On the calculation of transient response

Aaron, M. R.; Kaiser, Jeremias

doi:10.1109/proc.1965.4217

Cited by 10 publications

(5 citation statements)

References 1 publication

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“…1 When equations (3) and (6) are equated this must be true for all s. That is, if the two polynomials have a common zero with respect to s they could not be equated. I think it would be correct at the bottom of page 1 to define "s(0) " "6i~…”

Section: Discussion John H Georgementioning

confidence: 99%

Discussion: “A New Matrix Formula for the Inverse Laplace Transformation” (Chen, C. F., and Yates, R. E., 1967, ASME J. Basic Eng., 89, pp. 269–272)

George

1967

Journal of Basic Engineering

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It is interesting to note that the complicated multiple differentiations of the s-polynomial involved in the classical inverse Laplace transformation by the Heaviside expansion becomes a simple series differentiation of X as shown in equation (19). In very high-order systems with repeated and complex roots, this new general formula is more straightforward and more easily adapted to digital computation techniques. Conclusions A general formula for the inverse Laplace transformation of a transfer function is established. It involves the Vandermonde matrix, the diagonal or Jordan matrix, the numerator coefficient matrix, and the denominator matrix. The inverse Laplace transformation can almost be directly written. The only manipulations needed are matrix multiplications and inversions. The formula is particularly suitable for digital computer solutions of extremely high-order system problems.

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Section: Discussion John H Georgementioning

confidence: 99%

Discussion: “A New Matrix Formula for the Inverse Laplace Transformation” (Chen, C. F., and Yates, R. E., 1967, ASME J. Basic Eng., 89, pp. 269–272)

George

1967

Journal of Basic Engineering

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“…Assume Equation ( 3) has a unique and asymptotically stable equilibrium point x u ∈ R n , for a step input u. In addition, when x = x u , let y = h(x u ) = u∕k, where 1∕k ∈ R + is the DC gain of Equation (3). Then, the equilibrium point of the closed-loop system illustrated in Figure 2, with the dynamic of Equation ( 4) and 𝜆 > 0, has the following properties,…”

Section: Problem Definition and Extension To Nonlinear Systemsmentioning

confidence: 99%

“…We consider the following nonlinear system to demonstrate the concept discussed above ̇x = −20(x − u) 3 , y = x.…”

Section: Examplementioning

confidence: 99%

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Shaping transient response of nonlinear systems to satisfy a class of integral constraints

Aalipour

Das

2022

Adv Control Appl

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We consider the problem of shaping the transient step response of nonlinear systems to satisfy a class of integral constraints. Such constraints are inherent in hybrid energy systems consisting of energy sources and storage elements. While typical transient specifications aim to minimize overshoot, this problem is unique in that it requires the presence of an appreciable overshoot to satisfy the foregoing constraints. The problem was previously studied in the context of linear systems and this article extends that work to nonlinear systems. A combined integral and feedforward control, that requires minimal knowledge of the plant model, is shown to make the system amenable to meeting such constraints. Broadly, the compensation is effective for nonlinear plants with stable open-loop step response and a positive DC gain. However, stability of the resulting closed-loop system mandates bounds on the integral gain. In this regard, we state and prove generalized stability theorems for first and higher-order nonlinear plants.

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“…Other inefficiencies, such as the prevalence of fee-for-service payment models that create the incentive for physicians to provide more services rather than practice efficiently, also drive up costs. 54 On the other hand, evidence that malpractice litigation "perceptibly raises the growth of health care spending is almost nonexistent." 55 Even as the United States far outpaces all other countries in health care spending, we still fail to provide insurance to more than 50 million citizens.…”

Section: Rising Health Care Costs Have Little To Do With Malpractice mentioning

confidence: 99%

The Truth About Torts: Defensive Medicine and the Unsupported Case for Medical Malpractice 'Reform'

Shapiro

McGarity

Vidargas³

et al. 2012

SSRN Journal

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On the calculation of transient response

Cited by 10 publications

References 1 publication

Discussion: “A New Matrix Formula for the Inverse Laplace Transformation” (Chen, C. F., and Yates, R. E., 1967, ASME J. Basic Eng., 89, pp. 269–272)

Discussion: “A New Matrix Formula for the Inverse Laplace Transformation” (Chen, C. F., and Yates, R. E., 1967, ASME J. Basic Eng., 89, pp. 269–272)

Shaping transient response of nonlinear systems to satisfy a class of integral constraints

The Truth About Torts: Defensive Medicine and the Unsupported Case for Medical Malpractice 'Reform'

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