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Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Fast Adaptive Robust Differentiator Based Robust-Adaptive Control of Grid-Tied Inverters with a New L Filter Design Method
In this research, a new nonlinear and adaptive state feedback controller with a fast-adaptive robust differentiator is presented for grid-tied inverters. All parameters and external disturbances are taken as uncertain in the design of the proposed controller without the disadvantages of singularity and over-parameterization. A robust differentiator based on the second order sliding mode is also developed with a fast-adaptive structure to be able to consider the time derivative of the virtual control input. Unlike the conventional backstepping, the proposed differentiator overcomes the problem of explosion of complexity. In the closed-loop control system, the three phase source currents and direct current (DC) bus voltage are assumed to be available for feedback. Using the Lyapunov stability theory, it is proven that the overall control system has the global asymptotic stability. In addition, a new simple L filter design method based on the total harmonic distortion approach is also proposed. Simulations and experimental results show that the proposed controller assurances drive the tracking errors to zero with better performance, and it is robust against all uncertainties. Moreover, the proposed L filter design method matches the total harmonic distortion (THD) aim in the design with the experimental result
Switching Control for Parameter Identifiability of Uncertain Systems
This paper considers the problem of identifying the parameters of an
uncertain linear system by means of feedback control. The problem is approached
by considering time-varying controllers. It is shown that even when the
uncertainty set is not finite, parameter identifiability can be generically
ensured by switching among a finite number of linear time-invariant
controllers. The results are shown to have several implications, ranging from
fault detection and isolation to adaptive and supervisory control. Practical
aspects of the problem are also discussed in details
Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters
The paper extends a recently proposed indirect, certainty-equivalence,
event-triggered adaptive control scheme to the case of non-observable
parameters. The extension is achieved by using a novel Batch Least-Squares
Identifier (BaLSI), which is activated at the times of the events. The BaLSI
guarantees the finite-time asymptotic constancy of the parameter estimates and
the fact that the trajectories of the closed-loop system follow the
trajectories of the nominal closed-loop system ("nominal" in the sense of the
asymptotic parameter estimate, not in the sense of the true unknown parameter).
Thus, if the nominal feedback guarantees global asymptotic stability and local
exponential stability, then unlike conventional adaptive control, the newly
proposed event-triggered adaptive scheme guarantees global asymptotic
regulation with a uniform exponential convergence rate. The developed adaptive
scheme is tested to a well-known control problem: the state regulation of the
wing-rock model. Comparisons with other adaptive schemes are provided for this
particular problem.Comment: 29 pages, 12 figure
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