Mesicopter Progress Report
March 2001


Summary

See the February report for the previous update. See also the Instructions for uploading images and be sure to include all of the referenced figures.

Aerodynamics

The most recent 3-D CFD calculation for the 2.5cm diameter rotor has been completed. The surface grids used in this calculation correctly model the as-built geometry. Analysis and post-processing of the data is ongoing, but initial results have provided significant insight into the discrepancies in required motor input power between experimental and estimated performance. The calculated thrust from the Overflow analysis at 48,000 RPM is 4.1g and agrees with the current analysis/design code within 4%, but the calculated torque at 48,000 RPM is approximately 17% greater than the analysis/design code prediction. The rotor was designed for the 5mm Smoovy motor operating at 10 V and 26% efficiency. A 17% increase in the rotor torque and the experimental input power of 3.025 W results in an experimental efficiency of 16.1%. The increase in rotor torque at a given RPM forces the motor onto an operating curve with a lower efficiency. A 10% reduction in motor efficiency for a 17% increase in output power is reasonable.

The two figures below depict the radial thrust and torque distributions on a single blade. The non-dimensionalization is based on the rotor radius and tip velocity. Results from the design/analysis code with and without the current viscous swirl correction are provided. The thrust prediction with swirl is significantly better than without, and matches the CFD result reasonably well over the inboard 90% of the blade. The opposite is seen in the torque distribution, with the viscous swirl solution consistently under-estimating the local torque. It is surprising how accurately standard blade-element/ momentum theory estimates torque under these conditions. The current swirl model assumes and average wake deficit velocity applied uniformly to each blade. Due to the large discrepancies in torque estimation, the model is being modified to account for the effects of downwash and vertical wake deficit variations.





The CFD results outboard of 90% span are distinctly different from the design/analysis predictions due to the effects of wake contraction, which are not incorporated in to the current design/analysis method. The two figures below depict vorticity contours in two planes directly behind and ahead of a single blade. Apparent from these two images is how rapidly the region of strong vorticity originating at the tip contracts inboard, causing significant differences in the induced velocities as compared to a simple cylindrical wake model.





Rotor Fabrication

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.

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.

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.



Electronics, Power

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.

Micro motors from Mabuchi Motor will be tested. Samples of 1.6g micro motors have been ordered.

Dynamics and Simulation



Photo of second vehicle under construction.



Photo of second vehicle under construction.

Systems Integration Testbed

Control Issues

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.

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:

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.

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.

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.

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.

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).

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.

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.

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.

We are going to finalize a solution and incorportate it directly into our 6 degree of freedom controller design.

Systems, Applications, and Other Items

Last update: 14-May-01 12:21:32 PM

WebEdit servlet by I. Kroo, Oct. 1999.