Overcoming passivity violations: closed-loop stability, controller design and controller scheduling

Control of systems that have had their passive input-output map partially violated is the motivation of this study. The hybrid passivity/finite-gain systems framework is specifically well suited to systems that have experienced a passivity violation. The focus of this study is the extension and application of the hybrid passivity/finite-gain systems framework to a multi-input multi-output (MIMO) control problem. Calculation of the hybrid passivity/finite-gain parameters in a linear time-invariant (LTI) MIMO context is considered. Additionally, we show that a set of hybrid very strictly passive/finite-gain (VSP/finite-gain) controllers gain-scheduled in a particular way also possesses hybrid VSP/finite-gain properties. To synthesise hybrid VSP/finite-gain controllers a frequency-weighted optimal control scheme is used to parameterise controllers that are then constrained and optimised within a numerical optimisation framework. The theoretical contributions of this work are validated experimentally using a two-link flexible manipulator apparatus. Results highlight the utility of the hybrid passivity/finite-gain framework, the scheduling scheme and controller design method.