Neumann Boundary Control of a Linear Diffusion System Based on the Equivalent Distributed Control Model

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Dyhia Hamdadou ◽  
Ahmed Maidi ◽  
Jean-Pierre Corriou
Keyword(s):  
Boundary Control ◽  
Control Strategy ◽  
Neumann Boundary ◽  
State Equation ◽  
Diffusion System ◽  
Linear Diffusion ◽  
Finite Characteristic ◽  
Loop Control ◽  
Characteristic Index ◽  
Point Tracking

Abstract This paper deals with the boundary control of a one-dimensional diffusion system with Neumann actuation. The objective is to control a given punctual output. The control design is based on the concept of the characteristic index from geometric control theory. The idea consists of making the boundary condition homogeneous by inserting the manipulated variable into the state equation using a proposed linear transformation. Then, in order to overcome the controllability problem and to have a finite characteristic index, a weighted value of the system state, along the spatial domain, is considered as an auxiliary output. By calculating the successive derivatives of the measured output, a state feedback that enforces a set point tracking of the measured output is developed. The stability of the resulting closed-loop control system is demonstrated based on Lyapunov's method. Then, in order to meet the desired control objective of the punctual output, a control strategy is proposed based on the steady-state analysis. The tracking performance of the developed control strategy is evaluated through numerical simulation by considering the temperature control of a thin metal rod modeled by a linear heat equation.

The Control Strategy and Simulation of Three-Phase Grid-Connected Photovoltaic System

2012 ◽  
Vol 608-609 ◽  
pp. 164-168
Author(s):  
Jian Jun Su ◽  
Men Yue Hu ◽  
Hong Yan Gong ◽  
Hai Tao Sun ◽  
Zhi Jian Hu ◽  
...  
Keyword(s):  
Control Strategy ◽  
Photovoltaic System ◽  
Current Loop ◽  
Maximum Power Point ◽  
Loop Control ◽  
Point Tracking ◽  
Power Point Tracking ◽  
Three Phase ◽  
Power Point ◽  
Research Situation

Firstly the research situation for grid-connected photovoltaic (PV) is introduced, then, the engineering mathematical model of PV cells is introduced. The perturbation and observation algorithm is chosen as the maximum power point tracking (MPPT) algorithm. The SPWM double-loop control strategy with outer voltage loop and inner current loop is described and a three-phase grid-connected photovoltaic model is established. The simulation results demonstrate the validity and correctness of the simulation model built in this paper.

scholarly journals Design of a 2-DOF Control and Disturbance Estimator for a Magnetic Levitation System

2017 ◽  
Vol 7 (1) ◽  
pp. 1369-1376 ◽  
Author(s):  
A. Pati ◽  
V. C. Pal ◽  
R. Negi
Keyword(s):  
Control Strategy ◽  
Magnetic Levitation ◽  
Open Loop ◽  
Loop Control ◽  
Set Point ◽  
Point Tracking ◽  
Load Disturbance ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Disturbance Estimator

This work proposes a systematic two-degree freedom control scheme to improve the reference input tracking and load disturbance rejection for an unstable magnetic levitation system. The proposed control strategy is a two-step design process. Firstly, a proportional derivative controller is introduced purposely to get the desired set-point response of the magnetic levitation system and then, an integral square error (ISE) performance specification is used for designing a set-point tracking controller. Secondly, a disturbance estimator is designed using the desired closed loop complimentary sensitivity function for the rejection of load disturbances. This leads to the decoupling of the nominal set-point response from the load disturbance response similar to an open loop control manner. Thus, it is convenient to optimize both controllers simultaneously as well as separately. The effectiveness of the proposed control strategy is validated through simulation.

Error estimates for Neumann boundary control problems with energy regularization

2016 ◽  
Vol 24 (4) ◽  
Author(s):  
Thomas Apel ◽  
Olaf Steinbach ◽  
Max Winkler
Keyword(s):  
Error Estimates ◽  
Boundary Control ◽  
Convergence Rates ◽  
Piecewise Linear ◽  
Control Variable ◽  
Neumann Boundary ◽  
State Equation ◽  
Piecewise Constant ◽  
Boundary Control Problems ◽  
Unconstrained Problems

AbstractA Neumann boundary control problem for a second order elliptic state equation is considered. The problem is regularized by an energy term which is equivalent to theThe state and co-state are approximated by piecewise linear finite elements. For the approximation of the control variable we use carefully designed spaces of piecewise linear or piecewise constant functions, such that an inf-sup condition is satisfied. Error estimates for the approximate solution are proved for all three variables and we show a relation between convergence rate and the opening angles at corners of the domain. As the control grows in general unboundedly near the concave corners for unconstrained problems, it becomes active and hence regular when control constraints are present. We show that in this case the convergence rates are higher than in the unbounded case. Numerical tests suggest that the estimates derived are optimal in the unconstrained case but too pessimistic in the control constrained case.

Research on Control Strategy of Hydro-Viscous Driven Fan Cooling System

2014 ◽  
Vol 722 ◽  
pp. 182-189
Author(s):  
Li Gang Ma ◽  
Chang Le Xiang ◽  
Tian Gang Zou ◽  
Fei Hong Mao
Keyword(s):  
Control Strategy ◽  
Cooling System ◽  
Fuzzy Pid ◽  
Loop Control ◽  
Speed Regulation ◽  
Temperature Feedback ◽  
Loop Control System ◽  
System Temperature ◽  
Fan Cooling ◽  
Fan Speed

The paper proposes a cascade control strategy of speed feedback in inner loop and temperature feedback in outer ring for hydro-viscous driven fan cooling system, and compares the simulation of PID and fuzzy PID. The simulation result shows that the double-loop control system while the response time longer, but much smaller overshoot, can achieve a good feedback to adjust the fan speed and temperature and realize stepless speed regulation of hydro-viscous driven fan cooling system under the premise of stability for fan speed and system temperature.

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