicopter. In the previous testbed, each channel was given the same command. We've now modified the PIC to command the 8 channels individually. Commanding the rotor velocities seperately enables yaw control.
In the following months we will provide data related to this testbed including parameter and tracking information. The data will become available as soon as the testbed is complete.
Last update:15-Jan-01 11:40:16 PM
WebEdit servlet by I. Kroo, Oct. 1999.