Direct parametric control of fully-actuated second-order nonlinear systems—The normal case

Fully-actuated second-order systems occur in many applications, such as robotics systems, aircraft systems, mechanical systems etc. Yet what does a fully-actuated system offer? This paper proposes a direct parametric approach which solves the control of a fully-actuated second-order system completely. It is revealed that, with this proposed approach, fully-actuated systems, no matter linear or nonlinear, can actually be turned into a constant linear system with desire eigenstructure by state proportional plus derivative feedback. What is more, in such a realization the approach also provides all the degrees of freedom which may be further utilized to improve the system performance. Direct general complete parametrization of such a controller is proposed based on the solution to a type second-order Sylvester matrix equations, application to a robotic system shows the great convenience of the proposed direct parametric approach.