8,602 research outputs found
Computing Dynamic Output Feedback Laws
The pole placement problem asks to find laws to feed the output of a plant
governed by a linear system of differential equations back to the input of the
plant so that the resulting closed-loop system has a desired set of
eigenvalues. Converting this problem into a question of enumerative geometry,
efficient numerical homotopy algorithms to solve this problem for general
Multi-Input-Multi-Output (MIMO) systems have been proposed recently. While
dynamic feedback laws offer a wider range of use, the realization of the output
of the numerical homotopies as a machine to control the plant in the time
domain has not been addressed before. In this paper we present symbolic-numeric
algorithms to turn the solution to the question of enumerative geometry into a
useful control feedback machine. We report on numerical experiments with our
publicly available software and illustrate its application on various control
problems from the literature.Comment: 20 pages, 3 figures; the software described in this paper is publicly
available via http://www.math.uic.edu/~jan/download.htm
Some Remarks on Real and Complex Output Feedback
We provide some new necessary and sufficient conditions which guarantee
arbitrary pole placement of a particular linear system over the complex
numbers. We exhibit a non-trivial real linear system which is not controllable
by real static output feedback and discuss a conjecture from algebraic geometry
concerning the existence of real linear systems for which all static feedback
laws are real
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
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