Abstract
To ensure that an aircraft is safe to fly, a complex, lengthy and costly process must be undertaken. Current aircraft control systems verification methodologies are based on conducting extensive simulations in an attempt to cover all worst-case scenarios. A Nichols plot is a technique that can be used to conclusively determine if a control system is stable. However, to guarantee stability within a certain margin of uncertainty requires an informal visual inspection of many plots. To leverage the safety verification problem, we present in this paper a method for performing a formal Nichols Plot analysis using the MetiTarski automated theorem prover. First the transfer function for the flight control system is extracted from a Matlab/Simulink design. Next, using the conditions for a stable dynamical system, an exclusion region of the Nichols Plot is defined. MetiTarski is then used to prove that the exclusion region is never entered. We present a case study of the proposed approach applied to the lateral autopilot of a Model 24 Learjet.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Advisory Circular: System design and analysis. Tech. rep., Federal Aviation Adminisration (1988)
Akbarpour, B., Paulson, L.C.: MetiTarski: An automatic prover for the elementary functions. In: Autexier, S., Campbell, J., Rubio, J., Sorge, V., Suzuki, M., Wiedijk, F. (eds.) AISC 2008, Calculemus 2008, and MKM 2008. LNCS (LNAI), vol. 5144, pp. 217–231. Springer, Heidelberg (2008)
Akbarpour, B., Paulson, L.C.: Applications of MetiTarski in the verification of control and hybrid systems. In: Majumdar, R., Tabuada, P. (eds.) HSCC 2009. LNCS, vol. 5469, pp. 1–15. Springer, Heidelberg (2009)
Baik, K.: Flight control systems - final project. Tech. rep., Concordia University (2008)
Brown, C.W.: QEPCAD B: A program for computing with semi-algebraic sets using CADs. SIGSAM Bulletin 37(4), 97–108 (2003)
Fielding, C., Varga, A., Bennani, S., Selier, M. (eds.): Advanced techniques for clearance of flight control laws. LNCIS, vol. 283. Springer, Heidelberg (2002)
Hardy, R.: Formal methods for control engineering: A validated decision procedure for Nichols Plot analysis. Ph.D. thesis, School of Computer Science - University of St. Andrews (February 2006)
Khalil, H.: Nonlinear Systems. Prentice Hall, Englewood Cliffs (1996)
Langton, R.: Stability and Control of Aircraft Systems. Wiley, Chichester (2006)
National Air Traffic Controllers Association: Air trafic control: By the numbers (2009), http://www.natca.org/mediacenter/bythenumbers.msp
Padfield, G.D.: The birth of flight control: An engineering analysis of the Wright brothers 1902 glider. University of Liverpool, The Aeronautial Journal (2003)
Parrilo, P.A.: Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. Ph.D. thesis, California Institute of Technology (May 2000)
Prajna, S., Jadbabaie, A.: Safety verification of hybrid systems using barrier certificates. In: Hybrid Systems: Computation and Control, pp. 477–492. Springer, Heidelberg (2004)
Prajna, S., Papachristodoulou, A., Seiler, P., Parrilo, P.A.: SOSTOOLS and Its Control Applications. LNCIS, vol. 312, ch. 3, pp. 273–292. Springer, Heidelberg (2005)
The MathWorks: Simulink 7 reference (March 2010), http://www.mathworks.com/access/helpdesk/help/pdf_doc/simulink/slref.pdf
Tomlin, C., Mitchell, I., Bayen, A.M., Oishi, M.: Computational techniques for the verification of hybrid systems. Proceedings of the IEEE 91(7) (July 2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Denman, W., Zaki, M.H., Tahar, S., Rodrigues, L. (2011). Towards Flight Control Verification Using Automated Theorem Proving. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds) NASA Formal Methods. NFM 2011. Lecture Notes in Computer Science, vol 6617. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20398-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-20398-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20397-8
Online ISBN: 978-3-642-20398-5
eBook Packages: Computer ScienceComputer Science (R0)