Direct parametric approach for cascaded systems with application in robot control

Abstract

This paper considers the control of a system which is the cascaded result of a second-order nonlinear plant and a first-order actuator system. It is shown that such a system can be converted equivalently into a fully-actuated third-order quasi-linear system, and as soon as this is done, a simple complete general parametrization of the position-velocity-acceleration feedback controller can be immediately given, which provides, no matter the open loop system is linear or not, a constant linear closed-loop system with designed eigenstructure. Furthermore, the approach also provides all the degrees of design freedom represented by a stable matrix F; and another parameter matrix Z; which is in fact dense in the parameter space. They can be further optimized to achieve additional requirements on the closed-loop system.