distributed parameter
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2022 ◽  
Vol 27 ◽  
pp. 1-20
Yanfang Lei ◽  
Junmin Li ◽  
Ailiang Zhao

In this study, we focus on designing a robust piecewise adaptive controller to globally asymptotically stabilize a semilinear parabolic distributed parameter systems (DPSs) with external disturbance, whose nonlinearities are bounded by unknown functions. Firstly, a robust piecewise adaptive control is designed against the unknown nonlinearity and the external disturbance. Then, by constructing an appropriate Lyapunov–Krasovskii functional candidate (LKFC) and using the Wiritinger’s inequality and a variant of the Agmon’s inequality, it is shown that the proposed robust piecewise adaptive controller not only ensures the globally asymptotic stability of the closed-loop system, but also guarantees a given performance. Finally, two simulation examples are given to verify the validity of the design method.

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3180
Ivan Francisco Yupanqui Yupanqui Tello ◽  
Alain Vande Vande Wouwer ◽  
Daniel Coutinho

While state estimation techniques are routinely applied to systems represented by ordinary differential equation (ODE) models, it remains a challenging task to design an observer for a distributed parameter system described by partial differential equations (PDEs). Indeed, PDE systems present a number of unique challenges related to the space-time dependence of the states, and well-established methods for ODE systems do not translate directly. However, the steady progresses in computational power allows executing increasingly sophisticated algorithms, and the field of state estimation for PDE systems has received revived interest in the last decades, also from a theoretical point of view. This paper provides a concise overview of some of the available methods for the design of state observers, or software sensors, for linear and semilinear PDE systems based on both early and late lumping approaches.

Huirong Zhang ◽  
Wentao Sui ◽  
Chongqiu Yang ◽  
Leian Zhang ◽  
Rujun Song ◽  

Abstract This paper presents a detailed investigation on an asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester based on harmonic excitation. There is an eccentricity between the shape center of moving magnets and the axis of the piezoelectric beam, which results in the bending and torsion simultaneously in working condition. The distributed mathematical model is derived from the energy method to describe the dynamic characteristics of the harvester, and the correctness of the model is verified by experiments. To further demonstrate the improvement performance of the proposed energy harvester, the bending-torsion energy harvester (i.e. magnetic-coupled was not configured) is experimented and compared. The theoretical and experimental results indicate that the average power increases about 300% but the resonance frequency decreases approximately 2 Hz comparing to the harvester without magnetic-coupled. According to the characteristic of distributed parameter model, the magnetic force and the size of the piezoelectric beam are investigated respectively. And the lumped-parameter model is introduced to analyze the steady-state characteristic. Accordingly, this paper provides a feasible method to improve performance for piezoelectric energy harvester.

2021 ◽  
Vol 396 ◽  
pp. 139274
Yang Li ◽  
Mahinda Vilathgamuwa ◽  
Troy Farrell ◽  
San Shing Choi ◽  
Ngoc Tham Tran ◽  

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