2,529 research outputs found
Generalizing Negative Imaginary Systems Theory to Include Free Body Dynamics: Control of Highly Resonant Structures with Free Body Motion
Negative imaginary (NI) systems play an important role in the robust control
of highly resonant flexible structures. In this paper, a generalized NI system
framework is presented. A new NI system definition is given, which allows for
flexible structure systems with colocated force actuators and position sensors,
and with free body motion. This definition extends the existing definitions of
NI systems. Also, necessary and sufficient conditions are provided for the
stability of positive feedback control systems where the plant is NI according
to the new definition and the controller is strictly negative imaginary. The
stability conditions in this paper are given purely in terms of properties of
the plant and controller transfer function matrices, although the proofs rely
on state space techniques. Furthermore, the stability conditions given are
independent of the plant and controller system order. As an application of
these results, a case study involving the control of a flexible robotic arm
with a piezo-electric actuator and sensor is presented
Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems
Sufficient and necessary conditions for the stability of positive feedback
interconnections of negative imaginary systems are derived via an integral
quadratic constraint (IQC) approach. The IQC framework accommodates
distributed-parameter systems with irrational transfer function
representations, while generalising existing results in the literature and
allowing exploitation of flexibility at zero and infinite frequencies to reduce
conservatism in the analysis. The main results manifest the important property
that the negative imaginariness of systems gives rise to a certain form of IQCs
on positive frequencies that are bounded away from zero and infinity. Two
additional sets of IQCs on the DC and instantaneous gains of the systems are
shown to be sufficient and necessary for closed-loop stability along a homotopy
of systems.Comment: Submitted to Automatica, A preliminary version of this paper appeared
in the Proceedings of the 2015 European Control Conferenc
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
A general framework is presented for analyzing the stability and performance
of nonlinear and linear parameter varying (LPV) time delayed systems. First,
the input/output behavior of the time delay operator is bounded in the
frequency domain by integral quadratic constraints (IQCs). A constant delay is
a linear, time-invariant system and this leads to a simple, intuitive
interpretation for these frequency domain constraints. This simple
interpretation is used to derive new IQCs for both constant and varying delays.
Second, the performance of nonlinear and LPV delayed systems is bounded using
dissipation inequalities that incorporate IQCs. This step makes use of recent
results that show, under mild technical conditions, that an IQC has an
equivalent representation as a finite-horizon time-domain constraint. Numerical
examples are provided to demonstrate the effectiveness of the method for both
class of systems
Conditions for the equivalence between IQC and graph separation stability results
This paper provides a link between time-domain and frequency-domain stability
results in the literature. Specifically, we focus on the comparison between
stability results for a feedback interconnection of two nonlinear systems
stated in terms of frequency-domain conditions. While the Integral Quadratic
Constrain (IQC) theorem can cope with them via a homotopy argument for the
Lurye problem, graph separation results require the transformation of the
frequency-domain conditions into truncated time-domain conditions. To date,
much of the literature focuses on "hard" factorizations of the multiplier,
considering only one of the two frequency-domain conditions. Here it is shown
that a symmetric, "doubly-hard" factorization is required to convert both
frequency-domain conditions into truncated time-domain conditions. By using the
appropriate factorization, a novel comparison between the results obtained by
IQC and separation theories is then provided. As a result, we identify under
what conditions the IQC theorem may provide some advantage
Physical Interpretations of Negative Imaginary Systems Theory
This paper presents some physical interpretations of recent stability results
on the feedback interconnection of negative imaginary systems. These
interpretations involve spring mass damper systems coupled together by springs
or RLC electrical networks coupled together via inductors or capacitors.Comment: To appear in the Proceedings of the 10th ASIAN CONTROL CONFERENCE
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