doi: 10.17586/2226-1494-2015-15-6-1045-1053


I. V. Petranevsky, O. I. Borisov, V. S. Gromov, A. A. Pyrkin

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For citation: Petranevsky I.V., Borisov O.I., Gromov V.S., Pyrkin A.A. Output сontroller for quadrocopter with wind disturbance cancellation. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 6, pp. 1045–1053.

Subject of Research. The paper presents an output control approach for a class of nonlinear MIMO (Multiple Input Multiple Output) systems. Quadrocopter is chosen to illustrate proposed adaptive control approach based on the high-gain principle, the so-called, “consecutive compensator”. Basic Concepts. The dynamic properties of quadrocopter can be described by a non-linear multi-channel system. Accordingly, the first step is accomplished by its decomposition, whereby the model is divided into two parts: static conversion and several dynamical channels with one input and one output). After the decomposition, a derivation of the simplified mathematical model of the quadrocopter is carried out; and, in addition to the absolute coordinate system, the local system rigidly connected with the robot is introduced. The appropriate coordinate transformation is taken into account. Interim Results. Decomposition of the mathematical model gives the possibility to create control system in two steps. Firstly, the law is applied; in accordance with it the so-called virtual control actions for each model channel of the quadrocopter are generated. A well-known method of robust control, "consecutive compensator", is used here, successfully well-accepted as the most easily implemented one from an engineering point of view. This method gives the possibility to control an object output under its uncertainty quantification. Secondly, the inverse transformation is performed, resulting in real control actions distributed between the system actuators. We assume that wind disturbance affects each channel of the object. What is more, the values and directions of these disturbances are changed negligibly slow. Thus, we can treat them as unknown constants, subject to compensation. Main Result. We have developed a multi-channel control system for the quadrocopter by different methods (decomposition of the mathematical model and the output of its simplified analogue, coordinate transformation, "consecutive compensator"). The obtained closed-loop system has been successfully simulated and corresponding results have been received.

Keywords: output control, robust control, nonlinear systems, MIMO systems.

Acknowledgements. This article is supported by Government of Russian Federation (GOSZADANIE 2014/190 (project 2118)) and the Ministry of Russian Federation (project 14.Z50.31.0031).


1. Bobtsov A.A., Nikolaev N.A. Fradkov theorem-based design of the control of nonlinear systems with functional and parametric uncertainties. Automation and Remote Control, 2005, vol. 66, no. 1, pp. 108–118.
2. Fradkov A.L., Andrievsky B.R., Peaucelle D. Adaptive passification-based fault-tolerant flight control. Proc. 17th IFAC Symposium on Automatic Control in Aerospace, ACA’2007. Toulouse, France, 2007, vol. 17, pp. 715–720.
3. Kaufman H., Barkana I., Sobel K.S. Direct Adaptive Control Algorithms: Theory and Applications. 2nd ed. NY, Springer, 1998, 424 p.
4. Park B.S., Yoo S.J., Park J.B., Choi Y.H. A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots. IEEE Transactions on Control Systems Technology, 2010, vol. 18, no. 5, pp. 1199–1206. doi: 10.1109/TCST.2009.2034639
5. Rusnak I., Barkana I., Weiss H.M. Improving the performance of existing missile autopilot using simple adaptive control. Proc. 18th IFAC World Congress. Milano, Italy, 2011, vol. 18, no. 1, pp. 6567–6572. doi: 10.3182/20110828-6-IT-1002.01659
6. Zhang S., Luo F.L. An improved simple adaptive control applied to power system stabilizer. IEEE Transactions on Power Electronics, 2009, vol. 24, no. 2, pp. 369–375. doi: 10.1109/TPEL.2008.2007490
7. Bobtsov A. A note to output feedback adaptive control for uncertain system with static nonlinearity. Automatica, 2005, vol. 41, no. 12, pp. 2177–2180. doi: 10.1016/j.automatica.2005.08.006
8. Bobtsov A.A. A robust control algorithm for tracking the command signal with compensation for the parasitic effect of external unbounded disturbances. Automation and Remote Control, 2005, vol. 66, no. 8, pp. 1287–1295. doi: 10.1007/s10513-005-0169-z
9. Bobtsov A.A., Nikolaev N.A., Slita O. Adaptive control of libration angle of a satellite. Mechatronics, 2007, vol. 17, no. 4-5, pp. 271–276. doi: 10.1016/j.mechatronics.2007.02.002
10. Fradkov A.L. Synthesis of adaptive stabilization system of linear dynamic object. Automation and Remote Control, 1974, no. 12, pp. 96–103. (In Russian)
11. Fradkov A.L. Passification of non-square linear systems and feedback Yakubovich-Kalman-Popov Lemma. European Journal of Control, 2003, vol. 9, no. 6, pp. 577–586. doi: 10.3166/ejc.9.577-586
12. Barkana I. Parallel feedforward and simplified adaptive control. International Journal of Adaptive Control and Signal Processing, 1987, vol. 1, no. 2, pp. 95–109. doi: 10.1002/acs.4480010202
13. Barkana I. Comments on "Design of strictly positive real systems using constant output feedback". IEEE Transactions on Automatic Control, 2004, vol. 49, no. 11, pp. 2091–2093. doi: 10.1109/TAC.2004.837565
14. Andrievsky B.R., Fradkov A.L., Kaufman H. Necessary and sufficient conditions for almost strict positive realness and their application to direct implicit adaptive control systems. Proc. American Control Conference. Baltimore, USA, 1994, vol. 2, pp. 1265–1266.
15. Bobtsov A.A., Pyrkin A.A., Faronov M.V. Output control for time-delay nonlinear system providing exponential stability. Proc. 19th Mediterranean Conference on Control and Automation, MED 2011. Corfu, Greece, 2011, pp. 512–520. doi: 10.1109/MED.2011.5983020
16. Pyrkin A.A., Bobtsov A.A. Output control for nonlinear system with time-varying delay and stability analysis. Proc. 50th IEEE Conf. on Decision and Control and European Control Conference. Orlando, USA, 2011, pp. 7392–7397. doi: 10.1109/CDC.2011.6160224
17. Pyrkin A.A., Bobtsov A.A., Kolyubin S.A., Faronov M.V., Shavetov S.V., Kapitanyuk Y.A., Kapitonov A.A. Output control approach "consecutive compensator" providing exponential and L∞-stability for nonlinear systems with delay and disturbance. Proc. 20th Int. Conf. on Control Application. Denver, USA, 2011, pp. 1499–1504. doi: 10.1109/CCA.2011.6044373
18. Pyrkin A., Smyshlyaev A., Bekiaris-Liberis N., Krstic M. Rejection of sinusoidal disturbance of unknown frequency for linear system with input delay. Proc. American Control Conference. Baltimore, USA, 2010, pp. 5688–5693.
19. Pyrkin A., Smyshlyaev A., Bekiaris-Liberis N., Krstic M. Output control algorithm for unstable plant with input delay and cancellation of unknown biased harmonic disturbance. Proc. 9th IFAC Workshop on Time Delay System. Prague, Czech Republic, 2010, no. 1, pp. 39–44.
20. Krstic M. Delay Compensation for Nonlinear, Adaptive and PDE Systems. Birkhauser Boston, 2009, 466 p. doi: 10.1007/978-0-8176-4877-0
21. Krstic M., Smyshlyaev A. Backstepping boundary bontrol for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Proc. IEEE Conf. on Decision and Control. New Orleans, USA, 2007, pp. 225–230. doi: 10.1109/CDC.2007.4434474
22. Pyrkin A. Adaptive algorithm to compensate parametrically uncertain biased disturbance of a linear plant with delay in the control channel. Automation and Remote Control, 2010, vol. 71, no. 8, pp. 1562–1577. doi: 10.1134/S0005117910080060

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