Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot

Abstract This paper studies the point-to-point liquid container transfer control problem for a PPR robot. The robot manipulator is represented as three rigid links, and the liquid slosh dynamics are included using a multi-mass-spring model. It is assumed that two forces and a torque applied to the prismatic joints and the revolute joint, respectively, are available as control inputs. The objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these assumptions is first introduced. Then, Lyapunov-based feedback controllers are designed to achieve the control objective. Two cases are considered: partial-state feedback that does not use slosh state information and full-state feedback that uses both robot state and slosh state measurements or estimations. Computer simulations are included to illustrate the effectiveness of the proposed control laws.

[1]  Mahmut Reyhanoglu,et al.  Controllability and point-to-point control of 3-DOF planar horizontal underactuated manipulators , 2005 .

[2]  T. Blackburn,et al.  Application of linear optimal control and filtering theory to the Saturn V launch vehicle , 1971 .

[3]  Jae Weon Choi,et al.  Attitude controller design for a launch vehicle with fuel-slosh , 2000, SICE 2000. Proceedings of the 39th SICE Annual Conference. International Session Papers (IEEE Cat. No.00TH8545).

[4]  Prasanna S. Gandhi,et al.  Active stabilization of lateral and rotary slosh in cylindrical tanks , 2009, 2009 IEEE International Conference on Industrial Technology.

[5]  Ken'ichi Yano,et al.  Robust liquid container transfer control for complete sloshing suppression , 2001, IEEE Trans. Control. Syst. Technol..

[6]  G. Schmidt,et al.  Motion control of a cart-based container considering suppression of liquid oscillations , 1994, Proceedings of 1994 IEEE International Symposium on Industrial Electronics (ISIE'94).

[7]  Mahmut Reyhanoglu,et al.  Nonlinear control of space vehicles with multi-mass fuel slosh dynamics , 2011, Proceedings of 5th International Conference on Recent Advances in Space Technologies - RAST2011.

[8]  M. Reyhanoglu,et al.  Maneuvering control problems for a spacecraft with unactuated fuel slosh dynamics , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[9]  Arjan van der Schaft,et al.  Dynamics and control of a class of underactuated mechanical systems , 1999, IEEE Trans. Autom. Control..

[10]  K. C. Biswal,et al.  Dynamic characteristics of liquid filled rectangular tank with baffles , 2003 .

[11]  Arthur E. Bryson,et al.  Control of spacecraft and aircraft , 1994 .

[12]  Clark R. Dohrmann,et al.  Control for slosh-free motion of an open container , 1997 .

[13]  Ken'ichi Yano,et al.  Sloshing suppression control of automatic pouring robot by hybrid shape approach , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[14]  M. Grundelius,et al.  Control of liquid slosh in an industrial packaging machine , 1999, Proceedings of the 1999 IEEE International Conference on Control Applications (Cat. No.99CH36328).

[15]  Mahmut Reyhanoglu,et al.  Discontinuous Feedback Control of a Special Class of Underactuated Mechanical Systems , 2000 .

[16]  Bong Wie,et al.  Space Vehicle Dynamics and Control , 1998 .

[17]  H. Krishnan,et al.  Attitude stabilization of a rigid spacecraft using gas jet actuators operating in a failure mode , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[18]  Ken'ichi Yano,et al.  Liquid container transfer control on 3D transfer path by hybrid shaped approach , 2001, Proceedings of the 2001 IEEE International Conference on Control Applications (CCA'01) (Cat. No.01CH37204).

[19]  M. Grundelius.  Iterative optimal control of liquid slosh in an industrial packaging machine , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[20]  John D. Saugen,et al.  Adaptive control of propellant slosh for launch vehicles , 1991, Defense, Security, and Sensing.