scholarly journals Minimum-Phase Second-Order Systems and the Spectrum of the Semigroup Generator

PAMM ◽  
2006 ◽  
Vol 6 (1) ◽  
pp. 631-632
Author(s):  
Birgit Jacob ◽  
Kirsten Morris ◽  
Carsten Trunk
Keyword(s):  
Second Order ◽  
Minimum Phase ◽  
Second Order Systems ◽  
Semigroup Generator

Placing Minimum Phase Zeros to Shape Transient Response: Generalization From Control of Hybrid Power Systems

2017 ◽  
Author(s):  
Bilal S. Salih ◽  
Tuhin K. Das
Keyword(s):  
Power Systems ◽  
Transient Response ◽  
Transfer Functions ◽  
Higher Order ◽  
Second Order ◽  
Step Response ◽  
Minimum Phase ◽  
Hybrid Power Systems ◽  
Hybrid Power ◽  
Second Order Systems

Conservation of energy can be applied in designing control of hybrid power systems to manage power demand and supply. In practice, it can be used for designing decentralized controllers. In this paper, this idea is analyzed in a generalized theoretical framework. The problem is transformed to that of using minimum phase zeros to generate a specific type of transient response admitted by dynamical systems. Here, the transient step response is shaped using an underlying conservation principle. In this paper, emphasis is placed on second order systems. However, the analysis can be extended to higher order transfer functions. Analytical results relating zero location to the matched/ mismatched areas of the transient response are established for a class of second order systems. A combination of feedback and feedforward actions are shown to achieve the desired zero placement/addition and the desired transient response. The proposed analysis promises extension to nonlinear systems. Optimization studies also seem appropriate, especially for higher order transfer functions.

Novel control strategy for non-minimum-phase unstable second order systems: generalised predictor based approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Anil Bhaskaran ◽  
Chandramohan Goud Ediga ◽  
Seshagiri Rao Ambati
Keyword(s):  
Time Delay ◽  
Direct Synthesis ◽  
Synthesis Method ◽  
Absolute Error ◽  
Second Order ◽  
Delay Systems ◽  
Minimum Phase ◽  
Current Output ◽  
Servo Tracking ◽  
Second Order Systems

Abstract A control structure based on generalized predictor is proposed to control non-minimum phase unstable second order processes with time delay. The scheme contains a predictor structure and a direct synthesis method based primary controller for servo tracking. The predictor structure consists of two filters acting on input and current output which are designed to provide noise attenuation and disturbance rejection. A set-point filter minimises the overshoot caused by the introduction of additional zeros of the controller in the overall closed loop transfer function so as to smooth the tracking performance. Different second order unstable time delay systems are considered and Integral Absolute Error (IAE) and Total Variation (TV) measures are used for comparing the performances quantitatively. The method is implemented experimentally on an inverted pendulum. The proposed predictive strategy is found to provide enhanced control performances in comparison to the existing literature methods.

Minimum-Phase Infinite-Dimensional Second-Order Systems

2007 ◽  
Vol 52 (9) ◽  
pp. 1654-1665 ◽  
Author(s):  
Birgit Jacob ◽  
Kirsten Morris ◽  
Carsten Trunk
Keyword(s):  
Second Order ◽  
Minimum Phase ◽  
Infinite Dimensional ◽  
Second Order Systems

scholarly journals ℋ∞ Control Tunning to Guarantee the Output Performance of LTI Second-Order Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 4611-4616
Author(s):  
Ramón I. Verdés ◽  
Luis T. Aguilar ◽  
Yury Orlov
Keyword(s):  
Second Order ◽  
Output Performance ◽  
Second Order Systems

scholarly journals Search Patterns Based on Trajectories Extracted from the Response of Second-Order Systems

2021 ◽  
Vol 11 (8) ◽  
pp. 3430
Author(s):  
Erik Cuevas ◽  
Héctor Becerra ◽  
Héctor Escobar ◽  
Alberto Luque-Chang ◽  
Marco Pérez ◽  
...  
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Search Space ◽  
Second Order ◽  
Order System ◽  
Search Patterns ◽  
Multiple Behaviors ◽  
Complex Optimization ◽  
Second Order Systems ◽  
Order Algorithm

Recently, several new metaheuristic schemes have been introduced in the literature. Although all these approaches consider very different phenomena as metaphors, the search patterns used to explore the search space are very similar. On the other hand, second-order systems are models that present different temporal behaviors depending on the value of their parameters. Such temporal behaviors can be conceived as search patterns with multiple behaviors and simple configurations. In this paper, a set of new search patterns are introduced to explore the search space efficiently. They emulate the response of a second-order system. The proposed set of search patterns have been integrated as a complete search strategy, called Second-Order Algorithm (SOA), to obtain the global solution of complex optimization problems. To analyze the performance of the proposed scheme, it has been compared in a set of representative optimization problems, including multimodal, unimodal, and hybrid benchmark formulations. Numerical results demonstrate that the proposed SOA method exhibits remarkable performance in terms of accuracy and high convergence rates.

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