91.60 Solving cubics by solving triangles

Mitchell, Douglas W.

doi:10.1017/s0025557200182178

Cited by 8 publications

(3 citation statements)

References 2 publications

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“…The roots of the third-order equations are parametrically found using the formulas in Holmes 27 and Mitchell. 28 The division of the higher-order equation into the third-order equation series is made by constructing windows with three successive pole–zero couples that are the z i − p i couple that corresponds to s p i and two closest zero–pole couples on its right-hand side. These windows are depicted in Figure 3.…”

Section: Reduced Inverse Ioc Designmentioning

confidence: 99%

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Yumuk

Güzelkaya

Eksin

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this study, a reduced inverse integer-order controller design methodology for single fractional-order pole model is proposed. First, the higher integer-order equivalent of this model is found using the Oustaloup approximation to fractional operator. Then, the poles and zeros of the higher integer-order model are determined in terms of fractional-order system model parameters employing characteristic equation format and root-locus idea. The order of the higher integer-order model is reduced using dominant pole–zero couples. The proximity of the pole–zero couples to each other as well as their proximity to the origin is key dominance requirement for order reduction. The controller is obtained inverting the reduced order integer system model in terms of fractional-order system model parameters. The proposed controller is compared with integer and fractional proportional–integral–derivative (PID) controllers using the experiments carried out on two-tank liquid-level process. The real-time experiment outcomes demonstrate that the proposed controller has superior performance over integer and fractional proportional–integral–derivative controllers.

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Section: Reduced Inverse Ioc Designmentioning

confidence: 99%

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Yumuk

Güzelkaya

Eksin

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…In order to find the zeros ( z 1 , z 2 , z 3 ) of the controller in equation (19) in parametric form, the third order equation in the numerator should be solved. For this purpose, we refer to Holmes 44 and Mitchell 45 and find the following parametric closed form formulas…”

Section: Integer Order Pre-filtered Pi/pid Controller Designmentioning

confidence: 99%

Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems

Yumuk

Güzelkaya

Eksin

2018

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this study, we deal with systems that can be represented by single fractional order pole models and propose an integer order proportional–integral/proportional–integral–derivative controller design methodology for this class. The basic principle or backbone of the design methodology of the proposed controller relies on using the inverse of the fractional model and then approximating this fractional controller transfer function by a low integer order model using Oustaloup filter. The emerging integer order controller reveals itself either in pre-filtered proportional–integral or proportional–integral–derivative form by emphasizing on the dominancy concept of pole-zero configuration. Parameters of the proposed controllers depend on the parameters of the single fractional order pole model and the only free design parameter left is the overall controller gain. This free design parameter is determined via some approximating functions relying on an optimization procedure. Simulation results show that the proposed controller exhibits either satisfactory or better results with respect to some performance indices and time domain criteria when they are compared to classical integer order proportional–integral–derivative and fractional order proportional–integral–derivative controllers. Moreover, the proposed controller is applied to real-time liquid level control system. The application results show that the proposed controller outperforms the other controllers.

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“…3, where y 1 represents one of the three roots of y. We outline the proof as conceived by Mitchell [17] in the interest of readers. Using the cosine law, we obtain…”

Section: Closed-form Solution For ℓ 1 2 Regularizationmentioning

confidence: 99%

Adaptive Blind Channel Equalization

Abrar¹,

Zerguine²,

Nandi³

2012

Digital Communication

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In this article, a fractional-norm constrained blind adaptive algorithm is presented for sparse channel equalization. In essence, the algorithm improves on the minimisation of the constant modulus (CM) criteria by adding a sparsity inducing ℓ p -norm penalty. Simulation results demonstrate that the proposed regularised equalizer exploits the inherent channel sparsity effectively and exhibits faster convergence compared to its counterparts.

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91.60 Solving cubics by solving triangles

Cited by 8 publications

References 2 publications

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems

Adaptive Blind Channel Equalization

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