Rate control system algorithm developed in state space for models with parameter uncertainties

Teixeira, Adilson Jesus

doi:10.5028/jatm.2011.03033511

Abstract

researching in weightlessness above the atmosphere needs a payload to carry the experiments. To achieve the weightlessness, the payload uses a rate control system (RCS) in order to reduce the centripetal acceleration within the payload. The rate control system normally has actuators that supply a constant force when they are turned on. The development of an algorithm control for this rate control system will be based on the minimum-time problem method in the state space to overcome the payload and actuators dynamics uncertainties of the parameters. This control algorithm uses the initial conditions of optimal trajectories to create intermediate points or to adjust existing points of a switching function. It associated with inequality constraint will form a decision function to turn on or off the actuators. This decision function, for linear time-invariant systems in state space, needs only to test the payload state variables instead of spent effort in solving differential equations and it will be tuned in real time to the payload dynamic. It will be shown, through simulations, the results obtained for some cases of parameters uncertainties that the rate control system algorithm reduced the payload centripetal acceleration below µg level and keep this way with no limit cycle.

Keywords:
Rate control; Off-on control; Time optimal control; State space; Bang-bang control

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REFERENCES

Bryson, Jr., Arthur, E., Ho, Yu-Chi, 1997, "Applied Optimal Control - Optimization, Estimation and Control", Hemisphere Publishing Corporation, USA.
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Frisk, E., 1996, "Model-Based Fault Diagnosis Applied To A Si-Engine", Linköping University, Linköping, Sweden.
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Takahashi, Y., Rabins, M. J., Auslander, D. M., 1972, "Control and Dynamic Systems", Addison-Wesley Publishing Company, Massachusetts, USA.
Teixeira, A. J., 2009, "Rate Control System For Plant Parameter Uncertainties", Proceedings of the 19th ESA Symposium on European Rocket and Balloon Programmes and Related Research, SP-671 pg. 255-260, Bad Reichenhall, Germany.
Udrişte, C., 2008, "Multitime Controllability, Observability and Bang-Bang Principle", Journal of Optimal Theory Applications, Vol. 139, p. 141-157. DOI 10.1007/s10957-008-9430-2.
» https://doi.org/10.1007/s10957-008-9430-2

Publication Dates

Publication in this collection
Sep-Dec 2011

History

Received
04 Aug 2011
Accepted
06 Oct 2011

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Bryson, Jr., Arthur, E., Ho, Yu-Chi, 1997, "Applied Optimal Control - Optimization, Estimation and Control", Hemisphere Publishing Corporation, USA.

[2] Cornelisse, J. W., Schöyer, H. F. R., Wakker, K. F., 1979, "Rocket Propulsion and Spaceflight Dynamics", Pitman Publishing Limited, London, England.

[3] Ettl, J., Pfänder, J., 2009, "Rate Control System for Sounding Rockets", 19^th ESA Symposium on European Rocket and Balloon Programmesand and Related Research, Bad Reichenhall, Germany, (ESA SP-671).

[4] Frisk, E., 1996, "Model-Based Fault Diagnosis Applied To A Si-Engine", Linköping University, Linköping, Sweden.

[5] Lucas, S. K., Kaya, C. Y., 2001, "Switching-Time Computation for Bang-Bang Control Laws", Proceedings of the American Control Conference, Arlington, VA, USA.

[6] Nitulescu, M., 2005, "Controlling a Mobile Robot Along Planned Trajectories", Control Engineering and Applied Informatics, Vol. 7, N. 2, p. 18-24.

[7] O'Brien Jr., R.T., 2006, "Bang-Bang Control for Type-2 Systems", Proceedings of the 38^th Southeastern Symposium on System Theory, Tennessee Technological University, Cookeville, TN, USA.

[8] Ogata, K., 1982, "Modern Control Engineering", Editora Prentice/Hall do Brasil Ltda, Rio de Janeiro, RJ, Brazil.

[9] Takahashi, Y., Rabins, M. J., Auslander, D. M., 1972, "Control and Dynamic Systems", Addison-Wesley Publishing Company, Massachusetts, USA.

[10] Teixeira, A. J., 2009, "Rate Control System For Plant Parameter Uncertainties", Proceedings of the 19th ESA Symposium on European Rocket and Balloon Programmes and Related Research, SP-671 pg. 255-260, Bad Reichenhall, Germany.

[11] Udrişte, C., 2008, "Multitime Controllability, Observability and Bang-Bang Principle", Journal of Optimal Theory Applications, Vol. 139, p. 141-157. DOI 10.1007/s10957-008-9430-2.
» https://doi.org/10.1007/s10957-008-9430-2

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