A QFT robust controller as a remedy for TRMS
Abstract
Control of a Twin Rotor Multi-input Multi-output System (TRMS) is not a simple work. Because it has complex nonlinear dynamics, cross-coupling, uncertainties, and instability. This paper provides a practical method for control of a TRMS, named Quantitative Feedback Theory (QFT) as one of the robust approaches. Firstly, the TRMS set and modeling procedure are introduced. Secondly, the nonlinear and linear equations of electrical and mechanical parts in both vertical and horizontal planes are presented. Next, using the QFT method, a controller is designed for motion in each plane. Finally, the robustness of the control strategy is illustrated by simulations of vertical and horizontal motions, including controller and pre-filter in the presence of uncertainties. The results demonstrate that the proposed robust controller can guarantee the system stabilization, as well as pitch and yaw tracking of TRMS.
Keyword : QFT, robust control, TRMS, uncertainty, simulation, cross-coupling
How to Cite
Honari-Torshizi, M., Rahmani, H., Moeinkhah, H., Gharib, M. R., & Jahanpour, J. (2020). A QFT robust controller as a remedy for TRMS. Aviation, 24(4), 137-148. https://doi.org/10.3846/aviation.2020.12507
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Amiri-M, A.-A., Gharib, M., Moavenian, M., & Torabiz, K. (2009). Modelling and control of a SCARA robot using quantitative feedback theory. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 223(7), 919–928. https://doi.org/10.1243/09596518JSCE733
Butt, S. S., & Aschemann, H. (2015). Multi-variable integral sliding mode control of a two degrees of freedom helicopter. IFAC-PapersOnLine, 48(1), 802–807. https://doi.org/10.1016/j.ifacol.2015.05.129
Choudhary, S. K. (2017). Optimal feedback control of a twin rotor MIMO system. International Journal of Modelling and Simulation, 37(1), 46–53. https://doi.org/10.1080/02286203.2016.1233008
Christensen, R., Fogh, N., Hansen, R. H., Jensen, M. S., Larsen, S., & Paramanathan, A. (2006). Modelling and control of a twin-rotor MIMO System. Report of Department of Control Engineering Institute of Electronic Systems of Aalborg University.
D’Souza, A. F., & Garg, V. K. (1984). Advanced dynamics: modeling and analysis. Prentice-Hall, Inc.
de Oca, S., Puig, V., Witczak, M., & Dziekan, Ł. (2012). Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter. International Journal of Applied Mathematics and Computer Science, 22(1), 161–171. https://doi.org/10.2478/v10006-012-0012-y
Faris, F., Moussaoui, A., Djamel, B., & Mohammed, T. (2017). Design and real-time implementation of a decentralized sliding mode controller for twin rotor multi-input multi-output system. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 231(1), 3–13. https://doi.org/10.1177/0959651816680457
Feedback Instruments Ltd. (1998). Twin rotor MIMO System Advanced Teaching Manual 1 (33-007-4M5 User Manual). East Sussex, UK.
Feedback Instruments Ltd. (2006). Twin rotor MIMO System (33-949S User Manual). East Sussex, UK.
Gharib, M. R., Dabzadeh, I., Mousavi, S., & Kamelian, S. (2010). Robust controller design with QFT and sliding mode for boiler pressure. Proceedings of the 2010 International Conference on Modelling, Identification and Control (pp. 412–417). Okayama.
Gharib, M. R., & Daneshvar, A. (2019). Quantitative-fuzzy controller design for multivariable systems with uncertainty. International Journal of Control, Automation and Systems, 17(6), 1515–1523. https://doi.org/10.1007/s12555-018-0567-y
Gharib, M. R., Kamelian, S., Seyyed Mousavi, S. A., & Dabzadeh, I. (2011). Modelling and multivariable robust controller for a power plant. International Journal of Advanced Mechatronic Systems, 3(2), 119–128. https://doi.org/10.1504/IJAMECHS.2011.040683
Gharib, M. R., & Moavenian, M. (2016). Full dynamics and control of a quadrotor using quantitative feedback theory. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 29(3), 501–519. https://doi.org/10.1002/jnm.2101
Ginsberg, J. (2008). Engineering dynamics. Cambridge University Press.
Gorczyca, P., & Hajduk, K. (2004). Tracking control algorithms for a laboratory aerodynamical system. International Journal of Applied Mathematics and Computer Sciense, 14(4), 469–475.
Greenberg, M. D. (1998). Advanced engineering mathematics. Prentice Hall.
Harrison, H. R., & Nettleton, T. (1997). Advanced engineering dynamics. Arnold.
Horowitz, I. M. (1992). Quantitative Feedback Design Theory (QFT), vol. 1. QFT Publications.
Houpis, C. H., & Rasmussen, S. J. (1999). Quantitative feedback theory: fundamentals and applications. Marcel Dekker.
Jahanpour, J., Honari-Torshizi, M., & Gharib, M. R. (2015). VCNC contour following tasks using robust QFT controller. Iranian Journal of Science and Technology Transactions of Mechanical Engineering, 39(M1), 131–145.
Jahed, M., & Farrokhi, M. (2013). Robust adaptive fuzzy control of twin rotor MIMO system. Soft Computing, 17(10), 1847–1860. https://doi.org/10.1007/s00500-013-1026-6
Jeffrey, A. (2002). Advanced engineering mathematics. Harcourt Academic Press.
Juang, J.-G., Lin, R.-W., & Liu, W.-K. (2008). Comparison of classical control and intelligent control for a MIMO system. Applied Mathematics and Computation, 205(2), 778–791. https://doi.org/10.1016/j.amc.2008.05.061
Juang, J.-G., Liu, W.-K., & Lin, R.-W. (2011). A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation. ISA Transactions, 50(4), 609–619. https://doi.org/10.1016/j.isatra.2011.06.006
Meriam, J. L., & Kraige, L. G. (2002). Engineering mechanics: Dynamics. John Wiley and Sons Inc.
Moavenian, M., Gharib, M., Daneshvar, A., & Alimardani, S. (2011). Control of human hand considering uncertainties [Conference presentation]. The 2011 International Conference on Advanced Mechatronic Systems (pp. 17–22). Zhengzhou.
Moeinkhah, H., Akbarzadeh, A., & Rezaeepazhand, J. (2014). Design of a robust quantitative feedback theory position controller for an ionic polymer metal composite actuator using an analytical dynamic model. Journal of Intelligent Material Systems and Structures, 25(15), 1965–1977. https://doi.org/10.1177/1045389X13512906
Nataraj, P. S. (2002). Computation of QFT bounds for robust tracking specifications. Automatica, 38(2), 327–334. https://doi.org/10.1016/S0005-1098(01)00203-5
Oktay, T., Konar, M., Soylak, M., Sal, F., Onay, M., & Kizilkaya, O. (2016). Increasing performance of autopilot guided small unmanned helicopter. International Journal of Mechanical and Mechatronics Engineering, 10(1), 133–139.
Oktay, T., & Sal, F. (2015). Helicopter control energy reduction using moving horizontal tail. The Scientific World Journal, 2015. https://doi.org/10.1155/2015/523914
Oktay, T., & Sal, F. (2016). Combined passive and active helicopter main rotor morphing for helicopter energy save. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(6), 1511–1525. https://doi.org/10.1007/s40430-015-0401-x
Pandey, S. K., Dey, J., & Banerjee, S. (2016). Design and real-time implementation of robust PID controller for Twin Rotor MIMO System (TRMS) based on Kharitonov’s theorem. 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES) (pp. 1–6). Delhi. https://doi.org/10.1109/ICPEICES.2016.7853106
Pandey, S. K., Dey, J., & Banerjee, S. (2018). Design of robust proportional–integral–derivative controller for generalized decoupled twin rotor multi-input-multi-output system with actuator non-linearity. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 232(8), 971–982. https://doi.org/10.1177/0959651818771487
Pandey, V. K., Kar, I., & Mahanta, C. (2016). Control of twin-rotor MIMO system using multiple models with second level adaptation. IFAC-PapersOnLine, 49(1), 676–681. https://doi.org/10.1016/j.ifacol.2016.03.134
Pratap, B., & Purwar, S. (2014). Real-time implementation of neuro adaptive observer-based robust backstepping controller for twin rotor control system. Journal of Control, Automation and Electrical Systems, 25(2), 137–150. https://doi.org/10.1007/s40313-013-0098-y
Precup, R.-E., Radac, M.-B., Roman, R.-C., & Petriu, E. M. (2017). Model-free sliding mode control of nonlinear systems: Algorithms and experiments. Information Sciences, 381, 176–192. https://doi.org/10.1016/j.ins.2016.11.026
Raghavan, R., & Thomas, S. (2017). Practically Implementable Model Predictive Controller for a Twin rotor Multi-Input Multi-Output System. Journal of Control, Automation and Electrical Systems, 28(3), 358–370. https://doi.org/10.1007/s40313-017-0311-5
Rahideh, A., Shaheed, H., & Bajodah, A. (2007). Adaptive non-linear model inversion control of a twin rotor multi-input multi-output system using artificial intelligence. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 221(3), 343–351. https://doi.org/10.1243/09544100JAERO155
Rahideh, A., Shaheed, M., & Huijberts, H. (2008). Dynamic modelling of a TRMS using analytical and empirical approaches. Control Engineering Practice, 16(3), 241–259. https://doi.org/10.1016/j.conengprac.2007.04.008
Tao, C.-W., Taur, J.-S., & Chen, Y. (2010). Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system. Fuzzy Sets and Systems, 161(15), 2081–2103. https://doi.org/10.1016/j.fss.2009.12.007
Toha, S. F., & Tokhi, M. O. (2011). PID and inverse-model-based control of a twin rotor system. Robotica, 29(6), 929–938. https://doi.org/10.1017/S0263574711000154
Vilchis, J. A., Brogliato, B., Dzul, A., & Lozano, R. (2003). Nonlinear modelling and control of helicopters. Automatica, 39(9), 1583–1596. https://doi.org/10.1016/S0005-1098(03)00168-7
Wen, P., & Lu, T.-W. (2008). Decoupling control of a twin rotor MIMO system using robust deadbeat control technique. IET Control Theory Applications, 2(11), 999–1007. https://doi.org/10.1049/iet-cta:20070335
Zeghlache, S., Kara, K., & Saigaa, D. (2014). Type-2 fuzzy logic control of a 2-DOF helicopter (TRMS system). Central European Journal of Engineering, 4(3), 303–315. https://doi.org/10.2478/s13531-013-0157-y
Butt, S. S., & Aschemann, H. (2015). Multi-variable integral sliding mode control of a two degrees of freedom helicopter. IFAC-PapersOnLine, 48(1), 802–807. https://doi.org/10.1016/j.ifacol.2015.05.129
Choudhary, S. K. (2017). Optimal feedback control of a twin rotor MIMO system. International Journal of Modelling and Simulation, 37(1), 46–53. https://doi.org/10.1080/02286203.2016.1233008
Christensen, R., Fogh, N., Hansen, R. H., Jensen, M. S., Larsen, S., & Paramanathan, A. (2006). Modelling and control of a twin-rotor MIMO System. Report of Department of Control Engineering Institute of Electronic Systems of Aalborg University.
D’Souza, A. F., & Garg, V. K. (1984). Advanced dynamics: modeling and analysis. Prentice-Hall, Inc.
de Oca, S., Puig, V., Witczak, M., & Dziekan, Ł. (2012). Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter. International Journal of Applied Mathematics and Computer Science, 22(1), 161–171. https://doi.org/10.2478/v10006-012-0012-y
Faris, F., Moussaoui, A., Djamel, B., & Mohammed, T. (2017). Design and real-time implementation of a decentralized sliding mode controller for twin rotor multi-input multi-output system. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 231(1), 3–13. https://doi.org/10.1177/0959651816680457
Feedback Instruments Ltd. (1998). Twin rotor MIMO System Advanced Teaching Manual 1 (33-007-4M5 User Manual). East Sussex, UK.
Feedback Instruments Ltd. (2006). Twin rotor MIMO System (33-949S User Manual). East Sussex, UK.
Gharib, M. R., Dabzadeh, I., Mousavi, S., & Kamelian, S. (2010). Robust controller design with QFT and sliding mode for boiler pressure. Proceedings of the 2010 International Conference on Modelling, Identification and Control (pp. 412–417). Okayama.
Gharib, M. R., & Daneshvar, A. (2019). Quantitative-fuzzy controller design for multivariable systems with uncertainty. International Journal of Control, Automation and Systems, 17(6), 1515–1523. https://doi.org/10.1007/s12555-018-0567-y
Gharib, M. R., Kamelian, S., Seyyed Mousavi, S. A., & Dabzadeh, I. (2011). Modelling and multivariable robust controller for a power plant. International Journal of Advanced Mechatronic Systems, 3(2), 119–128. https://doi.org/10.1504/IJAMECHS.2011.040683
Gharib, M. R., & Moavenian, M. (2016). Full dynamics and control of a quadrotor using quantitative feedback theory. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 29(3), 501–519. https://doi.org/10.1002/jnm.2101
Ginsberg, J. (2008). Engineering dynamics. Cambridge University Press.
Gorczyca, P., & Hajduk, K. (2004). Tracking control algorithms for a laboratory aerodynamical system. International Journal of Applied Mathematics and Computer Sciense, 14(4), 469–475.
Greenberg, M. D. (1998). Advanced engineering mathematics. Prentice Hall.
Harrison, H. R., & Nettleton, T. (1997). Advanced engineering dynamics. Arnold.
Horowitz, I. M. (1992). Quantitative Feedback Design Theory (QFT), vol. 1. QFT Publications.
Houpis, C. H., & Rasmussen, S. J. (1999). Quantitative feedback theory: fundamentals and applications. Marcel Dekker.
Jahanpour, J., Honari-Torshizi, M., & Gharib, M. R. (2015). VCNC contour following tasks using robust QFT controller. Iranian Journal of Science and Technology Transactions of Mechanical Engineering, 39(M1), 131–145.
Jahed, M., & Farrokhi, M. (2013). Robust adaptive fuzzy control of twin rotor MIMO system. Soft Computing, 17(10), 1847–1860. https://doi.org/10.1007/s00500-013-1026-6
Jeffrey, A. (2002). Advanced engineering mathematics. Harcourt Academic Press.
Juang, J.-G., Lin, R.-W., & Liu, W.-K. (2008). Comparison of classical control and intelligent control for a MIMO system. Applied Mathematics and Computation, 205(2), 778–791. https://doi.org/10.1016/j.amc.2008.05.061
Juang, J.-G., Liu, W.-K., & Lin, R.-W. (2011). A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation. ISA Transactions, 50(4), 609–619. https://doi.org/10.1016/j.isatra.2011.06.006
Meriam, J. L., & Kraige, L. G. (2002). Engineering mechanics: Dynamics. John Wiley and Sons Inc.
Moavenian, M., Gharib, M., Daneshvar, A., & Alimardani, S. (2011). Control of human hand considering uncertainties [Conference presentation]. The 2011 International Conference on Advanced Mechatronic Systems (pp. 17–22). Zhengzhou.
Moeinkhah, H., Akbarzadeh, A., & Rezaeepazhand, J. (2014). Design of a robust quantitative feedback theory position controller for an ionic polymer metal composite actuator using an analytical dynamic model. Journal of Intelligent Material Systems and Structures, 25(15), 1965–1977. https://doi.org/10.1177/1045389X13512906
Nataraj, P. S. (2002). Computation of QFT bounds for robust tracking specifications. Automatica, 38(2), 327–334. https://doi.org/10.1016/S0005-1098(01)00203-5
Oktay, T., Konar, M., Soylak, M., Sal, F., Onay, M., & Kizilkaya, O. (2016). Increasing performance of autopilot guided small unmanned helicopter. International Journal of Mechanical and Mechatronics Engineering, 10(1), 133–139.
Oktay, T., & Sal, F. (2015). Helicopter control energy reduction using moving horizontal tail. The Scientific World Journal, 2015. https://doi.org/10.1155/2015/523914
Oktay, T., & Sal, F. (2016). Combined passive and active helicopter main rotor morphing for helicopter energy save. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(6), 1511–1525. https://doi.org/10.1007/s40430-015-0401-x
Pandey, S. K., Dey, J., & Banerjee, S. (2016). Design and real-time implementation of robust PID controller for Twin Rotor MIMO System (TRMS) based on Kharitonov’s theorem. 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES) (pp. 1–6). Delhi. https://doi.org/10.1109/ICPEICES.2016.7853106
Pandey, S. K., Dey, J., & Banerjee, S. (2018). Design of robust proportional–integral–derivative controller for generalized decoupled twin rotor multi-input-multi-output system with actuator non-linearity. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 232(8), 971–982. https://doi.org/10.1177/0959651818771487
Pandey, V. K., Kar, I., & Mahanta, C. (2016). Control of twin-rotor MIMO system using multiple models with second level adaptation. IFAC-PapersOnLine, 49(1), 676–681. https://doi.org/10.1016/j.ifacol.2016.03.134
Pratap, B., & Purwar, S. (2014). Real-time implementation of neuro adaptive observer-based robust backstepping controller for twin rotor control system. Journal of Control, Automation and Electrical Systems, 25(2), 137–150. https://doi.org/10.1007/s40313-013-0098-y
Precup, R.-E., Radac, M.-B., Roman, R.-C., & Petriu, E. M. (2017). Model-free sliding mode control of nonlinear systems: Algorithms and experiments. Information Sciences, 381, 176–192. https://doi.org/10.1016/j.ins.2016.11.026
Raghavan, R., & Thomas, S. (2017). Practically Implementable Model Predictive Controller for a Twin rotor Multi-Input Multi-Output System. Journal of Control, Automation and Electrical Systems, 28(3), 358–370. https://doi.org/10.1007/s40313-017-0311-5
Rahideh, A., Shaheed, H., & Bajodah, A. (2007). Adaptive non-linear model inversion control of a twin rotor multi-input multi-output system using artificial intelligence. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 221(3), 343–351. https://doi.org/10.1243/09544100JAERO155
Rahideh, A., Shaheed, M., & Huijberts, H. (2008). Dynamic modelling of a TRMS using analytical and empirical approaches. Control Engineering Practice, 16(3), 241–259. https://doi.org/10.1016/j.conengprac.2007.04.008
Tao, C.-W., Taur, J.-S., & Chen, Y. (2010). Design of a parallel distributed fuzzy LQR controller for the twin rotor multi-input multi-output system. Fuzzy Sets and Systems, 161(15), 2081–2103. https://doi.org/10.1016/j.fss.2009.12.007
Toha, S. F., & Tokhi, M. O. (2011). PID and inverse-model-based control of a twin rotor system. Robotica, 29(6), 929–938. https://doi.org/10.1017/S0263574711000154
Vilchis, J. A., Brogliato, B., Dzul, A., & Lozano, R. (2003). Nonlinear modelling and control of helicopters. Automatica, 39(9), 1583–1596. https://doi.org/10.1016/S0005-1098(03)00168-7
Wen, P., & Lu, T.-W. (2008). Decoupling control of a twin rotor MIMO system using robust deadbeat control technique. IET Control Theory Applications, 2(11), 999–1007. https://doi.org/10.1049/iet-cta:20070335
Zeghlache, S., Kara, K., & Saigaa, D. (2014). Type-2 fuzzy logic control of a 2-DOF helicopter (TRMS system). Central European Journal of Engineering, 4(3), 303–315. https://doi.org/10.2478/s13531-013-0157-y