Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

Yusuf Altun

Abstract


This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance.


Keywords


Robotic manipulator Gain scheduling LQR controller Descriptor system

Full Text:

PDF

References


Park BY, Yun SW, Park P (2012) H 2 state-feedback control for LPV systems with input saturation and matched disturbance. Nonlinear Dynamics 67(2):1083–1096.

Venkataraman R, Seiler P (2018) Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints. International Journal of Robust and Nonlinear Control 28(3):953–975.

He Z, Xie W (2014) Quadratic H2 gain performance analysis of LPV systems with realization of parametric transfer function. Proceedings of the 33rd Chinese Control Conference, CCC 2014 (IEEE), pp 1788–1792.

Peng C, Zhang Z, Zou J, Li K, Zhang J (2013) Internal model based robust inversion feedforward and feedback 2DOF control for LPV system with disturbance. Journal of Process Control 23(10):1415–1425.

Ku C-C, Chen G-W (2015) Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises. International Journal of Control, Automation and Systems 13(6):1382–1390.

Wu K, Zhang Q, Hansen A (2004) Modelling and identification of a hydrostatic transmission hardware-in-the-loop simulator. Int J Veh Des 34(1):63–75.

Lu B, Choi H, Buckner GD, Tammi K (2008) Linear parameter-varying techniques for control of a magnetic bearing system. Control Engineering Practice 16(10):1161–1172.

Altun Y (2017) A new extended LMI-based robust gain scheduled state feedback H 2 controller design. International Journal of Control, Automation and Systems 15(3):967–975.

Masubuchi I, Kurata I (2011) Gain-scheduled control via filtered scheduling parameters. Automatica 47(8):1821–1826.

Abdullah AA (2018) Robust model reference control of linear parameter-varying systems with disturbances. IET Control Theory & Applications 12(1):45–52.

Apkarian P, Adams RJ (1998) Advanced gain-scheduling techniques for uncertain systems. IEEE Transactions on Control Systems Technology 6(1):21–32.

Huang Y, Na J, Wu X, Gao G-B, Guo Y (2016) Robust adaptive control for vehicle active suspension systems with uncertain dynamics. Transactions of the Institute of Measurement and Control 40(4):1237–1249.

Altun Y (2017) The road disturbance attenuation for quarter car active suspension system via a new static two-degree-of-freedom design. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 7(2):142–148.

Yazici H, Sever M, Sever M (2017) Design of an optimal state derivative feedback LQR controller and its application to an offshore steel jacket platform. An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 8(1):84–91.

Lin C, Wang QG, Lee TH (2005) Robust normalization and stabilization of uncertain descriptor systems with norm-bounded perturbations. IEEE Transactions on Automatic Control 50(4):515–520.

Fang C-HFC-H (2002) Stability robustness analysis of uncertain descriptor systems - an LMI approach. Proceedings of the 41st IEEE Conference on Decision and Control, 2002 2(December):1459–1460.

Lin C, Wang J, Wang D, Soh CB (1997) Robustness of uncertain descriptor systems. Systems & Control Letters 31(3):129–138.

Chou JH, Chen SH, Zhang QL (2006) Robust controllability for linear uncertain descriptor systems. Linear Algebra and Its Applications 414(2–3):632–651.

Osorio-Gordillo GL, Darouach M, Astorga-Zaragoza CM (2015) H∞ dynamical observers design for linear descriptor systems. Application to state and unknown input estimation. European Journal of Control 26:35–43.

Bara GI (2011) Dilated LMI conditions for time-varying polytopic descriptor systems: The discrete-time case. International Journal of Control 84(6):1010–1023.

Masubuchi I, Suzuki A (2008) Gain-Scheduled Controller Synthesis Based on New LMIs for Dissipativity of Descriptor LPV Systems. IFAC Proceedings Volumes 41(2):9993–9998.

Bouali A, Yagoubi M, Chevrel P (2008) H2 H∞ gain scheduling control for rational LPV systems using the descriptor framework. IEEE Conference on Decision and Control (CDC) (IEEE), pp 3878–3883.

Rodrigues M, Hamdi H, Benhadj Braiek N, Theilliol D (2014) Observer-based fault tolerant control design for a class of LPV descriptor systems. Journal of the Franklin Institute 351(6):3104–3125.

Ali HS, Darouach M, Zasadzinski M, Alma M (2015) An H∞ LPV control for a class of LPV systems using a descriptor approach: Application to a wind turbine mode. IFAC-PapersOnLine 48(26):213–217.

Bara GI (2011) Robust analysis and control of parameter-dependent uncertain descriptor systems. Systems and Control Letters 60(5):356–364.

Altun Y (2017) Control Design for Nonsingular Descriptor Systems. Karaelmas Science and Engineering Journal 7(1):154–159.

Bouali A, Yagoubi M, Chevrel P (2008) Gain scheduled observer state feedback controller for rational LPV systems. IFAC Proceedings Volumes 41(2):4922–4927.

Adams R, Apkarian P, Chretien J (1996) Robust Control Approaches for a Two-Link Flexible Manipulator. 3rd International Conference on Dynamics and Control of Structures in Space, p 101‐116.

Karkoub M, Tamma K, Balas G (1999) Robust Control of Two-Link Flexible Manipulators Using the -Synthesis Technique. Journal of Vibration and Control 5(4):559–576.

Karagülle H, Malgaca L, Dirilmiş M, Akdağ M, Yavuz Ş (2015) Vibration control of a two-link flexible manipulator. Journal of Vibration and Control 23(12):2023–2034.

Li Y, Liu G, Hong T, Liu K (2005) Robust control of a two-link flexible manipulator with quasi-static deflection compensation using neural networks. Journal of Intelligent and Robotic Systems: Theory and Applications 44(3):263–276.

Halalchi H, Laroche E, Bara GI (2010) LPV Modeling and Control of a 2-DOF Robotic. 11th Pan-American Congress of Applied Mechanics.

Yadav PS, Singh N (2015) Robust Control of Two Link Rigid Manipulator. International Journal of Information and Electronics Engineering 5(3):3–8.

Halalchi H, Laroche E, Iuliana Bara G (2014) Flexible-Link Robot Control Using a Linear Parameter Varying Systems Methodology. International Journal of Advanced Robotic Systems 11(3):46.

Polat I, Eskinat E, Kose IE (2007) Dynamic output feedback control of quasi-LPV mechanical systems. IET Control Theory and Applications 1(4):1114–1121.

Bouali A, Yagoubi M, Chevrel P (2008) H2 gain scheduled observer based controllers for rational LPV systems. 2008 10th International Conference on Control, Automation, Robotics and Vision, ICARCV 2008 41(2):1811–1816.

Galvão RKH, Kienitz KH, Hadjiloucas S (2017) Conversion of descriptor representations to state-space form: an extension of the shuffle algorithm. International Journal of Control:1–15.

Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory, Society for Industrial and Applied Mathematics, Philadelphia.




DOI: http://dx.doi.org/10.11121/ijocta.01.2018.00564

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Yusuf Altun

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

footer_771

   ithe_170     crossref_284         ind_131_43_x_117_117  Scopus  EBSCO_Host    ULAKBIM   PROQUEST   ZBMATH more...