Aerospace and Electronic Systems Magazine April 2018 - 15

Wahl and Turkoglu
maining stable. (Stability was considered to be maintained as long
as the control system could produce successful simulations for
the entirety of the Monte Carlo run. If simulations failed during
a run, then the system was considered to be unstable.) Testing of
±12% showed results similar to those of ±10%, except with larger
variances in the result vs. the nominal case. Going up to ±15%
combined variances resulted in some simulations failing, indicating that the control system developed instabilities at that level of
variance and was not able to perform satisfactorily. Increasing to
±20% and ±25% resulted in greater instabilities, suggesting that
the highest variances tolerated by this system before becoming
unstable lie somewhere between ±12% and ±15%. Here, instabilities are considered to be caused by the coupling of plant dynamics, as well as the nonlinearities associated with the problem.

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CONCLUSIONS AND FUTURE WORK
This research conducts an investigation of real-time nonlinear controller design for a high-speed launch vehicle through a nonlinear
RHC methodology that provides single-shot, real-time solutions.
One of the novel approaches in this application is to provide a
real-time solution process for launch vehicles that can be run with
onboard computer hardware. From the results of the various simulations, it is clear that it is possible to design and implement such
a control system.
The reaction of the system to initial perturbation was favorable, and trajectory tracking (across a variety of trajectories) was
achieved within a relatively short time and then maintained. The
computation time was less than the simulation time by a comfortable margin, which confirms that real-time control is possible. The
Monte Carlo uncertainty analysis indicated that the system is robust to sensor noise and actuator deviation to a reasonable degree.
Future work would involve converting the code into a format
suitable for execution on an embedded system and optimizing it as
much as possible, as well as enhancing the current system to allow proper trajectory (not just α) tracking and handling of actuator
dynamics.

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[15]
[16]

[17]
[18]

[19]

[20]

REFERENCES
[1]
[2]
[3]
[4]

[5]
[6]

Shneydor, N. A. Missile Guidance and Pursuit: Kinematics, Dynamics and Control. Woodhead Publishing, PA, USA 1998.
Mackenzie, D. Inventing Accuracy-A Historical Sociology of Nuclear Missile Guidance. MIT Press, MA, USA, 1990.
Battin, R. An Introduction to the Mathematics and Methods of Astrodynamics. AIAA, VA, USA 1999.
Launius, R. D., and Jenkins, D. R. (Eds.). To Reach the High Frontier:
A History of US Launch Vehicles. University Press of Kentucky, KY,
USA 2015.
Friedberg, A. L. A history of the US strategic doctrine: 1945 to 1980.
Journal of Strategic Studies, Vol. 3, 3 (1980), 37-71.
Bilstein, R. E. Stages to Saturn: A Technological History of the Apollo/Saturn Launch Vehicle. NASA History Series, Washington, DC,
USA 1996.

APRIL 2018

[21]
[22]

[23]

[24]
[25]

IEEE A&E SYSTEMS MAGAZINE

Kim, B. S., and Calise, A. J. Nonlinear flight control using neural
networks. Journal of Guidance, Control, and Dynamics, Vol. 20, 1
(1997), 26-33.
Shtessel, Y., Hall, C., and Jackson, M. Reusable launch vehicle control
in multiple-time-scale sliding modes. Journal of Guidance, Control,
and Dynamics, Vol. 23, 6 (2000), 1,013-1,020.
Johnson, E. N., Calise, A. J., and Corban, J. E. Adaptive guidance and
control for autonomous launch vehicles. In Proceedings of the IEEE
Aerospace Conference, Vol. 6, 2001.
Luo, Y., et al. Model predictive dynamic control allocation with actuator dynamics. In Proceedings of the American Control Conference,
Vol. 2, 2004, Boston, MA, USA.
Camacho, E. F., and Alba, C. B. Model predictive control. Springer
Science & Business Media, 2013, London.
Menon, P. K., Sweriduk, G. D., Vaddi, S. S., and Ohlmeyer, E. J. Nonlinear discrete-time design methods for missile flight control systems.
In Proceedings of the AIAA Guidance, Navigation, and Control Conference and Exhibit, 2004.
Apollo 8 nominal launch profile. Available: http://history.nasa.gov/
ap08fj/01launch_ascent.htm, last access Oct. 2015.
Reichert, R., and Yost, D. J., "Modern robust control for missile autopilot design." AGARD, Missile Interceptor Guidance System Technology 15 p (SEE N 91-13434 05-05) (1990).
Lu, P. Nonlinear predictive controllers for continuous systems. Journal of Guidance, Control, and Dynamics, Vol. 17, 3 (1994), 553-560.
Ohtsuka, T. Time-variant receding-horizon control of nonlinear systems. Journal of Guidance, Control, and Dynamics, Vol. 21, 1 (1997),
174-176.
Cox, S. J., et al. Iridis-pi: A low-cost, compact demonstration cluster.
Cluster Computing, Vol. 17, 2 (2014), 349-358.
Abrahamsson, P., et al. Affordable and energy-efficient cloud computing clusters: The Bolzano raspberry pi cloud cluster experiment.
In Proceedings of the IEEE 5th International Conference on Cloud
Computing Technology and Science, Vol. 2, 2013, Honolulu, HI, USA.
Wahl, E., and Turkoglu, K. Non-linear receding horizon control based
real-time guidance and control methodologies for launch vehicles. In
Proceedings of the IEEE Aerospace Conference, 2016.
Chwa, D., Young Choi, J., and Seo, J. H. Compensation of actuator
dynamics in nonlinear missile control. IEEE Transactions on Control
Systems Technology, Vol. 12, 4 (2004), 620-626.
Wise, K. A., and Broy, D. J. Agile missile dynamics and control. Journal of Guidance, Control, and Dynamics, Vol. 21, 3 (1998), 441-449.
Liu, G. Control of robot manipulators with consideration of actuator performance degradation and failures. In Proceedings of the
IEEE International Conference on Robotics and Automation, Vol.
3, 2001.
Zhang, Y., and Jiang, J. Fault tolerant control system design with explicit consideration of performance degradation. IEEE Transactions
on Aerospace and Electronic Systems, Vol. 39, 3 (2003), 838-848.
Kapila, V., and Grigoriadis, K. (Eds.). Actuator Saturation Control.
Mercel Dekker, 2002, New York, USA.
Chen, B., Niu, Y., and Zou, Y. Adaptive sliding mode control for stochastic Markovian jumping systems with actuator degradation. Automatica, Vol. 49, 6 (2013), 1,748-1,754.

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http://history.nasa.gov/ap08fj/01launch_ascent.htm http://history.nasa.gov/ap08fj/01launch_ascent.htm
Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine April 2018
