7,080 research outputs found
Improving Transient Performance of Adaptive Control Architectures using Frequency-Limited System Error Dynamics
We develop an adaptive control architecture to achieve stabilization and
command following of uncertain dynamical systems with improved transient
performance. Our framework consists of a new reference system and an adaptive
controller. The proposed reference system captures a desired closed-loop
dynamical system behavior modified by a mismatch term representing the
high-frequency content between the uncertain dynamical system and this
reference system, i.e., the system error. In particular, this mismatch term
allows to limit the frequency content of the system error dynamics, which is
used to drive the adaptive controller. It is shown that this key feature of our
framework yields fast adaptation with- out incurring high-frequency
oscillations in the transient performance. We further show the effects of
design parameters on the system performance, analyze closeness of the uncertain
dynamical system to the unmodified (ideal) reference system, discuss robustness
of the proposed approach with respect to time-varying uncertainties and
disturbances, and make connections to gradient minimization and classical
control theory.Comment: 27 pages, 7 figure
Analysis and Output Tracking Design for the Direct Contact Membrane Distillation Parabolic System
This paper considers the performance output tracking for a boundary
controlled Direct Contact Membrane Distillation (DCMD) system. First, the
mathematical properties of a recently developed mathematical model of the DCMD
system are discussed. This model consists of parabolic equations coupled at the
boundary. Then, the existence and uniqueness of the solutions are analyzed,
using the theory of operators. Some regularity results of the solution are also
established. A particular case showing the diagonal property of the principal
operator is studied. Then, based on one-side feedback law the control problem,
which consists of tracking both the feed and permeate outlet temperatures of
the membrane distillation system is formulated. A servomechanism and an output
feedback controller are proposed to solve the control problem. In addition, an
extended state observer aimed at estimating both the system state and
disturbance, based on the temperature measurements of the inlet is proposed.
Thus, by some regularity for the reference signal and when the disturbance
vanishes, we prove the exponential decay of the output tracking error.
Moreover, we show the performance of the control strategy in presence of the
flux noise.Comment: 32 pages, 4 figure
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
In this paper we propose a new Koopman operator approach to the decomposition
of nonlinear dynamical systems using Koopman Gramians. We introduce the notion
of an input-Koopman operator, and show how input-Koopman operators can be used
to cast a nonlinear system into the classical state-space form, and identify
conditions under which input and state observable functions are well separated.
We then extend an existing method of dynamic mode decomposition for learning
Koopman operators from data known as deep dynamic mode decomposition to systems
with controls or disturbances. We illustrate the accuracy of the method in
learning an input-state separable Koopman operator for an example system, even
when the underlying system exhibits mixed state-input terms. We next introduce
a nonlinear decomposition algorithm, based on Koopman Gramians, that maximizes
internal subsystem observability and disturbance rejection from unwanted noise
from other subsystems. We derive a relaxation based on Koopman Gramians and
multi-way partitioning for the resulting NP-hard decomposition problem. We
lastly illustrate the proposed algorithm with the swing dynamics for an IEEE
39-bus system.Comment: 8 pages, submitted to IEEE 2018 AC
A Tractable Fault Detection and Isolation Approach for Nonlinear Systems with Probabilistic Performance
This article presents a novel perspective along with a scalable methodology
to design a fault detection and isolation (FDI) filter for high dimensional
nonlinear systems. Previous approaches on FDI problems are either confined to
linear systems or they are only applicable to low dimensional dynamics with
specific structures. In contrast, shifting attention from the system dynamics
to the disturbance inputs, we propose a relaxed design perspective to train a
linear residual generator given some statistical information about the
disturbance patterns. That is, we propose an optimization-based approach to
robustify the filter with respect to finitely many signatures of the
nonlinearity. We then invoke recent results in randomized optimization to
provide theoretical guarantees for the performance of the proposed filer.
Finally, motivated by a cyber-physical attack emanating from the
vulnerabilities introduced by the interaction between IT infrastructure and
power system, we deploy the developed theoretical results to detect such an
intrusion before the functionality of the power system is disrupted
Design of generalized minimum variance controllers for nonlinear multivariable systems
The design and implementation of Generalized Minimum Variance control laws for nonlinear multivariable systems that can include severe nonlinearities is considered. The quadratic cost index minimised involves dynamically weighted error and nonlinear control signal costing terms. The aim here is to show the controller obtained is simple to design and implement. The features of the control law are explored. The controller obtained includes an internal model of the process and in one form is a nonlinear version of the Smith Predictor
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