Model Tracking Control of Hamiltonian Systems

A new approach is presented for deriving control laws for dynamic systems that can be formulated by Hamilton’s canonical equations. The approach uses the complete nonlinear equations of the system without requiring linearization. It is shown that the error equations, between the system and a Hamiltonian model to be followed, can be described by Hamilton’s canonical equations. Using the concept of diagonal set in the cartesian product of the system and the model states, a control law is derived using the Liapunov stability approach. The resulting control law allows tracking within a stipulated precision, and also with a finite time horizon. To demonstrate the method, a control law is derived for a two degree of freedom manipulator, designed to follow a linear plant. Simulation studies show fast convergence of the state error for a large angle motion maneuver.