Control of feedback type systems — A direct parametric approach

A direct parametric control approach for a feedback type system which is composed of a main plant system and a feedback subsystem is proposed. The main plant is a matrix second-order quasi-linear system with an affection of the acceleration term of the feedback subsystem, while the feedback subsystem has a linear matrix second-order model with input being the acceleration of the plant. Different from the typical dimension expansion approach, this approach finds an equivalent third-order fully-actuated quasi-linear system, with decreased dimension, and propose for this fully-actuated high-order system a complete general parametrization of a type dynamical position-velocity-acceleration feedback controllers, which is very simple, provides all the degrees of design freedom, and, most importantly, results in a linear constant closed-loop system.