The bode diagram: An approach to regulating-system stability fundamentals

Koenig, L. A.

doi:10.1109/ee.1959.6445745

Cited by 3 publications

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“…(i) With the rapid development of electronics and automated machines, the control of the LTIS stability often favored the factorization of the transfer function H, in the simple form of the ratio of complex polynomials [24], in order to monitor the evolution of the phase and amplitude with respect to the frequency in Bode diagrams [25]. In electronics and automatic system control, singularities and zeros of multiple-order are not uncommon (nth order Butterworth filters [26] for instance).…”

Section: Introductionmentioning

confidence: 99%

Multiple-order singularity expansion method

Ben Soltane,

Colom,

Dierick

et al. 2023

New J. Phys.

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Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific complex frequencies could be used to describe both ordinary and exceptional physical properties. In particular, expansions and factorized forms of the harmonic-domain functions in terms of their poles and zeros under multiple physical considerations have been used. In this work, we start from a general property of continuity and differentiability of the complex functions to derive the multiple-order singularity expansion method. We rigorously derive the common singularity and zero expansion and factorization expressions, and generalize them to the case of singularities of arbitrary order, whilst deducing the behaviour of these complex frequencies from the simple hypothesis that we are dealing with physically realistic signals.

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Section: Introductionmentioning

confidence: 99%

Multiple-order singularity expansion method

Ben Soltane,

Colom,

Dierick

et al. 2023

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…(i)-With the rapid development of electronics and automated machines, the control of the LTIS stability often favoured the factorization of the transfer function H, in the simple form of the ratio of complex polynomials [24], in order to monitor the evolution of the phase and amplitude with respect to the frequency in Bode diagrams [25]. In electronics and automatic system control, singularities and zeros of multiple-order are not uncommon (n th order Butterworth filters [26] for instance).…”

Section: Introductionmentioning

confidence: 99%

Multiple-Order Singularity Expansion Method

Soltane¹,

Colom²,

Dierick³

et al. 2023

Preprint

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Graphical Control Tools to Design Control Systems

Liu¹,

Zhao²,

Yu³

2017

Proceedings of the 2017 5th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering (ICMMCCE 20

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Abstract:Engineers are sometimes asked to analyze the feasibility of existing control systems or design a new system. The conventional analysis and design methods heavily depend on mathematical calculation. In order to minimize calculation, graphical control is proposed. This paper aims to introduce three different graphical control tools (Root Locus, Bode diagram and Nyquist diagram) and then use these tools to analyze and design the control system. Finally, some realistic case studies are used to compare the advantages and disadvantages of graphical tools. The innovation of this paper is adding hand-drawn graphical control to greatly reduce the calculation complexity List of SymbolsTs-settling time (s) -damping ratio n -natural frequency (rad.s -1) %OS-percentage of overshoot Ess-steady state error K-gain of the system Z 1 , Z 2 -zeros of the system P 1 , P 2 -poles of the system T p -peak time (s) M-magnitude of the phasor Φ-phase angle of phasor (degrees) Θ-angle of asymptote Z-the number of closed loop poles P-the number of open-loop poles Nthe number of counter clockwise rotation P M -phase margin (degrees) G M -gain margin h 1 , h 2 -feedback coefficient IntroductionClassical control theory, modern control theory and robust control theory are commonly used today. In advanced engineering and science, automatic control plays a very important role. There are many applications using control systems: examples include rocket firing systems, splashing cooling water systems and car engine systems. Control theory is becoming incredibly important in daily life. [1][2]It is now well known the response of closed-loop system is much faster than the open-loop. Thus more mathematical methods were developed to solve the closed-loop control, however they are not straightforward. [3] A system's performance will be greatly influenced by the position of the poles, especially by a pair of dominant poles. Since conventional mathematical techniques are too complex to effectively analyze the system, new graphical methods have been proposed to analyze the performance of control system. [4] In [5], Kinnen proposes a graphical control method to control multivariable control systems, a significant breakthrough in the control area. Compared with the traditional method (utilizing matrix formulation), the calculation is greatly reduced. In [6] O'Brien attempts to design a discrete control system, simply based on the Root Locus method. In [7], Koenig worked on analyzing a system's frequency response and then determining the stability of the control system using a Bode diagram. In This paper focusses on an improved process to design the system in a simple way and analyze which graphical technique should be used in different cases.

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The bode diagram: An approach to regulating-system stability fundamentals

Cited by 3 publications

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Multiple-order singularity expansion method

Multiple-order singularity expansion method

Multiple-Order Singularity Expansion Method

Graphical Control Tools to Design Control Systems

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