Nonlinear Control and Synchronization of Mechanical Systems

Abstract

This thesis considers three issues: the problem of global output feedback tracking control of Euler-Lagrange systems; the problem of path following control of underactuated marine vehicles; and the problem of mutual synchronization and formation control of Euler-Lagrange systems and underactuated marine vehicles.

 

Innovative results are presented on global output feedback tracking control of Euler-Lagrange systems. In particular, an innovative position feedback control strategy for a general class of n-degrees-of-freedom (n -DOF) Euler-Lagrange systems is discussed that combines a new dynamic-gain nonlinear observer and a certainty equivalence control law with integral action. The observer is developed using a novel design approach where dynamic and nonlinear injection terms are applied to make the observer error dynamics globally exponentially stable. A controller with integral action is synthesized using integrator backstepping. The stability of the overall observer-controller system is analyzed and shown to be globally exponentially stable. The theoretical results are validated in experiments with a two-link robot manipulator.

 

This thesis also presents new results on path following control of underactuated marine vehicles, specifically path following control of underactuated 3-DOF surface vessels and 5-DOF underwater vehicles. Three different guidance-based path following control approaches are proposed for straight line path following, straight line path following in the presence of ocean currents and path following of curved paths, respectively. The closed loop stability of the proposed control approaches are analyzed in detail and explicit conditions are derived for stability of the closed loop systems. The theoretical results are backed by simulations, illustrating the performance of the proposed controllers. The performance of the straight line path following control strategy is also evaluated in experiments with a model ship.

 

This thesis also presents newresults on mutual synchronization control of Euler-Lagrange systems and formation control of underactuated marine vehicles. Here, a synchronization control strategy for mutual synchronization of Euler-Lagrange systems is described together with a synchronized path following control approach for formation control of underactuated marine vehicles. The proposed formation control approach builds on the results developed at an earlier stage for path following control of a single marine vehicle and on a new result for multisystem synchronization. This thesis describes a nonlinear synchronization protocol that respects the communication topology of the underlying inter-vehicle communication network and the conditions of the underlying path following controller. The closed loop system is analyzed in detail and explicit conditions are derived for exponential stability to the desired formation and the desired path. The theoretical results are backed by simulations and experiments.