On Transfer Function Zeros of General Colocated Control Systems With Mechanical Flexibilities

1994 ◽  
Vol 116 (1) ◽  
pp. 151-154 ◽  
Author(s):  
Denny K. Miu ◽  
Bingen Yang
Keyword(s):  
Transfer Function ◽  
Control Systems ◽  
Complex Conjugate ◽  
Distributed Parameter ◽  
Flexible Control ◽  
Linear Elastic ◽  
Sensor Actuator ◽  
Uniform Cross Section ◽  
Function Zeros ◽  
Additional Constraints

In our previous work, it was shown that for simple control systems with mechanical flexibilities such as spring-mass systems or uniform cross-section linear elastic beams, the complex conjugate transfer function zeros can be interpreted as the resonances of a sub-portion of the flexible structure with additional constraints imposed by the sensor and actuator. In this paper, the aforementioned intuitive physical observation is verified mathematically for general lumped and distributed parameter flexible control systems with colocated sensor/actuator.

Physical Interpretation of Transfer Function Zeros for Simple Control Systems With Mechanical Flexibilities

1991 ◽  
Vol 113 (3) ◽  
pp. 419-424 ◽  
Author(s):  
D. K. Miu
Keyword(s):  
Transfer Function ◽  
Control Systems ◽  
Physical Interpretation ◽  
Complex Conjugate ◽  
Flexible Structure ◽  
Resonant Frequencies ◽  
Nonminimum Phase ◽  
Flexible Control ◽  
Real Zeros ◽  
Function Zeros

Physical interpretation of the transfer function zeros of simple control systems with mechanical flexibilities is presented. It is shown that for discrete spring-mass systems and elastic beams, the poles are the resonant frequencies of the flexible structure and the complex conjugate zeros are the resonant frequencies of a substructure constrained by the sensor and actuator. It is also shown that when the flexible control systems become nonminimum phase, the real zeros are the results of nonpropagation of energy within the substructure.

scholarly journals Numerical optimization of the transfer function of the intelligent building management system

2019 ◽  
Vol 97 ◽  
pp. 01015
Author(s):  
Pavel Sadchikov ◽  
Tatyana Khomenko ◽  
Galina Ternovaya
Keyword(s):  
Transfer Function ◽  
Control Systems ◽  
Numerical Optimization ◽  
Parametric Models ◽  
Complex Conjugate ◽  
Intelligent Building ◽  
Building Management ◽  
Building Management System ◽  
And Control ◽  
Energy Information

The paper deals with structural-parametric models for describing dynamic processes of technical systems of an intelligent building. The task of searching for the transfer function of the synthesized elements and devices of its information-measuring and control systems based on the Mason method is formalized. The components of the transfer function are presented in the form of characteristic polynomials in the structural scheme of the energy-information model of the circuit. The results of a comparative analysis of search methods for multiple real and complex conjugate polynomial roots are presented. To organize their search, an iterative method of unconditional optimization of Fletcher-Reeves was chosen. This conjugate gradient method allows to solve the problem of numerical optimization in a finite number of steps and shows the best convergence in comparison with the methods of the fastest descent, with the same order of difficulty of performing the steps of the algorithm.

scholarly journals State Estimation for a Class of Distributed Parameter Systems with Time-Varying Delay over Mobile Sensor–Actuator Networks with Missing Measurements

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 661
Author(s):  
Huansen Fu ◽  
Baotong Cui ◽  
Bo Zhuang ◽  
Jianzhong Zhang
Keyword(s):  
State Estimation ◽  
Distributed Parameter Systems ◽  
Operator Semigroup ◽  
Distributed Parameter ◽  
Time Varying ◽  
Mobile Sensor ◽  
Missing Measurements ◽  
Time Varying Delay ◽  
Sensor Actuator ◽  
Varying Delay

This work proposes a state estimation strategy over mobile sensor–actuator networks with missing measurements for a class of distributed parameter systems (DPSs) with time-varying delay. Initially, taking advantage of the abstract development equation theory and operator semigroup method, this kind of delayed DPSs described by partial differential equations (PDEs) is derived for evolution equations. Subsequently, the distributed state estimators including consistency component and gain component are designed; the purpose is to estimate the original state distribution of the delayed DPSs with missing measurements. Then, a delay-dependent guidance approach is presented in the form of mobile control forces by constructing an appropriate Lyapunov function candidate. Furthermore, by applying Lyapunov stability theorem, operator semigroup theory, and a stochastic analysis approach, the estimation error systems have been proved asymptotically stable in the mean square sense, which indicates the estimators can approximate the original system states effectively when this kind of DPS has time-delay and the mobile sensors occur missing measurements. Finally, the correctness of control strategy is illustrated by numerical simulation results.

Physical Properties of Transfer Function Zeros for Collocated Control in Flexible Structure System

1995 ◽  
Author(s):  
Chingyei Chung ◽  
Chin-yuh Lin
Keyword(s):  
Transfer Function ◽  
Circulatory System ◽  
Flexible Structure ◽  
Structure System ◽  
Zero Dynamic ◽  
Damping Matrix ◽  
Generalized Force ◽  
Function Zeros ◽  
Gyroscopic Systems ◽  
Collocated Control

Abstract In this paper, the physical meaning of transfer function zeros for collocated control in a general flexible structure system is discussed. For a flexible structure system, we propose the “Zero Dynamic Theorem”. The theorem states that in a flexible structure system, the flexible structure can be a circulatory system (non-sysmetric stiffness matrix) with viscous and gyroscopic damping (non-symmetric damping matrix), if the sensor output (generalized displacement) and the actuator input (generalized force) are “dual type” and the transfer function is strict proper and coprime (no pole/zero cancellation); then, the transfer function zeros are the natural frequencies of constrained structure. Furthermore, with this theorem, the interlacing pole/zero property for the gyroscopic systems is presented.

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

1993 ◽  
Author(s):  
Bingen Yang ◽  
Houfei Fang
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
State Space ◽  
Fundamental Matrix ◽  
Function Analysis ◽  
Distributed Parameter Systems ◽  
System Response ◽  
Distributed Parameter ◽  
Transfer Function Analysis ◽  
Function Formulation

Abstract This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

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