Robust process control : a passivity theorum approach

Abstract

An approach to robust process control based on the passivity theorem has beennaddressed in this thesis. The aim of this work is to gain better understanding ofnpassive systems and develop systematic approaches to passivity-based robust process control, which can be less conservative than the main-streamed small-gain basednrobust control methods.Properties of Multi-Input Multi-Output (MIMO) passive systems are examinednin this thesis. The difference between Lyapunov stability and passivity has beenndiscussed and concepts of passivity and passive systems were interpreted in a morenintuitive language. In particular, new phase properties of linear MIMO passivensystems have been revealed.A passivity-based robust control strategy was investigated. The research scopesnare specified as follows:(1) To characterise the uncertainty by using the passivity index, an index whichnindicates how far the uncertainty system is from being passive.(2) To derive passivity-based robust stability conditions.(3) To design controllers that satisfy the passive-based stability condition so thatnrobust stability is guaranteed.As the major outcome of this study, two alternative control methods have beenndeveloped.In the qblendedq approach, the uncertainty was characterised in terms of thenpassivity index at low frequencies and the Hi norm at high frequencies. A newnstability condition which combines the passivity theorem and the small gain theoremnin different frequency bands was derived. The control performance was analysed andna controller design method was then developed to achieve both performance andnrobustness specifications. This approach can be used if the uncertainty is near passivenat low frequencies.n n n n n