Stabilization and set-point regulation of underactuated mechanical systems

Mia Loccufier

doi:10.1088/1742-6596/744/1/012065

Abstract

Mechanical systems are referred to as underactuated if the number of independent actuators are fewer than the number of degrees of freedom, a general encountered problem in engineering applications. The considered mechanical systems belong to the class of Euler- Lagrange systems where both kinetic energy and potential energy are modeled in their most general form and energy dissipation is modeled according to the dissipation function of Rayleigh, i.e. viscous damping forces are assumed. The control objectives are stabilization and set-point regulation. The structure of the controller is a parallel combination of static output feedback with dynamic output feedback where nonlinear amplifiers are included. An energy based approach with Liapunov functions and the Kalman-Yacubovich-Popov main lemma yields alternative stability theorems. A number of conditions are introduced with respect to the controller's structure in order to guarantee stability. However, sufficient design freedom is left to choose a proper tuning principle and obtain the specified control objectives such as fast convergence to a set-point combined with disturbance rejection. A restriction on the control input energy can be incorporated as well. The applicability of the method will be illustrated with planar manipulators. The main contribution is that a methodology is developed which incorporates many controllers and tuning facilities.

Highlights

The control of underactuated mechanical systems is and has been the focus of many researchers because of the broad range engineering applications
The considered mechanical systems belong to the class of EulerLagrange systems where both kinetic energy and potential energy are modeled in their most general form and energy dissipation is modeled according to the dissipation function of Rayleigh, i.e. viscous damping forces are assumed
A nice overview can be found in [9], where many methods and benchmark systems are classified and supported with appropriate references. Considering this classification it can be stated that we present a nonlinear control design frame work based on Liapunov functions to stabilize the closed loop systems

Summary

Introduction

The control of underactuated mechanical systems is and has been the focus of many researchers because of the broad range engineering applications. The implementation requires the solution of a set of partial differential equations, a cumbersome task for mechanical systems where the number of actuators is quite smaller than number of degrees of freedom. It is not the author’s intention to provide a literature overview. A nice overview can be found in [9], where many methods and benchmark systems are classified and supported with appropriate references Considering this classification it can be stated that we present a nonlinear control design frame work based on Liapunov functions to stabilize the closed loop systems.

Class of systems

Control loop

Stability

Findings

Conclusion