PID natural tracking control of a robot: theory

Elementwise exponential tracking is defined for a class of nonlinear systems described by mixed, general differential equations. In order to achieve this high-quality property the system must possess a property called natural trackability. A system having this property is to be controlled with a natural tracking control. The necessary and sufficient condition for a system to be naturally trackable is given and a PID natural tracking controller is synthesized using this property to guarantee elementwise exponential tracking.