104 research outputs found
On Robustness in the Gap Metric and Coprime Factor Uncertainty for LTV Systems
In this paper, we study the problem of robust stabilization for linear
time-varying (LTV) systems subject to time-varying normalized coprime factor
uncertainty. Operator theoretic results which generalize similar results known
to hold for linear time-invariant (infinite-dimensional) systems are developed.
In particular, we compute an upper bound for the maximal achievable stability
margin under TV normalized coprime factor uncertainty in terms of the norm of
an operator with a time-varying Hankel structure. We point to a necessary and
sufficient condition which guarantees compactness of the TV Hankel operator,
and in which case singular values and vectors can be used to compute the
time-varying stability margin and TV controller. A connection between robust
stabilization for LTV systems and an Operator Corona Theorem is also pointed
out.Comment: 20 page
Optimal Disturbance Rejection and Robustness for Infinite Dimensional LTV Systems
In this paper, we consider the optimal disturbance rejection problem for
possibly infinite dimensional linear time-varying (LTV) systems using a
framework based on operator algebras of classes of bounded linear operators.
This approach does not assume any state space representation and views LTV
systems as causal operators. After reducing the problem to a shortest distance
minimization in a space of bounded linear operators, duality theory is applied
to show existence of optimal solutions, which satisfy a "time-varying" allpass
or flatness condition. Under mild assumptions the optimal TV controller is
shown to be essentially unique. Next, the concept of M-ideals of operators is
used to show that the computation of time-varying (TV) controllers reduces to a
search over compact TV Youla parameters. This involves the norm of a TV compact
Hankel operator defined on the space of causal trace-class 2 operators and its
maximal vectors. Moreover, an operator identity to compute the optimal TV Youla
parameter is provided. These results are generalized to the mixed sensitivity
problem for TV systems as well, where it is shown that the optimum is equal to
the operator induced of a TV mixed Hankel-Toeplitz. The final outcome of the
approach developed here is that it leads to two tractable finite dimensional
convex optimizations producing estimates to the optimum within desired
tolerances, and a method to compute optimal time-varying controllers.Comment: 30 pages, 1 figur
Combating False Reports for Secure Networked Control in Smart Grid via Trustiness Evaluation
Smart grid, equipped with modern communication infrastructures, is subject to
possible cyber attacks. Particularly, false report attacks which replace the
sensor reports with fraud ones may cause the instability of the whole power
grid or even result in a large area blackout. In this paper, a trustiness
system is introduced to the controller, who computes the trustiness of
different sensors by comparing its prediction, obtained from Kalman filtering,
on the system state with the reports from sensor. The trustiness mechanism is
discussed and analyzed for the Linear Quadratic Regulation (LQR) controller.
Numerical simulations show that the trustiness system can effectively combat
the cyber attacks to smart grid.Comment: It has been submitted to IEEE International Conference on
Communications (ICC
Performance Guaranteed Inertia Emulation for Diesel-Wind System Feed Microgrid via Model Reference Control
In this paper, a model reference control based inertia emulation strategy is
proposed. Desired inertia can be precisely emulated through this control
strategy so that guaranteed performance is ensured. A typical frequency
response model with parametrical inertia is set to be the reference model. A
measurement at a specific location delivers the information of disturbance
acting on the diesel-wind system to the reference model. The objective is for
the speed of the diesel-wind system to track the reference model. Since active
power variation is dominantly governed by mechanical dynamics and modes, only
mechanical dynamics and states, i.e., a swing-engine-governor system plus a
reduced-order wind turbine generator, are involved in the feedback control
design. The controller is implemented in a three-phase diesel-wind system feed
microgrid. The results show exact synthetic inertia is emulated, leading to
guaranteed performance and safety bounds.Comment: 2017 IEEE PES Innovative Smart Grid Technologies Conferenc
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