56,874 research outputs found
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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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
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
A Nonlinear Negative Imaginary Systems Framework with Actuator Saturation for Control of Electrical Power Systems
In the transition to net zero, it has been suggested that a massive expansion
of the electric power grid will be required to support emerging renewable
energy zones. In this paper, we propose the use of battery-based feedback
control and nonlinear negative imaginary systems theory to reduce the need for
such an expansion by enabling the more complete utilization of existing grid
infrastructure. By constructing a novel Lur'e-Postnikov-like Lyapunov function,
a stability result is developed for the feedback interconnection of a nonlinear
negative imaginary system and a nonlinear negative imaginary controller.
Additionally, a new class of nonlinear negative imaginary controllers is
proposed to deal with actuator saturation. We show that in this control
framework, the controller eventually leaves the saturation boundary, and the
feedback system is locally stable in the sense of Lyapunov. This provides
theoretical support for the application of battery-based control in electrical
power systems. Validation through simulation results for
single-machine-infinite-bus power systems supports our results. Our approach
has the potential to enable a transmission line to operate at its maximum power
capacity, as stability robustness is ensured by the use of a feedback
controller.Comment: 8 pages, 5 figures, European Control Conferenc
Converse negative imaginary theorems
Converse negative imaginary theorems for linear time-invariant systems are
derived. In particular, we provide necessary and sufficient conditions for a
feedback system to be robustly stable against various types of negative
imaginary (NI) uncertainty. Both marginally stable and exponentially stable
uncertain NI systems with restrictions on their static or instantaneous gains
are considered. It is shown that robust stability against the former class
entails the well-known strict NI property, whereas the latter class entails a
new type of output strict NI property that is hitherto unexplored. We also
establish a non-existence result that no stable system can robustly stabilise
all marginally stable NI uncertainty, thereby showing that the uncertainty
class of NI systems is too large as far as robust feedback stability is
concerned, thus justifying the consideration of subclasses of NI systems with
constrained static or instantaneous gains.Comment: This paper has been submitted for possible publication at Automatic
Robust Output Feedback Consensus for Networked Heterogeneous Nonlinear Negative-Imaginary Systems
This paper provides a control protocol for the robust output feedback
consensus of networked heterogeneous nonlinear negative-imaginary (NI) systems.
Heterogeneous nonlinear output strictly negative-imaginary (OSNI) controllers
are applied in positive feedback according to the network topology to achieve
output feedback consensus. The main contribution of this paper is extending the
previous studies of the robust output feedback consensus problem for networked
heterogeneous linear NI systems to nonlinear NI systems. Output feedback
consensus is proved by investigating the internal stability of the closed-loop
interconnection of the network of heterogeneous nonlinear NI plants and the
network of heterogeneous nonlinear OSNI controllers according to the network
topology. The network of heterogeneous nonlinear NI systems is proved to be
also a nonlinear NI system, and the network of heterogeneous nonlinear OSNI
systems is proved to be also a nonlinear OSNI system. Under suitable
conditions, the nonlinear OSNI controllers lead to the convergence of the
outputs of all nonlinear NI plants to a common limit trajectory, regardless of
the system model of each plant. Hence, the protocol is robust with respect to
parameter perturbation in the system models of the heterogeneous nonlinear NI
plants in the network.Comment: 6 pages, 9 figure
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