On the absolute stability approach to quantized feedback control

Automatica ◽  
2010 ◽  
Vol 46 (2) ◽  
pp. 337-346 ◽  
Author(s):  
Bin Zhou ◽  
Guang-Ren Duan ◽  
James Lam
Keyword(s):  
Feedback Control ◽  
Absolute Stability ◽  
Quantized Feedback ◽  
The Absolute

scholarly journals Condition Absolute Stability Control System of Electromagnetoelastic Actuator for Communication Equipment

2020 ◽  
Vol 8 (1) ◽  
pp. 08-15 ◽  
Author(s):  
Sergey Mikhailovich Afonin
Keyword(s):  
Control System ◽  
Absolute Stability ◽  
Stability Control ◽  
Straight Line ◽  
Stability Control System ◽  
Stationary Set ◽  
The Absolute ◽  
Communication Equipment ◽  
Stable Control

We obtained the condition absolute stability on the derivative for the control system of electromagnetoelastic actuator for communication equipment. We applied the frequency methods for Lyapunov stable control system to calculate the condition absolute stability control system of electromagnetoelastic actuator. We used Yakubovich criterion absolute stability system with the condition on the derivative. The aim of this work is to determine the condition of the absolute stability on the derivative for the control system of electromagnetoelastic actuator. We received the stationary set of the control system of the hysteresis deformation of the electromagnetoelastic actuator. The stationary set is the segment of the straight line.

A Test-Based Methodology for A Priori Selection of Gain/Phase Relationships in Proportional, Phase-Shifting Control of Combustion Instabilities

2000 ◽  
Author(s):  
Michael A. Vaudrey ◽  
William R. Saunders ◽  
Bryan Eisenhower
Keyword(s):  
Feedback Control ◽  
Frequency Response ◽  
Limit Cycle ◽  
Design Method ◽  
Phase Relationship ◽  
Operating Conditions ◽  
Phase Shifting ◽  
Nonlinear Phenomena ◽  
The Absolute ◽  
Instability Frequency

Feedback control system design, for general single-in-single-out (SISO) applications, requires accurate knowledge of the loop transfer function. Active combustion control design is usually implemented using such SISO architectures, but is quite challenging because the thermoacoustic response results from a relatively unknown, self-excited system and nonlinear processes that must be understood before learning the gain/phase relationship of the system precisely at the instability frequency. However, recent experiments have shown that it is possible to obtain accurate measurements of the relevant loop transfer (frequency response) functions at frequencies adjacent to the instability frequency. Using a simple tube combustor, operating with a premixed, gaseous, burner-stabilized flame, the loop frequency response measurements have been used to develop a methodology that leads to ‘test-based predictions’ of the absolute phase settings and ‘best’ gain settings for a proportional, phase-shifting controller commanding an acoustic actuator in the combustor. The contributions of this methodology are twofold. First, it means that a manual search for the required phase setting of the controller is no longer necessary. In fact, this technique allows the absolute value of controller phase to be determined without running the controller. To the authors’ knowledge, this has not been previously reported in the literature. In addition, the ‘best’ gain setting of the controller, based on this new design approach, can be defined as one that eliminates or reduces the limit cycle amplitude as much as possible within the constraint of avoiding generation of any controller-induced instabilities. (This refers to the generation of ‘new’ peaks in the controlled acoustic pressure spectrum.) It is shown that this tradeoff in limit cycle suppression and avoidance of controller-induced instabilities is a manifestation of the well-known tradeoff in the sensitivity/complementary sensitivity function for feedback control solutions. The focus of this article is limited to the presentation of the design method and does not discuss the detailed nonlinear phenomena that must be understood to determine the optimal gain/phase settings at the limit cycle frequency for a real (versus theoretical) combustor system. A companion paper describes how the proposed design method can be used to generate an AI controller that maintains stabilizing control for a range of changing operating conditions.

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