Attitude Control of a Quadrotor with Optimized PID Controller

Affiliation(s)

Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran.

East Tehran (Qiam Dasht) Branch, Islamic Azad University, Tehran, Iran.

Electrical Engineering Department, Iran University of Science and Technology, Tehran, Iran.

East Tehran (Qiam Dasht) Branch, Islamic Azad University, Tehran, Iran.

ABSTRACT

A new approach to control, stabilization and disturbance rejection of attitude subsystem of quadrotor is presented in this article. Analytical method is used to tune conventional structure of PID controller. SISO approach is implemented for control structure to achieve desired objectives. The performance of the designed control structure is evaluated through time domain factors such as overshoot, settling time and integral error index, and robustness. A comparison is done between designed controller and back-step controller applied to main model of quadrotor. The results of simulation show the effectiveness of designed control scheme.

A new approach to control, stabilization and disturbance rejection of attitude subsystem of quadrotor is presented in this article. Analytical method is used to tune conventional structure of PID controller. SISO approach is implemented for control structure to achieve desired objectives. The performance of the designed control structure is evaluated through time domain factors such as overshoot, settling time and integral error index, and robustness. A comparison is done between designed controller and back-step controller applied to main model of quadrotor. The results of simulation show the effectiveness of designed control scheme.

Cite this paper

H. Bolandi, M. Rezaei, R. Mohsenipour, H. Nemati and S. Smailzadeh, "Attitude Control of a Quadrotor with Optimized PID Controller,"*Intelligent Control and Automation*, Vol. 4 No. 3, 2013, pp. 335-342. doi: 10.4236/ica.2013.43039.

H. Bolandi, M. Rezaei, R. Mohsenipour, H. Nemati and S. Smailzadeh, "Attitude Control of a Quadrotor with Optimized PID Controller,"

References

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[2] S. Bouabdallah and R. Siegwart, “Back-Stepping and Sliding-Mode Techniques Applied to an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Robotic and Automatic, Barcelona, 2005, pp. 2451-2456.

[3] A. Tayebi and S. McGilvray, “Attitude Stabilization of a VTOL Quadrotor Aircraft,” IEEE Tranactions on Control Systems Technology, Vol. 14, No. 3, 2006, pp. 562-571. doi:10.1109/TCST.2006.872519

[4] K. Alexis, G. Nikolakopoulos and A. Tzea, “Constrained Optimal Attitude Control of a Quadrotor Helicopter Subject to Wind-Gusts: Experimental Studies,” American Control Conference, Baltimore, 30 June-2 July 2010, pp. 44514455.

[5] H. Yang, R. Abousleiman, B. Sababaha, E. Gjoni, D. Korff and O. Rawashded, “Implementation of an Autonomous Surveillance Quadrotor System,” AIAA Infotech Aerospace Conference, Seattle, 2009, pp. 2009-2047.

[6] G. V. Raffo, M. G. Ortega and F. R. Rubio, “An Integral Predictive/Nonlinear H∞ Control Structure for a Quadrotor Helicopter,” Journal of Automatica, Vol. 46, No. 1, 2009, pp. 29-39. doi:10.1016/j.automatica.2009.10.018

[7] G. V. Raffo, M. G. Ortega and F. R. Rubio, “Back-Stepping/Nonlinear H∞ Control for Path Tracking of a QuadRotor Unmanned Aerial Vehicle,” Proceedings of the American Control Conference, Seattle, 2008, pp. 33563361.

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[9] A. Das and K. S. Lewis, “Dynamic Inversion with ZeroDynamics Stabilisation for Quadrotor Control,” IET Control Theory and Application, Vol. 3, No. 3, 2009, pp. 303-314. doi:10.1049/iet-cta:20080002

[10] A. Mokbari and A. Benallegue, “Dynamic Feedback Controller of Euler Angles and Wind Parameters Estimation for a Quadrotor Unmanned Aerial Vehicle,” Proceedings of the IEEE International Conference of Robotic and Automatic, New Orleans, 2004, pp.2359-2366.

[11] M. Huang, B. Xian, C. Diao, K. Yang and Y. Fung, “Adaptive Tracking Control of Under actuated Quadrotor Unmanned Aerial,” American Control Conference, Baltimore, 2010, pp. 2076-2081.

[12] S. Bouabdallah, A. Noth and R. Siegwart, “PID vs LQ Control Techniques Applied to an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Intelligent Robots Systems, Sendai, 2004, pp. 24512456.

[13] L. C. Lai, C. C. Yang and C. J. Wu, “Time-Optimal Control of a Hovering Quad-Rotor Helicopter,” Journal of Intelligent and Robotic Systems, Vol. 45, No. 2, 2006, pp. 115-135. doi:10.1007/s10846-005-9015-3

[14] V. Mistler, A. Benallegue and N. K. M’Sirdi, “Exact Linearization and Noninteracting Control of a 4 Rotors Helicopter via Dynamic Feedback,” Proceedings of the IEEE International Workshop on Robotic and Human Interactive Communication, Bordeaux, 18-21 September 2001, pp. 586-593.

[15] S. Bouabdallah, P. Murrieri and R. Siegwart, “Design and Control of an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Robotic and Automatic, New Orleans, 26 April-1 May 2004, pp. 43934398.

[16] Y. W. Jan and J. C. Chiou, “Minimum-Time Spacecraft Manoeuvre Using Sliding-Mode Control,” Acta Astronaut, Vol. 54, No. 1, 2003, pp. 69-75. doi:10.1016/S0094-5765(03)00194-2

[17] W. Wu, H. Chen and P. Y. Woo, “Optimal Motion Planning for a Wheeled Mobile Robot,” Proceedings of the IEEE International Conference of Robotic and Automatic, Detroit, 10-15 May 1999, pp. 41-46.

[18] S. L. Waslander, G. M. Hoffmann, J. S. Jang and C. J. Tomlin, “Multi Agent Quadrotor Test Bed Control Design Integral Sliding Mode vs. Reinforcement Learning,” Proceedings of the IEEE International Conference of Intelligent Robots Systems, USA, 2005, pp. 3712-3717.

[19] C. Balas, “Modeling and Linear Control of a Quadrotor,” M.S. Thesis, Cranfield University, Bedford, 2007.

[20] K. J. Astrom and T. Hagglund, “Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins,” Journal of Automatica, Vol. 20, No. 5, 1984, pp. 645-651. doi:10.1016/0005-1098(84)90014-1

[21] W. K. Ho, O. P. Gan, E. B Tay and E. L. Ang, “Performance and Gain and Phase Margins of Well-Known PID Tuning Formulas,” IEEE Transactions on Control System Technology, Vol. 4, No. 4, 1996, pp. 473-477. doi:10.1109/87.508897

[22] Q. G. Wang, T. H. Lee, H. W. Fung, Q. Bi and Y. Zhang, “PID Tuning for Improved Performance,” IEEE Transactions on Control Systems Technology, Vol. 7, No. 4, 1999, pp. 457-465. doi:10.1109/87.772161

[23] Y. C. Cheng and C. Hwang, “Stabilization of Unstable First-Order Time-Delay,” Journal of the Chinese Institute of Engineers, Vol. 29. No. 2, 2006, pp. 241-249. doi:10.1080/02533839.2006.9671121

[24] D. Vrancic, S. Strmcnik, J. Kocijan and P. B. M. Oliveira, “Improving Disturbance Rejection of PID Controllers by Means of the Magnitude Optimum Method,” ISA Transactions, Vol. 49, No. 1, 2009, pp. 47-56. doi:10.1016/j.isatra.2009.08.002

[25] Y. Li, K. H. Ang, G. Chong, W. Feng, K. C. Tan and H. Kashiwagi, “CAutoCSD-Evolutionary Search and Optimisation Enabled Computer Automated Control System Design,” International Journal of Automatic and Computer, Vol. 1, No. 1, 2004. pp. 76-88. doi:10.1007/s11633-004-0076-8

[26] C. Lin, Q. G. Wang, Y. He, G. Wen, X. Han and G. Z. H. Z. Li, “On Stabilizing PI Controller Ranges for Multivariable Systems,” Chaos, Solitons and Fractals, Vol. 35, No. 3, 2008, pp. 620-625.

[27] C. A. Smith and A. B. Corripio, “Principles and Practice of Automatic Process Control,” John Wiley & Sons, New York, 1985.

[28] O. J. Smith, “Closer Control of Loops with Dead Time,” Chemistry Engineering Progress, Vol. 53, No. 5, 1957, pp. 217-219.

[29] D. E. Rivera, M. Morari and S. Skogestad, “Internal Model Control. 4. PID Controller Design,” Industrial & Engineering Chemistry Research Process Design & Development, Vol. 25, No. 1, 1986, pp. 252-265. doi:10.1021/i200032a041

[30] I. L. Chien and P. S. Fruehauf, “Consider IMC Tuning to Improve Controller Performance,” Chemistry Engineering Progress, Vol. 86, No. 10, 1990, pp. 33-41.

[31] S. Skogestad, “Simple Analytic Rules for Model Reduction and PID Controller Tuning,” Journal of Process Control, Vol. 13, No. 4, 2003, pp. 291-309. doi:10.1016/S0959-1524(02)00062-8

[1] K. Valavanis, “Advances in Unmanned Aerial Vehicles: State of the Art and the Road to Autonomy, ser. Microprocessor-Based and Intelligent Systems Engineering,” Springer-Verlag, Berlin, 2007.

[2] S. Bouabdallah and R. Siegwart, “Back-Stepping and Sliding-Mode Techniques Applied to an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Robotic and Automatic, Barcelona, 2005, pp. 2451-2456.

[3] A. Tayebi and S. McGilvray, “Attitude Stabilization of a VTOL Quadrotor Aircraft,” IEEE Tranactions on Control Systems Technology, Vol. 14, No. 3, 2006, pp. 562-571. doi:10.1109/TCST.2006.872519

[4] K. Alexis, G. Nikolakopoulos and A. Tzea, “Constrained Optimal Attitude Control of a Quadrotor Helicopter Subject to Wind-Gusts: Experimental Studies,” American Control Conference, Baltimore, 30 June-2 July 2010, pp. 44514455.

[5] H. Yang, R. Abousleiman, B. Sababaha, E. Gjoni, D. Korff and O. Rawashded, “Implementation of an Autonomous Surveillance Quadrotor System,” AIAA Infotech Aerospace Conference, Seattle, 2009, pp. 2009-2047.

[6] G. V. Raffo, M. G. Ortega and F. R. Rubio, “An Integral Predictive/Nonlinear H∞ Control Structure for a Quadrotor Helicopter,” Journal of Automatica, Vol. 46, No. 1, 2009, pp. 29-39. doi:10.1016/j.automatica.2009.10.018

[7] G. V. Raffo, M. G. Ortega and F. R. Rubio, “Back-Stepping/Nonlinear H∞ Control for Path Tracking of a QuadRotor Unmanned Aerial Vehicle,” Proceedings of the American Control Conference, Seattle, 2008, pp. 33563361.

[8] P. Castillo, R. Lozano and A. Dzul, “Modelling and Control of Mini Flying Machines,” Springer-Verlag, London, 2005.

[9] A. Das and K. S. Lewis, “Dynamic Inversion with ZeroDynamics Stabilisation for Quadrotor Control,” IET Control Theory and Application, Vol. 3, No. 3, 2009, pp. 303-314. doi:10.1049/iet-cta:20080002

[10] A. Mokbari and A. Benallegue, “Dynamic Feedback Controller of Euler Angles and Wind Parameters Estimation for a Quadrotor Unmanned Aerial Vehicle,” Proceedings of the IEEE International Conference of Robotic and Automatic, New Orleans, 2004, pp.2359-2366.

[11] M. Huang, B. Xian, C. Diao, K. Yang and Y. Fung, “Adaptive Tracking Control of Under actuated Quadrotor Unmanned Aerial,” American Control Conference, Baltimore, 2010, pp. 2076-2081.

[12] S. Bouabdallah, A. Noth and R. Siegwart, “PID vs LQ Control Techniques Applied to an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Intelligent Robots Systems, Sendai, 2004, pp. 24512456.

[13] L. C. Lai, C. C. Yang and C. J. Wu, “Time-Optimal Control of a Hovering Quad-Rotor Helicopter,” Journal of Intelligent and Robotic Systems, Vol. 45, No. 2, 2006, pp. 115-135. doi:10.1007/s10846-005-9015-3

[14] V. Mistler, A. Benallegue and N. K. M’Sirdi, “Exact Linearization and Noninteracting Control of a 4 Rotors Helicopter via Dynamic Feedback,” Proceedings of the IEEE International Workshop on Robotic and Human Interactive Communication, Bordeaux, 18-21 September 2001, pp. 586-593.

[15] S. Bouabdallah, P. Murrieri and R. Siegwart, “Design and Control of an Indoor Micro Quadrotor,” Proceedings of the IEEE International Conference of Robotic and Automatic, New Orleans, 26 April-1 May 2004, pp. 43934398.

[16] Y. W. Jan and J. C. Chiou, “Minimum-Time Spacecraft Manoeuvre Using Sliding-Mode Control,” Acta Astronaut, Vol. 54, No. 1, 2003, pp. 69-75. doi:10.1016/S0094-5765(03)00194-2

[17] W. Wu, H. Chen and P. Y. Woo, “Optimal Motion Planning for a Wheeled Mobile Robot,” Proceedings of the IEEE International Conference of Robotic and Automatic, Detroit, 10-15 May 1999, pp. 41-46.

[18] S. L. Waslander, G. M. Hoffmann, J. S. Jang and C. J. Tomlin, “Multi Agent Quadrotor Test Bed Control Design Integral Sliding Mode vs. Reinforcement Learning,” Proceedings of the IEEE International Conference of Intelligent Robots Systems, USA, 2005, pp. 3712-3717.

[19] C. Balas, “Modeling and Linear Control of a Quadrotor,” M.S. Thesis, Cranfield University, Bedford, 2007.

[20] K. J. Astrom and T. Hagglund, “Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins,” Journal of Automatica, Vol. 20, No. 5, 1984, pp. 645-651. doi:10.1016/0005-1098(84)90014-1

[21] W. K. Ho, O. P. Gan, E. B Tay and E. L. Ang, “Performance and Gain and Phase Margins of Well-Known PID Tuning Formulas,” IEEE Transactions on Control System Technology, Vol. 4, No. 4, 1996, pp. 473-477. doi:10.1109/87.508897

[22] Q. G. Wang, T. H. Lee, H. W. Fung, Q. Bi and Y. Zhang, “PID Tuning for Improved Performance,” IEEE Transactions on Control Systems Technology, Vol. 7, No. 4, 1999, pp. 457-465. doi:10.1109/87.772161

[23] Y. C. Cheng and C. Hwang, “Stabilization of Unstable First-Order Time-Delay,” Journal of the Chinese Institute of Engineers, Vol. 29. No. 2, 2006, pp. 241-249. doi:10.1080/02533839.2006.9671121

[24] D. Vrancic, S. Strmcnik, J. Kocijan and P. B. M. Oliveira, “Improving Disturbance Rejection of PID Controllers by Means of the Magnitude Optimum Method,” ISA Transactions, Vol. 49, No. 1, 2009, pp. 47-56. doi:10.1016/j.isatra.2009.08.002

[25] Y. Li, K. H. Ang, G. Chong, W. Feng, K. C. Tan and H. Kashiwagi, “CAutoCSD-Evolutionary Search and Optimisation Enabled Computer Automated Control System Design,” International Journal of Automatic and Computer, Vol. 1, No. 1, 2004. pp. 76-88. doi:10.1007/s11633-004-0076-8

[26] C. Lin, Q. G. Wang, Y. He, G. Wen, X. Han and G. Z. H. Z. Li, “On Stabilizing PI Controller Ranges for Multivariable Systems,” Chaos, Solitons and Fractals, Vol. 35, No. 3, 2008, pp. 620-625.

[27] C. A. Smith and A. B. Corripio, “Principles and Practice of Automatic Process Control,” John Wiley & Sons, New York, 1985.

[28] O. J. Smith, “Closer Control of Loops with Dead Time,” Chemistry Engineering Progress, Vol. 53, No. 5, 1957, pp. 217-219.

[29] D. E. Rivera, M. Morari and S. Skogestad, “Internal Model Control. 4. PID Controller Design,” Industrial & Engineering Chemistry Research Process Design & Development, Vol. 25, No. 1, 1986, pp. 252-265. doi:10.1021/i200032a041

[30] I. L. Chien and P. S. Fruehauf, “Consider IMC Tuning to Improve Controller Performance,” Chemistry Engineering Progress, Vol. 86, No. 10, 1990, pp. 33-41.

[31] S. Skogestad, “Simple Analytic Rules for Model Reduction and PID Controller Tuning,” Journal of Process Control, Vol. 13, No. 4, 2003, pp. 291-309. doi:10.1016/S0959-1524(02)00062-8