Feedback Compensation Using Derivative Signals II - Mitrovic's Method

Elliott, D. W.; Thaler, G. J.; Heseltine, J. C. W.

doi:10.1109/tai.1963.5407843

Cited by 3 publications

(14 citation statements)

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“…Root-region of a 4th order equation [2][3][4][5][6][7][8] Root-region of a 5th order equation Ji("' is a function of 7? which can be varied. Assume -S. s~S 7 an d -5j are the three roots of the equation, then the root-coefficient relations are as follows:…”

Section: -7mentioning

confidence: 99%

“…Assume -S and -5, are a pair of complex conjugate roots of the equation , those two roots can be transformed to other two variables by the following transformations : S ( + S z = Z^Od n (1)(2)(3) iAfc =^n (1)(2)(3)(4) Where \ and C/J n are known as the damping ratio and the natural frequency of the pair of complex conjugate roots -5, and -_$, . By this transformation, both y and Uj n can be treated as independent variables.…”

Section: -7mentioning

confidence: 99%

“…For the same reason, if two variables are introduced to the coefficient of a n order characteristic equation, then two roots are arbitrary,, and for JT) variables to the coefficients, Consider a 5th order characteristic equation Assume the coefficients (3, and [3 are adjustable, then equation (1-5-1) can be written as follows:…”

Section: -7mentioning

confidence: 99%

“…Where -f (^f^\ and A terminology, "controlled characteristic equation" is given to equation (1)(2)(3)(4)(5)(6)(7) on the reason that its roots are controllable by the adjustable parameters.…”

Section: -7mentioning

confidence: 99%

“…Root-locus of Equation (2)(3)(4) 2-2 Root-locus of Equation (2)(3)(4)(5)(6)(7) 2-3 Root-locus of Equation (2)(3)(4)(5)(6)(7)(8)(9)(10) …”

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An analytical method for analysis and design of control systems

Liu

Thaler²

1965

IEEE Trans. Automat. Contr.

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Section: -7mentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

Section: -7mentioning

confidence: 99%

“…Root-locus of Equation (2)(3)(4) 2-2 Root-locus of Equation (2)(3)(4)(5)(6)(7) 2-3 Root-locus of Equation (2)(3)(4)(5)(6)(7)(8)(9)(10) …”

mentioning

confidence: 99%

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An analytical method for analysis and design of control systems

Liu

Thaler²

1965

IEEE Trans. Automat. Contr.

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Optimisation of alternator voltage regulators for steady-state stability using the Mitrovic method

Kabriel

1967

Proc. Inst. Electr. Eng. UK

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Generalization of the parameter plane method

Šiljak

1966

IEEE Trans. Automat. Contr.

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Absimcf-This paper presents a generalization of the parameter plane method in that it considers the case when the characteristic equation coefficients are nonlinear functions of the system adjustable parameters. The generalized method is then applied to the system analysis in which the coefficients are linear functions of two parameters and their product. As a simple and rapid procedure for factoring polynomials in the parameter plane, the method is used in the design of linear continuous multivariable control systems. A nonlinear system with two nonlinearities is also considered whereby the stability and existence of limit cycles are investigated. 1 N PREVIOUS papers [1]-[3]1 a parameter plane method has been applied to the analysis and synthesis of linear continuous, sampled-data, and nonlinear control s);stems. In the linear analysis [I], the method relates tn-o adjustable system parameters, which appear linearly in the coefficients of the relevant characteristic equation, to all the root locations. Asimple and rapid procedure has been developed for factoring characteristic polynomials in the plane of these two parameters. This enables the designer to maintain control over salient system characteristics of both transient and frequency responses [4]. The procedure extends in a straightforn-ard manner to sampled-data control systems [2], [SI. Recently, the parameter plane method has been applied to the simultaneous consideration of steady-state and transient responses of linear control systems [6].In nonlinear system analysis [SI, the stability of selfexcited oscillations has been investigated in the parameter plane with respect to both the system parameters and the initial conditions. Control systems with two nonlinearities and with amplitude-and frequencydependent describing functions have been designed. The proposed method has been extended to relative stability and sensitivity problems in nonlinear controls [7], [8].Limitations of the parameter plane method may arise when the adjustable system parameters enter nonlinearly into the coefficients of the characteristic equation. This paper considers a general case in v,-hich coefficients depend nonlinearly on two system parameters and applies the obtained results to the specific case when the coefficients are functions of the linear combination of two parameters and their product. The presented procedure is then applied to the design of a linear multivariable control system by giving in evidence the polezero locations of the closed-loop transfer functions as a function of adjustable system parameters. -4 nonlinear multivariable control system with tn-o nonlinearities is used to illustrate the stability anall-sis of nonlinear systems.In addition, certain rules for the mapping of the contours from the complex variable plane into the parameter plane, 11-hich have been given intuitively in the reference papers [1]- [3], are now proved. Some additional theorems are introduced to facilitate the interpretations of parameter plane diagrams. I t is also to be noted that ...

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Feedback Compensation Using Derivative Signals II - Mitrovic's Method

Cited by 3 publications

References 1 publication

An analytical method for analysis and design of control systems

An analytical method for analysis and design of control systems

Optimisation of alternator voltage regulators for steady-state stability using the Mitrovic method

Generalization of the parameter plane method

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