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Stability and stabilization of a delayed PIDE system via SPID control

NEURAL COMPUTING & APPLICATIONS 2017年第12期28卷 4139-4145页

作者： Yang, Chengdong Zhang, Ancai Chen, Xiao Chen, Xiangyong Qiu, Jianlong Linyi Univ Sch Informat Linyi 276005 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China Linyi Univ Sch Automobile Engn Linyi 276005 Peoples R China Linyi Univ Sch Sci Linyi 276005 Peoples R China

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results.

关键词： Partial integro-differential equation distributed parameter system Exponential stabilization Linear matrix inequality

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MODEL-REDUCTION AND CONTROL OF FLEXIBLE STRUCTURES USING KRYLOV VECTORS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1991年第2期14卷 260-267页

作者： SU, TJ CRAIG, RR UNIV TEXAS AEROSP ENGN & ENGN MECHAUSTINTX 78712

Krylov vectors and the concept of parameter matching are combined together to develop a model reduction algorithm for a damped structural dynamics system. The obtained reduced-order model matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, three types of control energy spillover generally exist: control, observation, and dynamic. The formulation based on Krylov vectors can eliminate both the control and observation spillovers while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method.

关键词： Flexible Structures Structural Dynamics distributed parameter system Finite Element Modeling Model Order Reduction Proportional Damping Linear Quadratic Gaussian Trusses Eigensystem Realization Algorithm Displacement Sensor

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Disturbance Rejection Control for a Vibrating String system

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ASIAN JOURNAL OF CONTROL 2019年第3期21卷 1367-1376页

作者： Zhao, Zhijia Xiao, Ying Li, Zhifu Liu, Hua Guangzhou Univ Sch Mech & Elect Engn Guangzhou 510006 Guangdong Peoples R China Guangzhou Univ Adv Technol Ctr Special Equipment Guangzhou 510006 Guangdong Peoples R China

This paper is concerned with disturbance rejection control for a vibrating flexible string system in the presence of unknown disturbances. First, the boundary disturbance observer is proposed to deal with the boundary disturbance and the infinite dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. Subsequently, the boundary control and distributed control are developed to suppress the vibration and globally stabilize the string system at its equilibrium position. Under the control proposed, the uniformly bounded stability of the controlled system is testified employing rigorous analysis without resorting to discretization of the partial differential equation dynamics depending on the time and space. Finally, the simulation and comparison results verify the performance of the derived control.

关键词： distributed parameter system disturbance rejection control boundary control distributed control disturbance observer

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Numerical Modeling and Control of the Dynamic Single Silicon Crystal Growth Process

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IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING 2021年第1期34卷 94-103页

作者： Zhang, Ni Liu, Ding Wan, Yin Xian Univ Posts & Telecommun Sch Automat Xian Key Lab Adv Control & Intelligent Proc Xian 710121 Peoples R China Xian Univ Technol Shaanxi Key Lab Complex Syst Control & Intelligen Xian 710048 Peoples R China

A new control strategy combing the Finite Element Method (FEM) with the control method is proposed to study the control of crystal growth process in this article. In the proposed control strategy, the crystal diameter control loop and the crystal temperature control loop are designed respectively to meet the requirements on crystal diameter and crystal temperature distribution. In the crystal diameter control loop, a bio-heuristic model based PID controller is designed to control crystal diameter. In the crystal temperature control loop, considering the undetectable characteristic of temperature distribution inside crystal, the control of crystal temperature distribution is transformed into the control of a key monitoring point in crystal and the constraint of crystal temperature gradient, and a model reference adaptive temperature controller is designed to achieve the control of the monitoring point temperature. Simulation results show that the crystal diameter and the temperature of the monitoring point are controlled well. Furthermore, the internal temperature distribution inside crystal is constrained within a reasonable range, avoiding the excessive thermal stress and dislocation defects. The proposed control strategy solves the problem of the traditional crystal growth system which cannot control crystal temperature, providing a new way for growing high-quality single silicon crystal.

关键词： Crystals Temperature distribution Heating systems Temperature measurement Optimization Mathematical model Semiconductor device modeling Crystal growth process control FEM modeling bio-heuristic inspired model distributed parameter system

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Controlling the Heating of a Rod Using the Current and Preceding Time Feedback

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AUTOMATION AND REMOTE CONTROL 2022年第1期83卷 106-122页

作者： Aida-zade, K. R. Abdullayev, V. M. Azerbaijan Natl Acad Sci Inst Control Syst AZ-1141 Baku Azerbaijan Azerbaijan Natl Acad Sci Inst Math & Mech AZ-1141 Baku Azerbaijan Azerbaijan State Oil & Ind Univ AZ-1010 Baku Azerbaijan

Using the process of heating a rod in a furnace as an example, we study the feedback control synthesis problem for plants with distributed parameters. To form the control values, it is proposed to use their linear dependence on the state values at the points of measurement, both at the current and at the preceding moments of time. The unknown coefficients involved in this dependence of the control on the measured state values are the feedback parameters. They are determined by minimizing the objective functional using first-order numerical optimization methods. To this end, formulas for the gradient of the objective functional with respect to the feedback parameters are obtained. The results of numerical experiments are presented.

关键词： distributed parameter system heating process feedback gain control point gradient of a functional feedback parameter

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Control Design for Nonlinear Flexible Wings of a Robotic Aircraft

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IEEE TRANSACTIONS ON CONTROL systemS TECHNOLOGY 2017年第1期25卷 351-357页

作者： He, Wei Zhang, Shuang Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing 100083 Peoples R China Univ Elect Sci & Technol China Sch Aeronaut & Astronaut Chengdu 611731 Peoples R China

In this brief, the control problem for flexible wings of a robotic aircraft is addressed by using boundary control schemes. Inspired by birds and bats, the wing with flexibility and articulation is modeled as a distributed parameter system described by hybrid partial differential equations and ordinary differential equations. Boundary control for both wing twist and bending is proposed on the original coupled dynamics, and bounded stability is proved by introducing a proper Lyapunov function. The effectiveness of the proposed control is verified by simulations.

关键词： Boundary control distributed parameter system flexible wings microaerial vehicle (MAV) robot vibration control

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End-Point Regulation and Vibration Suppression of a Flexible Robotic Manipulator

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ASIAN JOURNAL OF CONTROL 2017年第1期19卷 245-254页

作者： Zhang, Shuang Huang, Deqing Univ Elect Sci & Technol China Sch Aeronaut & Astronaut Chengdu 611731 Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China

In this paper, end-point regulation and vibration suppression are investigated for a flexible robotic manipulator subject to the external disturbances. The dynamics of the flexible robotic manipulator is represented by one partial differential equation (PDE) and five ordinary differential equations (ODEs). Based on the Lyapunov's direct method, boundary control is developed to drive the manipulator to the desired set-point and simultaneously suppress the vibrations of the flexible manipulator. Considering the unknown spatiotemporally varying disturbance, uniform boundedness of the closed-loop system is achieved. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulations are provided to illustrate the effectiveness of the proposed control.

关键词： Flexible robotic manipulator vibration control adaptive control distributed parameter system

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Spectral uncertainty modelling from experimental data with application to robust modal control of a packed-bed column

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JOURNAL OF CHEMICAL ENGINEERING OF JAPAN 2003年第1期36卷 25-34页

作者： Elisante, E Yoshida, M Matsumoto, S Tohoku Univ Dept Chem Engn Sendai Miyagi 9808579 Japan

In recent years robust control theory has met wide acceptance and made significant advances especially in terms of development of tools for analysis and design. However, the application of those tools, like the H-infinity optimal theory and mu-synthesis in MATLAB, to real-time control of chemical processes has not been very successful. Among the factors hindering widespread application is lack of systematic way to model uncertainty that occurs at different locations in the feedback structure. In this work, time series data is used to model additive plant uncertainty through power spectral methods by performing least-squares regression in frequency domain. The concept is illustrated for real-time control of axial temperature distribution in a packed-bed column, which is modelled by partial differential equations and Fourier transforms to obtain an eigen-mode plant for controller design and robust analysis. Spectral uncertainty description is obtained from error analysis of smooth signals from the nominal and the perturbed plant and robustness is evaluated using the structured singular value (SSV). It is shown that through a proper choice of parameters, the spectral method gives better uncertainty description for robustness analysis than parametric methods.

关键词： process control distributed parameter system robust control spectral uncertainty description packed-bed column

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Output-Feedback Control of an Extended Class of Sandwiched Hyperbolic PDE-ODE systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2021年第6期66卷 2588-2603页

作者： Wang, Ji Krstic, Miroslav Univ Calif San Diego Dept Mech & Aerosp Engn La Jolla CA 92093 USA

Motivated by an engineering application in brake control of cable mining elevators, where the dynamics consist of a brake, a shock absorber, a time-varying-length cable, and a cage, we address a theoretical problem of control of a particular class of coupled hyperbolic PDEs sandwiched between a nonlinear ODE on the actuated side and a linear ODE on the opposite side, with a PDE domain that is time-varying. A state-feedback controller entering a single ODE state is designed to exponentially stabilize the overall system through several backstepping transformations. An observer which only uses the boundary values at the actuated side is constructed to recover all the states of the overall system, based on which a "collocated" type output-feedback control system is proposed. The global exponential stability of the closed-loop system, boundedness, and exponential convergence of the controller, are proved via Lyapunov analysis. The performance is investigated via numerical simulation.

关键词： Backstepping boundary control distributed parameter system hyperbolic PDE

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Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

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TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL 2019年第9期41卷 2666-2677页

作者： Fu, Yun Liu, Yu Huang, Daoping South China Univ Technol Sch Automat Sci & Engn Guangzhou Guangdong Peoples R China

In this paper, the vibration suppression problem of a flexible satellite system is addressed. The dynamic model of the flexible satellite system is expressed by a set of non-homogeneous partial differential equations (PDEs). By using the theory of systems with uniform ultimate bounded (UUB) solutions and adaptive techniques, adaptive boundary control is presented to suppress the vibration of the flexible satellite with parametric uncertainties. A disturbance adaptive law is constructed to compensate for the effect of the boundary disturbance, and an auxiliary system is considered to mitigate the effect of input saturation. The well-posedness of the closed-loop system is discussed, and UUB stability can be ensured through a rigorous Lyapunov-like analysis. Numerical simulation results show the effectiveness of the proposed control scheme.

关键词： Adaptive boundary control distributed parameter system disturbance adaptive law vibration control input saturation

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