Model reference adaptive control in Hamiltonian systems

In this thesis we examine model reference control systems (MRC) in Hamiltonian formulation. The MRC system is then developed into a model reference adaptive control system. We then examine the sliding mode technique in Hamiltonian formulation. Comparison of controller performance is given by way of simulated control of a cylindrical robotic manipulator.

In this thesis we apply the so called Lyapunov direct method. The aim in this method is to construct an energy-like function (Lyapunov function), satisfying certain conditions, and using a control law, force it to decrease with the passage of time. The synthesis problem using the Lyapunov direct method is to select a Lyapunov function candidate and a mechanism to adjust the parameters of the system so that the Lyapunov function satisfies the conditions for stability.

A brief introduction to Newtonian, Lagrangian and Hamiltonian formulation of dynamics is given and illustrated on the same example of a two-link revolute robotic manipulator.

Model reference control is considered for nonlinear plant and reference models which are given in the Hamiltonian format. We show how the Hamiltonian for the reference model can be used as a Lyapunov function for MRC. The method is applied to linear and nonlinear plants, with particular application to robot control.

Model reference adaptive control (MRAC) is introduced as an extension of the MRC results. We use the Liapunov method to determine controllers for adaptive tracking and at the same time give sufficient conditions to ensure that the resulting system is stable.

The sliding mode approach provides a simple and robust method of dealing with modelling imprecision. We next adapt the sliding mode technique to the Hamiltonian formulation and design the control and adaptation laws. We design a stabilising controller for the sliding mode method.