Passivity-based control of dynamic systems

Passivity-based controllers have been proved to be highly effective in the control of "inherently passive" systems. It has been shown that the negative feedback connection of a passive system and a strictly passive system is guaranteed to be stable. The main advantage of using passivity-based controllers is the stability robustness of the closed-loop system. For non-passive systems, however, passivity-based control techniques do not extend directly. One way of making non-passive systems amenable to passivity-based control is to passify them using suitable compensation. The objective of this research is to investigate the design methods for passivity-based controllers and the passification techniques for non-passive systems.; For linear time-invariant (LTI) passive systems, a design methodology is proposed for the design of an optimal constant-gain positive-real controller. For multi-input multi-output (MIMO) linear non-passive systems, new passification methodologies are proposed based on linear matrix inequalities (LMIs). The LMI formulation is given for three basic passification techniques, namely, series, feedback and feedforward. For linear systems with sector nonlinearities, a sector passification technique is proposed which renders the systems passive in a given sector. A numerical algorithm is developed to synthesize a sector passification which optimizes some quadratic performance index. The passivity-based control design methodology together with the passification techniques offers a useful synthesis tool for the design of robust controllers for passive systems as well as for non-passive systems. Several numerical examples are given for the validation of the proposed design methodologies.