DOI:https://doi.org/10.15407/kvt185.03.021
KVT, 2016, Issue 185, pp.21-34
UDC 681.5
l1-OPTIMIZATION APPROACH TO DESIGN OF DIGITAL AUTOPILOTS FOR LATERAL MOTION CONTROL OF AN AIRCRAFT
Zhiteckii L.S., Pilchevsky A.Yu., Solovchuk K.Yu.
International Research and Training Center for Information Technologies and Systems of the National Academy of Science of Ukraine and Ministry of Education and Sciences of Ukraine, Kiev, Ukraine
leonid_zhiteckii@i.ua , terosjj@gmail.com , solovchuk_ok@mail.ru
Introduction. The optimal digital autopilot needed to control of the roll for an aircraft in the presence of an arbitrary unmeasured disturbances is addressed in this paper. This autopilot has to achieve a desired lateral motion control via minimizing the upper bound on the absolute value of the difference between the given and true roll angles. It is ensured by means of the two digital controllers. The inner controller is designed as the discrete-time PI controller in order to stabilize a given roll rate. This variable is formed by the external discrete-time P controller. To optimize this control system, the controller parameters are derived utilizing the so-called l1-optimization approach advanced in modern control theory. The motion parameters are assumed to be known.
The purpose of the paper is to synthesize a digital autopilot which is able to maintain a given roll orientation of an aircraft with a desired accuracy and to cope with an arbitrary external disturbance (a gust) whose bounds may be unknown.
Results. The necessary and sufficient conditions guaranteeing the stability of the two-circuit feedback discrete-time control system are established. First, the l1-optimal PI and P controller parameters are calculated simultaneously (in contrast with [14]). Second, the aileron servo dynamics are taken into account to establish the stability condition for optimizing the controller parameters. Third, random search algorithm is used to calculate the three optimal values of the autopilot parameters. To support the theoretical results obtained, in this work, several simulation experiments were conducted. We have established that the simultaneous l1-optimization of both controllers was more efficient than the sequential l1-optimization of inner and external controllers.
Conclusion. It was established that the two-circuit l1-optimal PI and P control laws can cope with the wind gust and ensure the desired roll orientation. This makes it possible to achieve the control objective which was stated. A distinguishing feature of the control algorithms is that they are sufficiently simple. This is important from the practical point of view.
Keywords: aircraft, lateral dynamics, digital control system, discrete time, stability, l1-optimization, random search algorithm.
References:
1 Stevens B.L., Lewis F.L. Aircraft Control and Simulation, 2nd ed. New York: John Willey & Sons, 2003, 680 p.
2 William D.E., Friedland B, Madiwale A.N. Modern conrtol theory for design of autopilots for bank-to-turn missiles. J. Guidance Control, 1987, vol. 10, pp. 378–386. https://doi.org/10.2514/3.20228
3 Teoh E.K., Mital D.P., Ang K.S. A BTT CLOS autopilot design. The EEE Journal, 1992, vol. 4, pp. 1–7.
4 Ang K.S., Teoh E.K., Mital D.P. Adaptive control of a missile autopilot system. Proc. 12th IFAC World Congress, 1993, vol. 1, pp. 293–296.
5 Malaek S.M.B., Izadi H., Pakmehr M. Intelligent Autolanding Controller Based on Neural Networks. Proc. 1st African Control Conference (AFCON2003), Cape Town, South Africa, 2003, vol. 1, pp. 113–119.
6 Khrosravani M.R. Apllication of Neural Network on Flight Control. Int. Journal of Machine Learning and Computing, 2012, vol. 6, pp. 882–885. https://doi.org/10.7763/IJMLC.2012.V2.258
7 Lavretsky E., Wise K. A. Robust and Adaptive Control with Aerospace Aplication. London: Springer-Verlag. 2013, 454 p. https://doi.org/10.1007/978-1-4471-4396-3
8 Astrom K.J., Wittenmark B. Computer Controlled Systems. Theory and Design, 2nd ed. N.J.: Prentice Hall, Englewood Cliffs, 1990, 555 p.
9 Goodwin G.C., Graebe S.F., Salgado M.E. Control Systems Design. N.J.: Prentice Hall, 2001, 908 p.
10 Yuz J.I., Goodwin G.C. Sampled-Data Models for Linear and Nonlinear System. London: Springer-Verlag, 2014, 289 p. https://doi.org/10.1007/978-1-4471-5562-1
11 Dahleh M.A., Pearson J.B. l1-optimal feedback controllers for discrete-time systems. Proc. American Control Conference, Seattle, WA, 1986, pp. 1964–1968.
12 Vidyasagar M. Optimal rejection of persistent bounded disturbances. IEEE Trans. on Autom. Control, 1986, vol. 31, pp. 527–517.
13 Khammash M.H. A new approach to the solution of the l1 control problem: the scaled-Q method. IEEE Trans. on Autom. Control, 2000, vol. 45, pp. 180–187.
14 Melnyk K.V., Zhiteckii L.S., Bogatyrov A.M., Pilchevsky A.Yu. Digital control of lateral autopilot system applied to an UAV: optimal control strategy. Proc. 2013 2nd IEEE Int. Conf. “Actual Problems of Unmanned Air Vehicles Developments”, Oct., 15-17, Kiev, Ukraine, 2013, pp. 189–192. https://doi.org/10.1109/APUAVD.2013.6705322
15 Blakelock J.H. Automatic Control of Aircraft and Missiles, 2nd ed. New York: John Wiley & Sons, Inc., 1991, 672 p.
16 Tou J.T. Digital and Sampled-Data Control Systems. New-York: McGraw-Hill Book Company, 1959, 631 p.
17 Jury E.I. Sampled-Data Control Systems. New York: John Willey & Sons Inc., 1958, 332 p.
18 Polyak B.T., Shcherbakov P.S. Robust Stability and Control. Moscow: Nauka, 2002, 303 p. (in Russian)
19 Polyak B.T. Introduction to Optimization. New-York: Optimization Software Inc., 1987, 438 p.
Received 01.06.16