Robust Performance Analysis for a Cascade Nonlinear H∞ Control Algorithm in Quadrotor Position Tracking

Document Type : Research Article

Authors

School of Mechanical Engineering, University of Tehran

Abstract

This paper presents a new hierarchical robust algorithm to solve the position tracking problem, in presence of exogenous disturbances and modeling uncertainties, of a quadrotor helicopter. The suggested controller includes a nonlinear H∞ algorithm to track the reference trajectory in the outer loop and a nonlinear H∞ controller to stabilize the rotational movements in the inner loop. The resultant controller consists of three important parts to regulate tracking errors for translational and rotational motions, maintain robust performance confronting random disturbances and modeling uncertainties and reject the sustained disturbances from the system to vanish the steady-state errors. Analytical study on the stability of the cascade system is mentioned to verify the compatibility of two controllers considering coupling terms. Numerical performance analysis is accomplished using Monte-Carlo simulation. Statistical results obtained from 1000 simulations considering environmental disturbances and modeling uncertainties depict less than 5 cm for position tracking error and less than 2 degrees for attitude tracking error in steady state performance. The closed-loop performance of the controller is also compared with two previous algorithms by determining two numerical indexes for state tracking performance and control efforts, respectively. Simulation results of the suggested control algorithm depict a significant reduction in both indexes for a similar mission.

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References

[1] P. Castillo, R. Lozano, A. Dzul, Stabilization of a mini-rotorcraft having four rotors, in: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566), IEEE, 2004, pp. 2693-2698.
[2] S. Roelofsen, D. Gillet, A. Martinoli, Reciprocal collision avoidance for quadrotors using on-board visual detection, in: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), IEEE, 2015, pp. 4810-4817.
[3] A. Shukla, H. Karki, Application of robotics in onshore oil and gas industry—A review Part I, Robotics and Autonomous Systems, 75 (2016) 490-507.
[4] J.J. Lugo, A. Zell, Framework for autonomous on-board navigation with the AR. Drone, Journal of Intelligent & Robotic Systems, 73(1-4) (2014) 401-412.
[5] W. Dong, G.-Y. Gu, X. Zhu, H. Ding, Development of a quadrotor test bed—modelling, parameter identification, controller design and trajectory generation, International Journal of Advanced Robotic Systems, 12(2) (2015) 7.
[6] F. Kendoul, Z. Yu, K. Nonami, Guidance and nonlinear control system for autonomous flight of minirotorcraft unmanned aerial vehicles, Journal of Field Robotics, 27(3) (2010) 311-334.
[7] N. Cao, A.F. Lynch, Inner–outer loop control for quadrotor UAVs with input and state constraints, IEEE Transactions on Control Systems Technology, 24(5) (2016) 1797-1804.
[8] M. Hayajneh, M. Melega, L. Marconi, Design of autonomous smartphone based quadrotor and implementation of navigation and guidance systems, Mechatronics, 49 (2018) 119-133.
[9] J. Guerrero-Castellanos, N. Marchand, A. Hably, S. Lesecq, J. Delamare, Bounded attitude control of rigid bodies: Real-time experimentation to a quadrotor mini-helicopter, Control Engineering Practice, 19(8) (2011) 790-797.
[10]  J. Kim, M.-S. Kang, S. Park, Accurate modeling and robust hovering control for a quad-rotor VTOL aircraft, in: Selected papers from the 2nd International Symposium on UAVs, Reno, Nevada, USA June 8–10, 2009, Springer, 2009, pp. 9-26.
[11] H. Liu, Y. Bai, G. Lu, Y. Zhong, Robust attitude control of uncertain quadrotors, IET Control Theory & Applications, 7(11) (2013) 1583-1589.
[12] Y. Wang, Y. Chenxie, J. Tan, C. Wang, Y. Wang, Y. Zhang, Fuzzy radial basis function neural network PID control system for a quadrotor UAV based on particle swarm optimization, in: 2015 IEEE International Conference on Information and Automation, IEEE, 2015, pp. 2580-2585.
[13] C. Peng, Y. Bai, X. Gong, Q. Gao, C. Zhao, Y. Tian, Modeling and robust backstepping sliding mode control with Adaptive RBFNN for a novel coaxial eight-rotor UAV, IEEE/CAA Journal of Automatica Sinica, 2(1) (2015) 56-64.
[14] C. Nicol, C. Macnab, A. Ramirez-Serrano, Robust adaptive control of a quadrotor helicopter, Mechatronics, 21(6) (2011) 927-938.
[15] A.C. Satici, H. Poonawala, M.W. Spong, Robust optimal control of quadrotor UAVs, IEEE Access, 1 (2013) 79-93.
[16] C. Mu, Y. Zhang, Learning-Based Robust Tracking Control of Quadrotor With Time-Varying and Coupling Uncertainties, IEEE transactions on neural networks and learning systems, (2019).
[17] N. Koksal, M. Jalalmaab, B. Fidan, Adaptive Linear Quadratic Attitude Tracking Control of a Quadrotor UAV Based on IMU Sensor Data Fusion, Sensors, 19(1) (2019) 46.
[18] O. Mofid, S. Mobayen, Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties, ISA transactions, 72 (2018) 1-14.
[19] F. Rekabi, F.A. Shirazi, M.J. Sadigh, ADAPTIVE-NONLINEAR H∞ HIERARCHICAL ALGORITHM FOR QUADROTOR POSITION TRACKING, in: 2018 6th RSI International Conference on Robotics and Mechatronics (IcRoM), IEEE, 2018, pp. 12-17.
[20] W. Lei, C. Li, M.Z. Chen, Robust Adaptive Tracking Control for Quadrotors by Combining PI and Self-Tuning Regulator, IEEE Transactions on Control Systems  Technology, (2018).
[21] J. Moreno-Valenzuela, R. Pérez-Alcocer, M. Guerrero-Medina, A. Dzul, Nonlinear PID-Type Controller for Quadrotor Trajectory Tracking, IEEE/ASME Transactions on Mechatronics, 23(5) (2018) 2436-2447.
[22] H. Ríos, R. Falcón, O.A. González, A. Dzul, Continuous Sliding-Mode Control Strategies for Quadrotor Robust Tracking: Real-Time Application, IEEE Transactions on Industrial Electronics, 66(2) (2019) 1264-1272.
[23] A. L’afflitto, R.B. Anderson, K. Mohammadi, An Introduction to Nonlinear Robust Control for Unmanned Quadrotor Aircraft: How to Design Control Algorithms for Quadrotors Using Sliding Mode Control and Adaptive Control Techniques [Focus on Education], IEEE Control Systems, 38(3) (2018) 102-121.
[24] G.V. Raffo, M.G. Ortega, F.R. Rubio, Path tracking of a UAV via an underactuated control strategy, European Journal of Control, 17(2) (2011) 194-213.
[25] L. Luque-Vega, B. Castillo-Toledo, A.G. Loukianov, Robust block second order sliding mode control for a quadrotor, Journal of the Franklin Institute, 349(2) (2012) 719-739.
[26] H. Liu, J. Xi, Y. Zhong, Robust hierarchical control of a laboratory helicopter, Journal of the Franklin Institute, 351(1) (2014) 259-276.
[27] H. Liu, D. Li, J. Xi, Y. Zhong, Robust attitude controller design for miniature quadrotors, International Journal of Robust and Nonlinear Control, 26(4) (2016) 681-696.
[28] B. Zhao, B. Xian, Y. Zhang, X. Zhang, Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method, International Journal of Robust and Nonlinear Control, 25(18) (2015) 3714-3731.
[29] G.V. Raffo, M.G. Ortega, F.R. Rubio, An integral predictive/nonlinear H∞ control structure for a quadrotor helicopter, Automatica, 46(1) (2010) 29-39.
[30] R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive nonlinear control, Springer Science & Business Media, 2012.
[31] A.J. Van Der Schaft, L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback h/sub infinity/control, IEEE transactions on automatic control, 37(6) (1992) 770-784.
AUT Journal of Mechanical Engineering
Volume 4, Issue 2
June 2020
Pages 151-168

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