Superiority of finite time SDRE and non-singular terminal SMC controller for n-DOF manipulators

In this paper, a global non-singular terminal sliding mode (NTSM) controller is presented for a class of nonlinear dynamical systems with uncertainty parameters and external disturbances. In addition, it investigates finite-time state-dependent Riccati equation (FTSDRE) for time-varying systems with state and control nonlinearities. A finite-time constraint that has been imposed on the equation will consequently changes it to a differential equation and also strongly decreases state error and operation time. These two methods are both nonlinear with a systematic structure that enable user control systems for a wide range of applications, explicitly in control of manipulators and robots. Finite time state-dependent Riccati equation (FTSDRE) is one of the optimal nonlinear controllers, in which time can be given as input value. On the other hand, sliding mode control systems are robust to uncertainties and disturbance and are able to direct the states to desire portion perfectly. Also, to eliminate the effect of chattering which is a drawback to siding mode controller, hyperbolic tangent function is used. The formulation of both systems are presented and then a model for a five-DOF arm, ATLAS II ROBOT, are designed and then simulated for both methods and only then they are illustrated and discussed.

[1]  Ali Heydari,et al.  Approximate closed-form solutions to finite-horizon optimal control of nonlinear systems , 2012, 2012 American Control Conference (ACC).

[2]  G. Cook,et al.  Suboptimal control for the nonlinear quadratic regulator problem , 1975, Autom..

[3]  J. R. Cloutier,et al.  The capabilities and art of state-dependent Riccati equation-based design , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[4]  J. D. Pearson.  Approximation Methods in Optimal Control I. Sub-optimal Control† , 1962 .

[5]  Moharam Habibnejad Korayem,et al.  Application of recursive Gibbs-Appell formulation in deriving the equations of motion of N-viscoelastic robotic manipulators in 3D space using Timoshenko Beam Theory , 2013 .

[6]  M. H. Korayem,et al.  Maximum payload path planning for redundant manipulator using indirect solution of optimal control problem , 2009 .

[7]  Vahid Azimirad,et al.  Maximum load determination of nonholonomic mobile manipulator using hierarchical optimal control , 2012, Robotica.

[8]  S. Gulati,et al.  Control of Nonlinear Systems Using Terminal Sliding Modes , 1992, 1992 American Control Conference.

[9]  Moharam Habibnejad Korayem,et al.  Load maximization of flexible joint mechanical manipulator using nonlinear optimal controller , 2011 .

[10]  Moharam Habibnejad Korayem,et al.  Trajectory optimization of flexible mobile manipulators , 2005, Robotica.

[11]  Stephen P. Banks,et al.  ASYMPTOTICALLY OPTIMAL NONLINEAR FILTERING , 2007 .

[12]  Mario Innocenti,et al.  Manipulator path control using SDRE , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[13]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[14]  Moharam Habibnejad Korayem,et al.  Path planning algorithm in wheeled mobile manipulators based on motion of arms , 2015 .

[15]  Moharam Habibnejad Korayem,et al.  Dynamic load-carrying capacity of mobile-base flexible joint manipulators , 2005 .

[16]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[17]  S. R. Nekoo,et al.  Finite-time state-dependent Riccati equation for time-varying nonaffine systems: rigid and flexible joint manipulator control. , 2015, ISA transactions.