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1 American Institute of Aeronautics and Astronautics

Approved for Public Release, Distribution Unlimited

Optimized Guidance of a Supersonic Projectile using Pin Based Actuators

K. C. Massey* and K. B. Guthrie Georgia Inst. of Technology/GTRI/ATAS, Atlanta, GA 30332-0844

Sidra I. Silton* Weapons and Materials Research Directorate, ARL, Aberdeen Proving Ground, MD 21005-5066

6-DOF simulations were used to investigate various control schemes for a guided supersonic projectile. The 6-DOF simulation results were compared with actual range data acquired at ARL. Very favorable comparisons were made between predicted and actual performance of the projectile. After verifying the 6-DOF tool, projectile guidance schemes were developed based on the pin based actuators developed by GTRI that have been described in a companion paper. Pitch oscillations of the projectile were predicted using the 6-DOF tool and it was also shown that these oscillations could be controlled by appropriate deployment of the pins. Deployment schemes were developed that greatly reduced the oscillations in pitch. For a notional projectile that was undergoing a roll, multiple control schemes were developed that steered the projectile in a single direction. These control schemes were compared on two figures of merit and the optimal pin based guidance control scheme was determined.

I. Introduction

There has been a recent interest in both missiles and guided projectiles that operate in the high supersonic to hypersonic range for various missions. ONR has been pursuing HyFly1 since early 2002. HyFly is a proposed Mach 6 missile that would be used to strike targets of opportunity in a timely fashion before they could reposition. Another area of interest revolves around defending against threats with small RCS that can not be engaged at long ranges due to problems with detecting them. These threats include small objects such as mortars and rockets as well as stealthy larger targets such as cruise missiles. One possible scheme for defense against these threats assumes that large caliber guns (2 inch or larger) with high rates of fire would fire multiple supersonic projectiles that could be guided into the threat. The course corrections would greatly enhance the hit probability of a single round and thus expand the defended area of a single gun. Warnash and Killen2 describe several military programs where high speed guided munitions are in development or are under consideration. In all cases, it is found that the high closure rates between the projectile and the target may necessitate large turning forces.

It was the goal of this effort to examine how one might use the pin based actuators to guide a supersonic projectile. While other control techniques such off-set masses have been investigated using 6-DOF by Frost and Costello3, these methods are typically used to increase accuracy and do not produce the high turning rates required to intercept a target. Previous work had demonstrated that the control forces needed to guide a projectile could be developed by the pin based actuators, however, dynamic considerations had not been investigated. Further, it was desired to estimate the required forces to actuate the pins to perform a set mission. Thus various control schemes were investigated to determine the optimal control scheme to meet the mission requirements.

* Research Engineer II, Aerospace Transportation Advanced Systems Laboratory, GTRI, Smyrna, GA, 30080, Associate Fellow AIAA. * Aerospace Engineer, Ballistic and Weapons Concept Division, Aerodynamics Branch, AMSRD-ARL-WM-BC, Member AIAA.

23rd AIAA Applied Aerodynamics Conference6 - 9 June 2005, Toronto, Ontario Canada

AIAA 2005-4966

Copyright © 2005 by Kevin C. Massey and the Georgia Tech Research Institute. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.



II. Prior Work Nearly three years of experimental tests at the Georgia Tech Research Institute4,5 and the Army Research Lab6,7 have demonstrated that a pin based actuator can develop the forces required to steer a supersonic projectile. The guidance pins concept† shown in Figure 1 takes advantage of a complex shock interaction between the pin and the corner of the body and fin to create a strong asymmetric force. By appropriate combination of these pins, forces can be induced that introduce a pure pitching moment, a pure rolling moment, or combinations of the two. The primary case of interest is using the pins to change the orientation of the projectile in order to initiate a high g turn. In Figure 2, the pin configuration used to pitch the projectile is shown where the interaction forces generated will induce a rapid change in angle of attack. Laboratory tests detailed in Ref. 4 and 5 and range tests (Ref. 6 and 7) have both been used to quantify the forces developed by the guidance pins.

Figure 1 Pin fin concept (patent pending). Figure 2 Pin configuration for pitch control.

The range tests performed at ARL were key to the effort described in this paper as many of the aerodynamic coefficients and forces developed by the pins used in the following 6-DOF simulations were verified or established during the range tests. In the range tests, projectiles were fired with pins fixed near opposing fins for the purpose of generating roll. Two different pin lengths were used and the projectiles were fired at three different Mach numbers. Prior to the actual firing of the projectiles on the range, predictions of the forces generated by the pins were made using CFD and these forces were fed into 6-DOF simulations. The predicted and actual results were quite close and thus only minor efforts were needed to tweak the forces and aerodynamic coefficients for the 6-DOF simulations to accurately model the fired data. The resulting comparison of the 6-DOF simulation and the measured data from the range are shown in Figure 3 for the degrees of revolution induced by the pins as the projectile traverses the range. In Figure 3, it is shown that the rolling moment developed by the pins is enough to rapidly spin the projectile. Further, it is seen that the moment developed depends strongly on the pin height and less strongly on the Mach number in the range of Mach 2 to Mach 3. In Figure 4, a comparison between the measured and simulated roll rates is shown and again it is demonstrated that the 6-DOF simulations are accurately modeling the flight of the projectile and that the forces developed by the pins are accurately modeled. Based on these efforts, a high degree of confidence was obtained for the 6-DOF simulations.

† The use of these actuators or similar actuators to produce steering forces and moments is a proprietary technology developed by the Georgia Tech Research Institute and is protected under US Patent Law. Patent Pending.



X (m)

Phi

(deg

)

0 25 50 75 1000

1000

2000

3000

4000

5000

6000

7000 Mach 2.0 short pin - simulated24093 - Mach 2.0 (short pin)Mach 2.4 short pin - simulated24098 - Mach 2.4 (short pin)Mach 2.9 short pin - simulated24096 - Mach 2.9 (short pin)Mach 2.93 long pin - simulated24095 (long pin) - M2.9

Figure 3. Degrees of revolution for projectile over the length of range compared to 6DOF simulation.

X (m)

Rol

l(de

g/m

)

0 25 50 75 1000

10

20

30

40

50

60

70

80

90

100

110

120

130

140

24093 - Mach 2.024098 - Mach 2.424096 - Mach 2.924095 (long pin) - Mach 2.9

Mach 2.0 short pin - simulatedMach 2.4 short pin - simulatedMach 2.9 short pin - simulatedMach 2.9 long pin - simulated

Figure 4. Roll rate comparison between range tests and 6DOF.

III. Tailoring the Forces to Reduce Pitch Oscillations A 6-DOF model was created of the projectile where the forces developed by the pins were applied as

point forces using one force for each pin. A horizontal turn was simulated and the pins were used to induce a yaw (in a non rolling frame) on the projectile. Initially these forces were applied as step forces, either off or on, and the model was used to determine whether a 50 g turn was achievable. Based on the mass properties of the projectile tested at ARL and the forces determined from the experiments and CFD, a simulation was run with a launch Mach number of 5 and the pins deploying 1000 m downrange. The cross range versus the range for the projectile as fired at ARL is shown in Figure 5 as the dashed line. Some 100 m of cross range was developed in the 4500 m after the turn, however, it was desired to have the capability for more aggressive turns. To achieve the desired 50 g turn, the static margin of the projectile was reduced by changing the cg of the projectile. It should be noted that the previously fired round was intended to be very stable and thus had a large static margin. After reducing the static margin from 27 mm to 8.4 mm, the projectile’s cross range was increased by a factor of four as shown in Figure 5 by the solid line.

For the same two cases described above, the lateral accelerations are shown in Figure 6 where the differences in the levels of acceleration are clearly apparent. An acceleration of roughly 15 g’s was achieved for the projectile with 27 mm of static margin while the acceleration was over 50 g’s for the projectile with a static margin of 8 mm. It is also apparent that there were large oscillations in the acceleration for both cases. These oscillations were a result of yaw oscillations that were brought about by the instantaneous change in the forces on the projectile induced by modeling the pin forces as step inputs. The instantaneous application of these forces resulted in an overshoot in the desired yaw angle which resulted in nearly double the acceleration desired. The yaw oscillations were undesirable, but also unrealistic as it is not physically possible to have the pins deploy instantaneously. It should also be noticed in Figure 5 that the yaw oscillations do not noticeably affect the turn. Nevertheless, an effort was made to determine if a force schedule could be developed that would reduce the oscillations.

Acknowledging that the pins could not deploy instantaneously, the forces were ramped in a linear fashion assuming that the pins would take 30 ms to deploy and that it would take the same time for the forces to fully develop. A comparison of the induced yaw angles for the application of an instantaneous or step force and a ramped force is shown in Figure 7 where it is seen that the ramped force reduces the yaw oscillation magnitude by over 2º. While this is an improvement and represents a more realistic case than the step force, the 30 ms pin deployment is slower than desired and the yaw oscillations also remain larger than desired. In light of this result, several other pin deployment schedules were investigated.

One scheme that showed promising results and also proved practical was a double step deployment. In this scheme, the force developed to 60% of its final value and held that value for 20 ms before rising to its final full force. Several other schemes were tried, but this force deployment schedule was the best at



reducing the amplitude of the yaw oscillations, and as shown in Figure 8 the yaw excursions of over 7º were reduced to around 1.5º. Clearly the overshoot due to the initial force application is reduced in magnitude and the delay allows for the oscillations to be damped before the final application of the force. In addition, the pin deployment time has been reduced by a third, resulting in a more rapidly responding projectile.

Parallel experimental investigations using a scale model in a wind tunnel measured the pin deployment times for a pin that is rotated into the flow using a pneumatic system. The resultant pin deployment time in terms of angle for insertion into a Mach 2.5 stream is shown in Figure 9. Here it is seen that the pin rotates rapidly into the flow for the first 70% of the deployment and then more slowly finishes the full deployment. This behavior is primarily a resultant of the fact that the aerodynamic forces resisting the pin deployment are very non linear. During its initial rotation into the flow, the pin is in the boundary layer of the projectile and thus the dynamic pressure is relatively low. As the pin continues to rotate and extend further away from the body, eventually it is subjected to much higher flow velocities and dynamic pressure. At some point the flow becomes highly supersonic and the force on the pin rises quickly thus slowing down its deployment. Perhaps nature abhors lightly damped systems, perhaps it is coincidence, but the experimental pin deployment and thus force schedule, is not too different than the force schedule found using the 6-DOF that greatly reduces the oscillatory amplitude.

The 6-DOF studies showed that it is possible to greatly reduce the oscillations in yaw on the projectile by appropriate tailoring of the forces. The experimental studies showed that pin deployment times on the order of 20 - 30 ms are reasonable and that to some extent the desired delay in the force schedule is practical to implement. With this knowledge in hand, several different pin configurations and guidance schemes were modeled to to determine which had the best overall performance.

Figure 5. Effect of static margin on cross range.

Figure 6. Pitch oscillations evident during high g turn.



Figure 7. Effect of 30 ms ramped force on yaw oscillations.

Figure 8. Reduction in induced yaw angle through using a double step pin deployment.

Figure 9. Experimentally measured pin deployment.



IV. Optimizing the Pin Configuration for Maximum Turning Authority Four different pin configurations were modeled to determine which configuration provided the most

turning authority. For this set of studies, there was no fin cant on the projectile and the projectile was commanded to roll to a specified bank angle and make a course correction. The maneuver was considered complete when the projectile achieved 100 m of cross range, which was intended to represent a middle of the road divert that was neither a very small nor a very large correction.

The four different pin geometries are shown in Figure 10 where it is seen both 4 pin and 2 pin configurations were considered. The 2 pin configurations have an advantage of requiring less hardware and would thus be easier to package inside a projectile, however, the 4 pin configurations offer a faster response time as it takes less time to roll the projectile to a desired orientation. It can also be seen in Figure 10 that the other major difference is whether the fins upon which the forces are applied are adjacent or opposing. For the adjacent pin cases, Interior X and Interior V, a portion of the force developed by the pin-fin interaction on one fin is canceled on the adjacent fin. This downfall is offset by the fact that the forces induced on the body of the projectile act in the desired direction. For the opposing fin cases, Short I and Planar, the fin forces do not cancel, but the majority of the forces generated on the body cancel each other.

Figure 10. Pin geometries modeled.

For all of the simulations, the projectiles were initially flying straight and level at Mach 4 and were

commanded to initiate a left turn 0.1 s into the simulation. Each projectile was also oriented such that it had to execute the maximum roll maneuver necessary that would bring the pins into the proper orientation. For the 4 pin configurations, the projectile had to roll 90º while for the 3 pin configurations the projectile had to roll 180º. To increase the response time, the projectiles were commanded to use pins to initiate the required roll and to use pins to stop the roll. (Using the natural roll damping instead of active braking considerably increases the response time.) As seen in Figure 11, the number of pins (and thus the amount of rotation required) affected the time to reach the 100 m cross range threshold, T100, but this effect was secondary to the location of the pins. The primary difference in the T100 times of the projectiles outfitted with different pin configurations is a result of the turning force generated by the projectile at angle of attack. As the angle of attack was driven by the moment generated by the pins, and the interior pin configurations generated more moment, their T100 time was less than that of the planar pin configurations. As denoted on Figure 11 by ∆Tα, the difference in response time was on the order of 0.2 s for the different pin geometries. Increasing the number of pins from 2 to 4 for the interior configurations resulted in an additional reduction in the T100 time of roughly 0.05 s. It was decided to carry forward both the Interior X and Interior V configurations as the trade between response time and the additional complexity of 4 pins versus 2 pins was not clear.

For this set of simulations, the Interior X configuration was judged the most desirable. It had the shortest time to divert 100 m and also had the shortest total time of pin deployment. In this non rolling frame, this is likely to always be true as no more than 2 pins are deployed for any significant portion of the maneuver, and thus the shortest time to complete the maneuver will also be the shortest total pin deployment time. As seen in the next section, the situation becomes more complex on a rolling projectile.

Interior X Short I Interior V Planar 4 Pins 2 Pins



Figure 11. Time to achieve 100 m cross range for different pin configurations.

V. Optimizing Pin Deployment Schedule for Maximum Turning Authority Even after narrowing the candidates for the optimum pin geometry, further work remained to determine

the optimal pin deployment schedule to achieve maximum turning authority for a rolling projectile. For these simulations, it was assumed that the projectile would be undergoing a relatively slow roll induced by a fin cant. A rolling projectile complicates the guidance algorithm, but was deemed necessary for an onboard sensor package that was being considered at the same time. Several figures of merit (FOM) were used to compare the different configurations. The first FOM was the time taken for the projectile to complete the 100 m cross range maneuver after the command was initiated, while the second FOM was based on the estimated control input forces to deploy the pins to complete the 100 m divert. Either FOM could conceivably drive the system depending on the mission and system requirements. Two other FOMs were investigated one of which was the time to change the projectile’s heading by 5º and the total pin force required to change the heading by 5º.

Three different control algorithms were studied in this effort. The simplest of these algorithms was the No Hold case where no effort was made to control the roll of the projectile. In this case, the pins were deployed when the pins were in a defined angular region and then retracted when past a given angular region. There is no net effect on the roll of the projectile. In Figure 12, a projectile is shown at four different times for the No Hold control algorithm. In frame 1 the pins are not yet in position, but in frame 2 the projectile has rolled further and two pins deploy to initiate a left turn. In frame 3, the pins remain deployed as the projectile continues to roll, and finally in frame 4 the pins have retracted as the projectile has rolled past the desired angle. Another way to visualize the differences between the control algorithms is to compare strip charts of the maneuvers. In the strip charts below, the pin position is shown as a function of time along with the roll angle, roll rate, AoA and yawing angle or lateral deviation. In Figure 13, the strip chart for the No Hold control, we can see that roll rate is constant during the time that the projectile is maneuvering. This is by design; both pins are always engaged at the same time, so all rolling moments induced by the pins will be cancelled leaving only the pitching force on the fins and body.

The second control scheme considered was the Roll Control algorithm. In this pin deployment scheme, the goal was to control the roll of the projectile with the pins. In Figure 14, the time lapse initially shows the projectile at frame 1 where it is rolling into the region where the pin deployment is initiated. In frame 2, two pins deploy similarly to the No Hold case described above, but as the projectile continues to roll, one of the pins is retracted as shown in frame 3, which results in the projectile rolling in the opposite direction (note arrow on frame 3). Both pins are again deployed, frame 4, and the process is repeated (frames 2-4)

-100

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0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Interior XInterior VShort IPlanar

Cro

ss R

ange

(m)

Time (s)0.7765 s 0.8205 s 0.9815 s 0.9905 s

∆T α

∆T Φ

T100



until the maneuver is completed. This algorithm completes the maneuver faster, but also may interfere with the performance of onboard seekers that require roll, as the projectile roll is effectively stopped as seen from the strip chart for the Roll Control algorithm, Figure 15. After a flight time of 0.2 seconds, the roll angle remains mostly constant due to the introduction of rolling moments from having only one pin out at certain times (these times are seen as brief drops in the activity of pin 2) which correspond to the third frame of the time lapse.

The third control algorithm considered was sort of a hybrid approach between the two previously described schemes. The Stutter control, shown in Figure 16, uses a single pin to halt the rotation of the projectile, shown in frame 2, and then two pins deploy to initiate the projectile yaw (frame 3). The projectile then begins to roll again due to the fin cant, and once the pins are out of the desired zone, both pins are retracted (frame 4). Once the projectile rolls back around to where the pins are in the desired region the process begins anew and is repeated until the maneuver is completed. For the Stutter algorithm, the projectile continues to roll during the maneuver, although the roll is affected and the effects on any seeker or sensor system would require further investigation. In the strip chart, Figure 17, the same roll controlling idea is seen; one pin is deployed slightly before the other to create a rolling moment for only a short time. This rolling moment slows down the roll rate of the round to zero; this effect can be seen in the behavior of roll angle from the top line of the strip chart as it stops moving just after 0.1s and just before 0.4s.

The rolling airframe also introduced additional complications in that there was additional out of plane motion induced and that an additional instability mode was added. There was a clear trade between the rolling frequency of the projectile and the pin deployment times that led to a family of solutions, but it was decided that pin deployment times less than 10 ms were not practical and that rolling frequencies greater than 15 Hz were not desirable. A rolling frequency for each of the control algorithms was found and the fin cant was set to provide this roll rate for each case. These frequencies ranged from 3 Hz for the Roll Hold case to 13 Hz for the No Hold case with the Stutter case frequency falling in the middle at 4.5 Hz. Each frequency was chosen based on a compromise between the natural roll rate and the duration of the control.

Figure 12. Time lapse of No Hold control.

Figure 13. No Hold algorithm strip chart.


Figure 14. Time lapse of Roll Control.

Figure 15. Roll Control algorithm strip chart.

Figure 16. Time lapse of Stutter control.

Figure 17. Stutter Control algorithm strip chart.

A comparison of the different control algorithms in terms of how quickly they induced cross range is shown in Figure 18. This result clearly indicates that the Roll Control algorithm provides the most rapid turning and further that having 4 pins (Interior X) only provides marginally better performance than 2 pins (Interior V). For the No Hold algorithm there is a difference of over 0.5 s in the 4 pin and the 2 pin performance while this algorithm generally provides the slowest time required to divert 100 m. The Stutter algorithm also experiences a substantial degradation in performance as the number or pins is reduced. The 4 pin case is however comparable to the Roll Control algorithm which may be important if projectile roll is required for continued sensor updates. As a summary of this FOM, the time for the projectile to achieve 100 m divert for each configuration is shown in Table 1.

A driving factor in the design of a guided projectile is the onboard power required to actuate the guidance pins. Different pin deployment schemes can result in different power requirements. For example, consider a pin deployment mechanism that requires a constant power to maintain pin deployment. In this case the sum total time that all pins are deployed will be proportional to the power requirements. Table 2 shows the total pin deployment times for the same 100 m divert case and here the Stutter control appears optimal. If a pin effectiveness is defined as the power input multiplied by the time to divert 100 m, where the lower the number the better, the clear winner is the Stutter control using the Interior X configuration.

Under certain semi passive pin deployment schemes where power is only required to change the pin state, it is clear from examining the strip charts that the Stutter control would again have the greatest effectiveness. For the No Hold algorithm, the regular motion of the pins would lead to high power requirements. While both the Stutter and the Roll Control algorithms would have similar power requirements, the Stutter control completes the maneuver faster thus leading to a better over performance.

If the desired goal of the guidance command is to change the flight path of the projectile as rapidly as possible, a different FOM must be used to evaluate the different control algorithms. Depending on the max change in heading required, for example by a proportional navigation control attempting to intercept a


target, several control algorithms offer potential solutions as shown in Figure 19. For a 5° heading change, the times for each of the control algorithms and pin configuration combinations are shown in Table 3, and again the Roll Control algorithm offers the most rapid response. It is also found that the number of pins used produces only a minimal change in the response time for this algorithm, and that the 4 pin Stutter algorithm provides a viable alternative to the Roll Control algorithm. However, it is important to note that if a course correction of 4.5° or less is required the Stutter control is probably a better choice and if a correction of less than 2° is commanded almost any of the configurations would be viable. In terms of the total pin force required to achieve a desired course correction, it obviously depends on the degree of course correction demanded, but it would once again appear that the Stutter algorithm provides the best performance of those investigated. Clearly some thought would need to be given to determine the best pin configuration and control algorithm combination based on a combination of anticipated mission profile and projectile design considerations.

Figure 18. Cross Range versus time for two and four pin control algorithms.


Table 1 Time to divert 100 m.

Table 2 Pin time to divert 100 m.

Figure 19. Lateral deviation from muzzle azimuth versus time for two and four pin control algorithms.

0.812s0.986s1.155sInterior X

0.861s1.245s1.590sInterior V

Roll Control

Stutter Control

No Hold

Control

ControlAlgorithm

PinConfiguration



Roll Control

Stutter Control

No Hold

Control

ControlAlgorithm

PinConfiguration

1.311 Pin-sec0.876 Pin-sec0.884 Pin-secInterior X

1.391 Pin-sec0.801 Pin-sec0.628 Pin-secInterior V

Roll Control

StutterControl

No Hold Control

ControlAlgorithm

PinConfiguration

1.311 Pin-sec0.876 Pin-sec0.884 Pin-secInterior X

1.391 Pin-sec0.801 Pin-sec0.628 Pin-secInterior V

Roll Control

StutterControl

No Hold Control

ControlAlgorithm

PinConfiguration


Table 3 Time for 5° heading change.

VI. Conclusions A series of 6DOF simulations were used to investigate the control authority of pin based guidance

actuators developed by GTRI. The aerodynamic coefficients in the 6DOF simulations were shown to compare very favorably with prior range tests conducted at ARL. It was shown that large turning forces could be generated that would lead to high g maneuvers suitable for intercepting a target. While it was found that oscillations in the projectile angle of attack occurred upon applying the forces developed by the pins, it was also shown that these oscillations could be mitigated by properly tailoring the control forces.

Further simulations of different pin configurations clearly demonstrated that placing the pins on the interior of two adjacent fins was superior to placing them on opposing fins. A final series of simulations were conducted for a rolling projectile that explored three different control algorithms. Several figures of merit were used to compare these algorithms and it was found that while certain algorithms provided a more rapid response, other guidance algorithms may perform better from a system standpoint as they would require less onboard power. Through these simulations and validation of these simulations with actual range data, the use of the guidance pins for mid course correction of a supersonic projectile has been shown to be an effective solution. Further, the guidance pins can be implemented on a rolling projectile and the force levels can tailored to reduce pitch oscillations which leads to practical applications on realistic rounds.

References

1 Kandebo, Stanley W., “New Powerplant Key to Missile Demonstrator,” Aviation Week, Sept. 2, 2002. 2 Warnash, A. and Killen, A., “Low Cost, High G, Micro Electro-Mechanical (MEMS), Inertial Measurements Unit (IMU) Program,” 23rd Army Science Conference, Dec. 2002. 3 Frost, G. W., and Costello, M. F., “Control Authority of a Projectile Equipped With an Internal Unbalanced Part,” Army Research Lab Report, ARL-CR-555, November 2004. 4 Massey, K. C., McMichael, J., Warnock, T., and Hay, F., “Design and Wind Tunnel Testing of Guidance Pins for Supersonic Projectiles,” 25th Army Science Conference, Dec. 2004. 5 Massey, K. C., McMichael, J., Warnock, T., and Hay, F., “Mechanical Actuators for Guidance of a Supersonic Projectile,” 23rd AIAA Applied Aerodynamics Conference, June 2005, AIAA 2005-4970. 6 Silton, S., “Comparison of Predicted Actuator Performance for Guidance of Supersonic Projectiles to Measured Range Data,” AIAA-2004-5195, Aug. 2004.



Roll Control

StutterControl

No Hold

Control

ControlAlgorithm

PinConfiguration



Roll Control

StutterControl

No Hold

Control

ControlAlgorithm

PinConfiguration


7 Silton, S. and Massey, K. C., “Integrated Numerical and Experimental Investigation of Actuator Performance for Guidance of Supersonic Projectiles,” 2004 Army Sciences Conference, Paper CO-04.

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