851 research outputs found
Zero dynamics and funnel control of general linear differential-algebraic systems
We study linear differential-algebraic multi-input multi-output systems which are not necessarily regular and investigate the zero dynamics and tracking control. We use the concepts of autonomous zero dynamics and (E,A,B)-invariant subspaces to derive the so called zero dynamics form - which decouples the zero dynamics of the system - and exploit it for the characterization of system invertibility. Asymptotic stability of the zero dynamics is characterized and some implications for stabilizability in the behavioral sense are shown. A refinement of the zero dynamics form is then exploited to show that the funnel controller (that is a static nonlinear output error feedback) achieves - for a special class of right-invertible systems with asymptotically stable zero dynamics - tracking of a reference signal by the output signal within a pre-specified performance funnel. It is shown that the results can be applied to a class of passive electrical networks
Asymptotic Tracking via Funnel Control
Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control β without any further assumptions β can achieve asymptotic tracking
Asymptotic Tracking via Funnel Control
Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control β without any further assumptions β can achieve asymptotic tracking
Funnel control of nonlinear systems
Tracking of reference signals is addressed in the context of a class of
nonlinear controlled systems modelled by -th order functional differential
equations, encompassing inter alia systems with unknown "control direction" and
dead-zone input effects. A control structure is developed which ensures that,
for every member of the underlying system class and every admissible reference
signal, the tracking error evolves in a prescribed funnel chosen to reflect
transient and asymptotic accuracy objectives. Two fundamental properties
underpin the system class: bounded-input bounded-output stable internal
dynamics, and a high-gain property (an antecedent of which is the concept of
sign-definite high-frequency gain in the context of linear systems)
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