Graphical method of prediction of limit cycle for multivariable nonlinear systems

Patra, K.C.; Singh, Yash Pal

doi:10.1049/ip-cta:19960520

Cited by 14 publications

(21 citation statements)

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“…G 1 , G 2 are the transfer functions of the linear elements. The graphical method based on normalised phasor diagram [21,26] is used for prediction of limit cycle in the system which has been illustrated through an example. The whole system is assumed to exhibit oscillation predominantly at a single frequency.…”

Section: B2 Backlash Nonlinearity B21 Graphical Methodsmentioning

confidence: 99%

“…4a. Following the procedure as outlined in [23], the limit cycle is predicted using the digital simulation technique.…”

Section: B12 Digital Simulationmentioning

confidence: 99%

“…Consider a system having two interconnected subsystems as given in Fig. 1, which represents a class of general 2 × 2 systems [25,26]. In the system N 1 , N 2 are two nonlinear elements with Rectangular Hysteresis input-output characteristics as shown in Fig.…”

Section: A Introductionmentioning

confidence: 99%

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Archives of Control Sciences

Patra¹,

Dakua²

2018

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The paper presents a simple, systematic and novel graphical method which uses computer graphics for prediction of limit cycles in two dimensional multivariable nonlinear system having rectangular hysteresis and backlash type nonlinearities. It also explores the avoidance of such self-sustained oscillations by determining the stability boundary of the system. The stability boundary is obtained using simple Routh Hurwitz criterion and the incremental input describing function, developed from harmonic balance concept. This may be useful in interconnected power system which utilizes governor control. If the avoidance of limit cycle or a safer operating zone is not possible, the quenching of such oscillations may be done by using the signal stabilization technique which is also described. The synchronization boundary is laid down in the forcing signal amplitudes plane using digital simulation. Results of digital simulations illustrate accuracy of the method for 2 × 2 systems.

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Section: B2 Backlash Nonlinearity B21 Graphical Methodsmentioning

confidence: 99%

“…4a. Following the procedure as outlined in [23], the limit cycle is predicted using the digital simulation technique.…”

Section: B12 Digital Simulationmentioning

confidence: 99%

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Archives of Control Sciences

Patra¹,

Dakua²

2018

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“…Katebi [14] extended the graphical techniques to multi-loop systems with coupled multivalued nonlinear elements. Patra, et al [15] suggested another graphical method based on phasor diagram which particularly gave accurate limit cycle prediction for relay systems. Paoletti, et al [16] presented a Computer Aided Design tool for limit cycle prediction in single loop nonlinear systems which are aimed at educational purposes.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Search for Limit Cycle and Controller Design in Multivariable Nonlinear Systems

Eftekhari

Katebi

2006

Asian Journal of Control

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A feature of many practical control systems is a Multi‐Input Multi‐Output (MIMO) interactive structure with one or more gross nonlinearities. A primary controller design task in such circumstances is to predict and ensure the avoidance of limit cycling conditions followed by achieving other design objectives. This paper outlines how such a system may be investigated using the Sinusoidal Input Describing Function (SIDF) philosophy quantifying magnitude, frequency and phase of any possible limit cycle operation. While Sinusoidal Input Describing function is a suitable linearization technique in the frequency domain for assessment of stability and limit cycle operation, it can not be employed in time domain. In order to be able to incorporate the time domain requirements in an overall controller design technique, the appropriate linearization technique suggested here is the Exponential Input Describing Function (EIDF). First, an evolutionary search based on a multi‐objective formulation is employed for the direct solution of the harmonic balance system matrix equation. The search is based on Multi‐Objective Genetic Algorithms (MOGA) and is capable of predicting specified modes of theoretically possible limit cycle operation. Second, the design requirements in time as well as frequency domain are formulated by a set of constraint inequalities. A numerical synthesis procedure also based on Multi‐Objective Genetic Algorithm is employed to adjust the initial compensator parameters to meet the imposed constraints. Robust stability and robust performance are investigated with respect to linearization uncertainty within the context of multiobjective formulation. In order to make the Genetic Algorithm (GA) search more amenable to design trade‐off between different and often contradictory specifications, a weighted sum of the functions is introduced. This criterion is subsequently optimized subject to the nonlinear system dynamics and a set of design requirements. Examples of use are given to illustrate the effectiveness of the proposed approach.

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“…These methods are based upon the graphical or numerical solutions of the linearized harmonic-balance equations [1][2][3][4][5][6][7][8][9][10]. It has been shown that for multivariable systems, over arbitrary ranges of amplitudes (A i ), frequency (ω) and phases (θ i ), an infinite number of possible solutions may exist.…”

Section: Introductionmentioning

confidence: 99%

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

Tsay

2011

Journal of Control Science and Engineering

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A practical method is developed for limit-cycle predictions in the nonlinear multivariable feedback control systems with large transportation lags. All nonlinear elements considered are linear independent. It needs only to check maximal or minimal frequency points of root loci of equivalent gains for finding a stable limit-cycle. This reduces the computation effort dramatically. The information for stable limit-cycle checking can be shown in the parameter plane also. Sinusoidal input describing functions with fundamental components are used to find equivalent gains of nonlinearities. The proposed method is illustrated by a simple numerical example and applied to one 2 × 2 and two 3 × 3 complicated nonlinear multivariable feedback control systems. Considered systems have large transportation lags. Digital simulation verifications give calculated results provide accurate limit cycle predictions of considered systems. Comparisons are made also with other methods in the current literature.

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Graphical method of prediction of limit cycle for multivariable nonlinear systems

Cited by 14 publications

References 0 publications

Archives of Control Sciences

Archives of Control Sciences

Evolutionary Search for Limit Cycle and Controller Design in Multivariable Nonlinear Systems

Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

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