12 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
201
Dissipative Linear Stochastic Hamiltonian Systems
This paper is concerned with stochastic Hamiltonian systems which model a
class of open dynamical systems subject to random external forces. Their
dynamics are governed by Ito stochastic differential equations whose structure
is specified by a Hamiltonian, viscous damping parameters and
system-environment coupling functions. We consider energy balance relations for
such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems
with quadratic Hamiltonians and linear coupling. For LSH systems, we also
discuss stability conditions, the structure of the invariant measure and its
relation with stochastic versions of the virial theorem. Using Lyapunov
functions, organised as deformed Hamiltonians, dissipation relations are also
considered for LSH systems driven by statistically uncertain external forces.
An application of these results to feedback connections of LSH systems is
outlined.Comment: 10 pages, 1 figure, submitted to ANZCC 201
Negative imaginary theorem with an application to robust control of a crane system
This paper presents an integral sliding mode (ISM) control for a case of negative imaginary (NI) systems. A gantry crane system (GCS) is considered in this work. ISM is a nonlinear control method introducing significant properties of precision, robustness, stress-free tuning and implementation. The GCS model considered in this work is derived based on the x direction and sway motion of the payload. The GCS is a negative imaginary (NI) system with a single pole at the origin. ISM consist of two blocks; the inner block made up of a pole placement controller (NI controller), designed using linear matrix inequality for robustness and outer block made up of sliding mode control to reject disturbances. The ISM is designed to control position tracking and anti-swing payload motion. The robustness of the control scheme is tested with an input disturbance of a sine wave signal. The simulation results show the effectiveness of the control scheme
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
Stability analysis and vibration control of a class of negative imaginary systems
This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB