LMI-based state feedback controller design for vibration control of a negative imaginary system

This paper presents state feedback control via linear matrix inequality (LMI) for vibration control of a flexible link manipulator (FLM) system. FLM is a negative imaginary (NI) system with high amplitude vibration and oscillation. In this work, pole placement controller (PPC) which is NI controller is used to control the FLM vibration, to achieve a precise hub angle positioning with minimum tip deflection. A decay rate is introduced to improve the speed of the system and investigate the effect on the system performance. LMI optimization technique is used to obtain the optimal and best control gains of PPC using Matlab LMI toolbox with different values of the decay rate. Simulation results show that satisfactory hub angle and tip deflection responses are achieved using the proposed controller. Damping is successfully added into the system and reduces the system vibration at the first two vibration modes by 40 dB. Hub angle positioning is achieved with minimum tip deflection by changing the value of decay rate.

[1]  Bidyadhar Subudhi,et al.  Linear matrix inequality-based robust proportional derivative control of a two-link flexible manipulator , 2016 .

[2]  Mustapha Muhammad,et al.  A PD-type fuzzy logic control approach for vibration control of a single-link flexible manipulator , 2013 .

[3]  Ian R. Petersen,et al.  Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures With Free Body Motion , 2013, IEEE Transactions on Automatic Control.

[4]  Ian R. Petersen,et al.  A negative-imaginary lemma without minimality assumptions and robust state-feedback synthesis for uncertain negative-imaginary systems , 2012, Syst. Control. Lett..

[5]  Ian R. Petersen,et al.  A stability result on the feedback interconnection of negative imaginary systems with poles at the origin , 2012, 2012 2nd Australian Control Conference.

[6]  S. C. Saini,et al.  Comparison of Pole Placement and LQR Applied to Single Link Flexible Manipulator , 2012, 2012 International Conference on Communication Systems and Network Technologies.

[7]  Ian R. Petersen,et al.  Negative imaginary systems theory in the robust control of highly resonant flexible structures , 2011, 2011 Australian Control Conference.

[8]  Chen Wang,et al.  Scheduling parallel Kalman filters for multiple processes , 2011, Autom..

[9]  Ian R. Petersen,et al.  A new stability result for the feedback interconnection of negative imaginary systems with a pole at the origin , 2011, IEEE Conference on Decision and Control and European Control Conference.

[10]  Vicente Feliu,et al.  Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator , 2011, IEEE/ASME Transactions on Mechatronics.

[11]  Alexander Lanzon,et al.  Feedback Control of Negative-Imaginary Systems , 2010, IEEE Control Systems.

[12]  Mohd Ashraf Ahmad,et al.  Dynamic Modelling and Characterisation of a Two-Link Flexible Robot Manipulator , 2010 .

[13]  Ian R. Petersen,et al.  Finite Frequency Negative Imaginary Systems , 2010, IEEE Transactions on Automatic Control.

[14]  Ian R. Petersen,et al.  A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems , 2010, IEEE Transactions on Automatic Control.

[15]  M. H. Suid,et al.  PD Fuzzy Logic with non-collocated PID approach for vibration control of flexible joint manipulator , 2010, 2010 6th International Colloquium on Signal Processing & its Applications.

[16]  Siti Fauziah Toha,et al.  PID-Based Control of a Single-Link Flexible Manipulator in Vertical Motion with Genetic Optimisation , 2009, 2009 Third UKSim European Symposium on Computer Modeling and Simulation.

[17]  Ian R. Petersen,et al.  Stability analysis of positive feedback interconnections of linear negative imaginary systems , 2009, 2009 American Control Conference.

[18]  Ian R. Petersen,et al.  Stability Robustness of a Feedback Interconnection of Systems With Negative Imaginary Frequency Response , 2008, IEEE Transactions on Automatic Control.

[19]  Ian R. Petersen,et al.  A modified positive-real type stability condition , 2007, 2007 European Control Conference (ECC).

[20]  I.A. Mahmood,et al.  Vibration and Position Control of a Flexible Manipulator , 2007, 2007 Information, Decision and Control.

[21]  Ming-Tzu Ho,et al.  PID Controller Design for a Flexible-Link Manipulator , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[22]  S. O. Reza Moheimani,et al.  Resonant control of structural vibration using charge-driven piezoelectric actuators , 2005, IEEE Transactions on Control Systems Technology.

[23]  Amor Jnifene,et al.  Experimental study on active vibration control of a single-link flexible manipulator using tools of fuzzy logic and neural networks , 2005, IEEE Transactions on Instrumentation and Measurement.

[24]  Miguel Ayala Botto,et al.  Vibration control of a very flexible manipulator system , 2005 .

[25]  Atsushi Konno,et al.  A singularly perturbed method for pole assignment control of a flexible manipulator , 2002, Robotica.

[26]  Z Mohamed,et al.  Vibration control of a single-link flexible manipulator using command shaping techniques , 2002 .

[27]  M. Osman Tokhi,et al.  Dynamic characterisation of a flexible manipulator system , 2001, Robotica.

[28]  P. Gahinet,et al.  Robust pole placement in LMI regions , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[29]  A. Preumont.  Vibration Control of Active Structures , 1997 .

[30]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..