12,205 research outputs found
Arbitrary pole placement by state feedback with minimum gain
We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a gain matrix that delivers the desired pole placement with minimum gain
Decentralized pole assignment for interconnected systems
Given a general proper interconnected system,
this paper aims to design a LTI decentralized controller to
place the modes of the closed-loop system at pre-determined
locations. To this end, it is first assumed that the structural
graph of the system is strongly connected. Then, it is shown
applying generic static local controllers to any number of
subsystems will not introduce new decentralized fixed modes
(DFM) in the resultant system, although it has fewer inputoutput
stations compared to the original system. This means
that if there are some subsystems whose control costs are
highly dependent on the complexity of the control law, then
generic static controllers can be applied to such subsystems,
without changing the characteristics of the system in terms of
the fixed modes. As a direct application of this result, in the
case when the system has no DFMs, one can apply generic static
controllers to all but one subsystem, and the resultant system
will be controllable and observable through that subsystem.
Now, a simple observer-based local controller corresponding to
this subsystem can be designed to displace the modes of the
entire system arbitrarily. Similar results can also be attained
for a system whose structural graph is not strongly connected.
It is worth mentioning that similar concepts are deployed in the
literature for the special case of strictly proper systems, but as
noted in the relevant papers, extension of the results to general
proper systems is not trivial. This demonstrates the significance
of the present work
Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined
Design of parameter-scheduled state-feedback controllers using shifting specifications
In this paper,the problem of designing aparameter-scheduled state-feedback controller is investigated. The paper presents an extension of the classical regional pole placement, H2 control and H1 control problems, so as to satisfy new specifications, that will be referred to as shifting pole placement control, shifting H2 control and shifting H1 control, respectively. By introducing some parameters, or using the existing ones, the controller can be designed in such away that different values of the separameters imply different regions where the closed-loop poles are situated, or different performances in the H2 or H1 sense. The proposed approach is derived within the so-called Lyapunov Shaping Paradigm, where a single quadratic Lyapunov function is used for ensuring stability and desired performances in spite of arbitrary parameter time variation. The problem is analyzed in the continuous-time LPV case, oventhough the developed theory could be applied to LTI systems in cases when it is desired to vary the control system performances online. Results obtained in simulation demonstrate the effectiveness and the relevant features of the proposed approach.Peer ReviewedPostprint (published version
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