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.

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 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.

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.

A Method of Model Reduction

1986 ◽  
Vol 108 (4) ◽  
pp. 368-371 ◽  
Author(s):  
Jium-Ming Lin ◽  
Kuang-Wei Han
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Model Reduction ◽  
Control Systems ◽  
Response Curve ◽  
Nonlinear Control Systems ◽  
Frequency Response Curve ◽  
Stability Boundaries ◽  
Parameter Variations ◽  
The Stability

In this brief note, the effects of model reduction on the stability boundaries of control systems with parameter variations, and the limit-cycle characteristics of nonlinear control systems are investigated. In order to reduce these effects, a method of model reduction is used which can approximate the original transfer function at S=0, S=∞, and also match some selected points on the frequency response curve of the original transfer function. Examples are given, and comparisons with the methods given in current literature are made.

EFFECT OF SECONDARY PATH NONLINEARITY IN ACTIVE NOISE CONTROL SYSTEMS BEHAVIOR

2005 ◽  
Vol 05 (02) ◽  
pp. L143-L151 ◽  
Author(s):  
F. TARINGOO ◽  
J. POSHTAN ◽  
M. H. KAHAEI
Keyword(s):  
Transfer Function ◽  
Control Systems ◽  
Noise Control ◽  
Actuator Saturation ◽  
Active Noise Control ◽  
State Behavior ◽  
Statistical Solution ◽  
Acoustic Transducers ◽  
Active Noise ◽  
Saturation Effects

In this paper the behavior of an active noise control system is analyzed considering the nonlinearity of the secondary path transfer function. This nonlinearity may be due to actuator saturation in the operating condition. The statistical solution of the filter weighs adaptation and convergence behavior are obtained. It is shown that the degree of nonlinearity and the error estimation of secondary path transfer function can affect the transient and steady state behavior. The saturation function is considered as a nonlinear system in adaptive filter output. This function models saturation effects in active noise control systems when the acoustic transducers are driven by large-amplitude signals.

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