Research Papers

Gain-Scheduled Two-Loop Autopilot for an Aircraft

[+] Author and Article Information
Laleh Ravanbod

Université Paul Sabatier,
Institut de Mathématiques,
Toulouse 31062, France
e-mail: LalehRavanbod@yahoo.fr

Dominikus Noll

Université Paul Sabatier,
Institut de Mathématiques,
Toulouse 31062, France
e-mail: d.noll@math.univ-toulouse.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 14, 2012; final manuscript received February 6, 2014; published online April 28, 2014. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 136(4), 041021 (Apr 28, 2014) (13 pages) Paper No: DS-12-1262; doi: 10.1115/1.4026832 History: Received August 14, 2012; Revised February 06, 2014

We present a new method to compute output gain-scheduled controllers for nonlinear systems. We use structured H-control to precompute an optimal controller parametrization as a reference. We then propose three practical methods to implement a control law which has only an acceptable loss of performance with regard to the optimal reference law. Our method is demonstrated in longitudinal flight control, where the dynamics of the aircraft depend on the operational conditions velocity and altitude. We design a structured controller consisting of a PI-block to control vertical acceleration, and another I-block to control the pitch rate.

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Becker, G., and Mantz, R., 1994, “Robust Performance of Linear Parametrically Varying Systems Using Parametrically-Dependent Linear Feedback,” Syst. Control Lett., 23, pp. 205–213. [CrossRef]
Apkarian, P., and Gahinet, P., 1995, “A Convex Characterization of Gain-Scheduled H Controllers,” IEEE Trans. Autom. Control, 40, pp. 853–864. [CrossRef]
Apkarian, P., Gahinet, P., and Becker, G., 1995, “Self-Scheduled H Control of Linear Parameter-Varying Systems: A Design Example,” Automatica, 31(9), pp. 1251–1261. [CrossRef]
Zhang, Y. S., and SaadatMehra, A., 2012, “Hinfty PID Control for Multivariable Networked Control Systems With Disturbance Noise Attenuation,” Int. J. Robust Nonlinear Control, 22(2), pp. 183–204. [CrossRef]
Lu, B., and Wu, F., 2004, “Switching LPV Control Design Using Multiple Parameter-Dependent Lyapunov Functions,” Automatica, 40, pp. 1973–1980. [CrossRef]
Lu, B., Wu, F., and Kim, S., 2006, “Switching LPV Control of an F-16 Aircraft via Controller State Reset,” IEEE Trans. Control Syst. Technol., pp. 267–277.
Mattei, M., 2001, “Robust Multivariable PID Control for Linear Parameter Varying Systems,” Automatica, 37(12), pp. 1997–2003. [CrossRef]
Bolea, Y., Puig, V., and Blesa, J., 2008, “Gain-Scheduled Smith PID Controllers for LPV Systems With Time Varying Delay: Application to an Open-Flow Canal,” Proceedings of IFAC, Korea, pp. 14564–14569.
Mattei, M., and Scordamaglia, V., 2008, “A Full Envelope Small Commercial Aircraft Flight Control Design Using Multivariable Proportional- Integral Control,” IEEE Trans. Control Syst. Technol., 16(1), pp. 169–176. [CrossRef]
Jenie, S. D., and Budiyono, A., 2006, Automatic Flight Control System—Classical Approach and Modern Control Perspective (Lecture Notes), Bandung Institute of Technology, Indonesia.
Stevens, B., and Lewis, F. L., 1992, Aircraft Control and Simulation, John Wiley and Sons, Inc., New York.
Sonneveldt, L., 2006, Nonlinear F-16 Model Description, Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands.
Magni, J., Bennani, S., and Terlouw, J., 1997, Robust Flight Control: A Design Challenge, Vol. 224 (Lecture notes in Control and Information Sciences), Springer, Berlin.
Zolghadri, A., 2000, “A Redundancy-Based Strategy for Safety Management in a Modern Civil Aircraft,” Control Eng. Pract., 8, pp. 545–554. [CrossRef]
Robust toolbox of Matlab R2010b, MathWorks, Natick, MA.
Apkarian, P., and Noll, D., 2006, “Nonsmooth H-Control,” IEEE Trans. Autom. Control, 51(1), pp. 71–78. [CrossRef]
Noll, D., Prot, O., and Rondepierre, A., 2008, “A Proximity Control Algorithm to Minimize Nonsmooth and Nonconvex Functions,” Pacific J. Optim., 4(3), pp. 569–602.
Pottmann, H., Krasauskas, R., Hamann, B., Joy, K., and Seibold, W., 2000, “On Piecewise Linear Approximation of Quadratic Functions,” J. Geom. Graphics, 4(1), pp. 31–53.
Keviczky, T., and Balas, G. J., 2006, “Receding Horizon Control of an F-16 Aircraft: A Comparative Study,” Control Eng. Pract., 14, pp. 1023–1033. [CrossRef]
Hassin, R., and Levin, A., 2006, “A Better-Than-Greedy Approximation Algorithm for the Minimum Set Cover Problem,” SIAM J. Comput., 35, pp. 189–200. [CrossRef]
Shamma, J., and Athans, M., 1990, “Analysis of Gain Scheduled Control for Nonlinear Plants,” IEEE Trans. Autom. Control, 35(4), pp. 898–907. [CrossRef]
Helton, J., and James, M. R., 1999, Extending H Control to Nonlinear Systems, SIAM Advances in Design and Control, Philadelphia, PA.
Gabarrou, M., Alazard, D., and Noll, D., 2010, “Structured Flight Control Law Design Using Non-Smooth Optimization,” 18th IFAC Symposium on Automatic Control in Aerospace.


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Fig. 1

rct_airframe1 scheme of simulink

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Fig. 2

Schemes used for (a) linearizing the nonlinear aircraft in closed-loop and (b) H synthesis

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Fig. 3

Left: flight envelope in geometry (M,q¯). Right: optimal H performance over flight envelope geometry e = (h, V).

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Fig. 4

Graphs of the optimal gains ki*(e),kp*(e), and kg*(e) and the optimal closed-loop performance (lower right) displayed over E

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Fig. 5

Two triangulations together with the performance graphs

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Fig. 10

Second approximation of the controller parameters and its performance

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Fig. 6

Example of preprocessing of the regions N(e): (a) without smoothing and (b) with smoothing

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Fig. 7

Seven regions N(ei) which cover E, performance error margin is respected in Eq. (2)

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Fig. 8

Performance optimal (left) and its estimation by greedy (right)

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Fig. 9

First approximation of the controller parameters and the performance obtained

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Fig. 11

Detectability rate, respectively, e→‖(sI-Acl(e))-1Bcl(e)‖∞, visualized over the flight envelope E. Ideal K* upper left, Kint upper right, Ktri (35 controllers) lower left, and Kgreedy lower right.

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Fig. 12

Vertical acceleration hold for high altitude

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Fig. 13

Vertical acceleration hold for low altitude

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Fig. 14

Control scheme for flight control

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Fig. 15

Optimal performance for flight control case



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