scholarly journals Performance Output Tracking for a One-Dimensional Wave-Heat Cascade System with Unmatched Disturbance

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Yulong Liu

The objective of this paper is to solve the performance output regulation problem for a wave-heat cascade system with unmatched disturbance. Applying the series expansion, the auxiliary trajectory for the cascade system is constructed and the unmatched disturbance is rejected. Meanwhile, the controller and observer only based on error signal are designed, and the performance output regulation problem is solved. Under the control feedback, the performance output can track the reference signal, and the regulation error goes to zero asymptotically. Finally, some numerical simulations are presented for illustration.

Author(s):  
Guopeng Zhou ◽  
Fang Zhou ◽  
Naiding Zhou ◽  
Feng Liang

This paper studies energy storage based output tracking and disturbance rejection problems for a simple interconnected power system suffered from a periodic load disturbance with unknown amplitude and frequency. By constructing a new exosystem, the problem is converted into output regulation problem of a composite system. Internal model theorem is introduced for the composite system, and output regulation problem is changed into stabilization problem of a new augmented system by imposing an appropriate transformation. An adaptive dynamical energy storage based controller can solve stabilization problem of the augmented system as well as output tracking and disturbance rejection problem for the original system. Finally, simulation results show the effectiveness of the proposed controller.


2018 ◽  
Vol 41 (1) ◽  
pp. 246-262 ◽  
Author(s):  
Jianjun Gu ◽  
Chunqiu Wei ◽  
Junmin Wang

Output regulation is considered in this paper for ordinary differential equations cascaded by a wave equation, in which both the body equations and the uncontrolled end are subject to disturbances. The disturbances are generated by an exosystem. A backstepping state-feedback regulator is first designed to force the output to track the reference signal. The design is based on solving cascaded regulator equations, and the solvability condition of the equations is characterized in terms of a transfer function and the eigenvalues of the exosystem. An observer-based output-feedback regulator is then designed to solve the output regulation problem. Finally, the regulator tracking performance is illustrated through numerical simulations.


2020 ◽  
Vol 37 (4) ◽  
pp. 1447-1467
Author(s):  
Ziqing Tian ◽  
Xiao-Hui Wu

Abstract In this paper, we consider output tracking for a one-dimensional wave equation, where the boundary disturbances are either collocated or non-collocated with control. The regulated output and the control are supposed to be non-collocated with control, which represents a difficult case for output tracking of PDEs. We apply the trajectory planning approach to design an observer, in terms of tracking error only, to estimate both states of the system and the exosystem from which the disturbances are produced. An error-based feedback control is proposed by solving a standard regulator equation. It is shown that (a) the closed-loop system is uniformly bounded whenever the exosystem is bounded; (b) when the disturbance is zero, the closed-loop is asymptotically stable; and (c) the tracking error converges to zero asymptotically as time goes to infinity. Numerical simulations are performed to validate the effectiveness of the proposed control.


Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 879
Author(s):  
Jorge Rivera ◽  
Susana Ortega-Cisneros ◽  
Florentino Chavira

This work deals with the novel application of the sliding mode (discontinuous) output regulation theory to a nonlinear electrical circuit, the so-called boost power converter. This theory has excelled due to the fact that trajectory tracking plays a central role. The control of a boost power converter for the output tracking of a DC biased sinusoidal signal is a challenging problem for control engineers. The main difficulties are the computation of a proper reference signal for the inductor current, and the stabilization of the inductor current dynamics or to guarantee the correct output tracking of the capacitor voltage. With the application of the discontinuous output regulation these problems are solved in this work. Simulations and real time experiments were carried out with an unknown variation of the DC input voltage, where the good output tracking of the capacitor voltage was verified along with the stabilization of the inductor current. The discontinuous output regulation theory has proven to be a suitable tool in the output tracking for the boost power converter.


2021 ◽  
Vol 31 (06) ◽  
pp. 2150115
Author(s):  
Fei Wang ◽  
Junmin Wang ◽  
Zhaosheng Feng

In this paper, we consider the chaotic oscillation of coupled one-dimensional wave equations. The symmetric nonlinearities of van der Pol type are proposed at the two boundary endpoints, which can cause the energy of the system to rise and fall within certain bounds. At the interconnected point of the wave equations, the energy is injected into the system through an anti-damping velocity feedback. We prove the existence of the snapback repeller when the parameters enter a certain regime, which causes the system to be chaotic. Numerical simulations are presented to illustrate our theoretical results.


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