On approximating the step response of a third-order linear system by a second-order linear system

Monzingo, Robert A.

doi:10.1109/tac.1968.1099055

Cited by 4 publications

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“…Determine a BA function u(s) which interpolates to u ( q ) = b j , j = 1, I, where Re a, > 0 and loj\ < 1. The classical N-P interpolation algorithm is defined by the mapping, see [3] for the corresponding mapping on the unit circle Unfortunately, difficulties occur .with this algorithm when some of the interpolation points are complex numbers, i.e., aj = uj + jwj and oj # 0.…”

Section: (1)mentioning

confidence: 99%

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On computational algorithms for pole assignment

Nichols

1986

IEEE Trans. Automat. Contr.

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The exact expression for the transient response to a unit step input is 643 c ( T ) = 1 +-The dimensionless settling time T,, for { < {-, is the lowest value of dimensionless time T, equal to or greater than T,,, for which c(T) = 1 =F B and thereafter stays within the limits 1 f B. Here, T,, is the time corresponding to the maximum overshoot and is given byDetermination of whether the (1 + B) limit or the (1 -B) limit governs depends upon the value of { and is probably best found by direction substitution and consequent iteration. For example, by referring to the graphical presentation of the dimensionless transient response versus dimensionless time in Fig. 6-14 in [2, p. 3351, it can be seen that for {=0.3, there are two values of T,; 1) for the case of two extrema (maximum or minimum) before staying within the (1 + B ) limits, the lower limit (1 -B ) governs and T, 3 7.98; and 2) for the case of three extrema before staying within the limits, the upper limit (1 + B) governs and T, G Abstract-A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct

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Section: (1)mentioning

confidence: 99%

“…This theory also finds wide application in filter design and general system theory. For an excellent survey of the theory and its applications to systems, see [3].…”

Section: Introductionmentioning

confidence: 99%

On computational algorithms for pole assignment

Nichols

1986

IEEE Trans. Automat. Contr.

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“…IEEE Log Number 8608732. approximation of the response of higher order systems [2], [3]. A number of criteria have been established for time-domain performance of control systems.…”

Section: Ihtroductionmentioning

confidence: 99%

An improved approximation for settling time of second-order linear systems

Bert

1986

IEEE Trans. Automat. Contr.

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It is felt that the efficient and exact method for calculating the sensitivities of the stability constraint functions presented here provides a very useful tool for the gradient optimization approach to a number of design problems, especially in the robustness area. The method is based on the stability criterion introduced in 111 which can be shown to be slightly better than the Routh criterion and much superior over the most popular Routh-Hunvitz criterion. The other two criteria could also be used for numerical calculation of the sensitivities. In the case of a version of the Routh criterion without divisions, the algorithm would be very similar to the one proposed. For the Routh-Hunvitz criterion, the rule of differentiating determinants of higher order could be used, however, the algorithm would be much more complicated and much less efficient. ACKNOWLEDGMENT The author is grateful to Dr. M. A. Styblinski of Texas A&M University for his careful reading of the manuscript and for suggesting to run an example on centering. The author also expresses his gratitude to Dr. J. W. Bandler of McMaster University, Canada, from whom he learned a great deal on optimization techniques and on design centering tolerancing methods. REFERENCES R. M. Biemacki, "A new algebraic criterion for stability,"Abstract-A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct Manuscript

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“…Understanding the DC motor's behavior in the laboratory is expected to significantly improve if the second order response is viewed within the confines of a third order one [4]. This makes it important to model a second-order transfer function of the motor's velocity.…”

Section: Introductionmentioning

confidence: 99%

“…These discrepancies will most probably be experienced during the course of a control lab if a first order motor velocity transfer function (2 nd order position transfer function) is used as the model of the motor process. Understanding the DC motor's behavior in the laboratory is expected to significantly improve if the second order response is viewed within the confines of a third order one [4]. This makes it important to model a second-order transfer function of the motor's velocity.…”

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Experimental Determination of an Extended DC Servo-Motor State Space Model: An Undergraduate Experiment

2020

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State space systems and experimental system identification are essential components of control education. Early introduction of these tools to the curriculum of a control laboratory in an interconnected and accessible manner that does not over-dilute the concepts is important in two ways. First, it facilitates a student's transition to more senior and graduate level control concepts. It also provides an effective link to industrial applications. This paper provides two novel experimental procedures for directly identifying the state space model of a DC motor in an undergraduate control laboratory. The procedures do not require any specialized hardware and can be performed using standard laboratory equipment. They also do not place any simplifying assumptions on the motor's model. The first procedure is based on direct pseudo inversion of the state space model. It does not require advanced knowledge of the state space approach or signal filtering. It is easy to understand and suits a first control laboratory. The second procedure is more efficient. It is based on the Markov approach commonly used for realizing, indirectly, a state space model from an estimated transfer function. While the procedure is designed for use by undergraduate students, it requires relatively advanced knowledge in state space that makes it suitable for a second undergraduate control laboratory.

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On approximating the step response of a third-order linear system by a second-order linear system

Cited by 4 publications

References 2 publications

On computational algorithms for pole assignment

On computational algorithms for pole assignment

An improved approximation for settling time of second-order linear systems

Experimental Determination of an Extended DC Servo-Motor State Space Model: An Undergraduate Experiment

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