Controllers which guarantee robustness with respect to unmodelled flexibilities for a class of uncertain mechanical systems

We consider a class of uncertain mechanical systems containing flexible elements and subject to memoryless output-feedback controllers. The damping and stiffness properties of some of the flexible elements are parametrized linearly in μ−1 and μ−2 respectively, where μ > 0 and these components become more rigid as μ approaches zero. We propose a class of ‘stabilizing’ controllers for a system model in which the above components are rigid. Subject to a ‘linear growth condition’, the controllers also stabilize the model in which the components are flexible provided μ > 0 is sufficiently small.

[1]  M. Corless,et al.  Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems , 1981 .

[2]  Hassan K. Khalil,et al.  Singular perturbations in systems and control , 1986 .

[3]  Martin Corless.  Stability robustness of linear feedback-controlled mechanical systems in the presence of a class of unmodelled flexibilities , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[4]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[5]  M. Corless,et al.  A new class of stabilizing controllers for uncertain dynamical systems , 1982, 1982 21st IEEE Conference on Decision and Control.

[6]  Martin Corless,et al.  Tracking Controllers for Uncertain Systems: Application to a Manutec R3 Robot , 1989 .

[7]  G. Ambrosino,et al.  Tracking control of high-performance robots via stabilizing controllers for uncertain systems , 1986 .

[8]  P. Kokotovic,et al.  A Slow Manifold Approach to Feedback Control of Nonlinear Flexible Systems , 1985, 1985 American Control Conference.

[9]  Mark W. Spong,et al.  Robust linear compensator design for nonlinear robotic control , 1985, IEEE J. Robotics Autom..

[10]  M. Spong.  Modeling and Control of Elastic Joint Robots , 1987 .

[11]  P. Kokotovic,et al.  Feedback linearization of a flexible manipulator near its rigid body manifold , 1985 .

[12]  S. Gutman.  Uncertain dynamical systems--A Lyapunov min-max approach , 1979 .

[13]  Martin Corless,et al.  Practical stabilizability of uncertain dynamical systems: Application to robotic tracking , 1985 .

[14]  Martin Corless,et al.  Deterministic control of uncertain systems : a Lyapunov theory approach , 1990 .

[15]  Rahmatallah Shoureshi,et al.  Control of Industrial Manipulators With Bounded Uncertainties , 1987 .

[16]  Jean-Jacques E. Slotine,et al.  The Robust Control of Robot Manipulators , 1985 .

[17]  James M. Kelly,et al.  Robust control of base-isolated structures under earthquake excitation , 1987 .

[18]  G. Ambrosino,et al.  Robust model tracking control for a class of nonlinear plants , 1985 .