Pid And Pid‐Like Controller Design By Pole Assignment Within D‐Stable Regions

Wang, Yongji; Schinkel, M.; Schmitt-Hartmann, Tilmann; Hunt, K.J.

doi:10.1111/j.1934-6093.2002.tb00083.x

Cited by 21 publications

(5 citation statements)

References 19 publications

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“…In this case, the region of the vertex D‐partition for boundaries and can be constructed employing the following expression:

k_{0} ((), β) goodbreak= Δ_{1} / normalΔ, k_{1} ((), β) goodbreak= Δ_{2} / normalΔ,

where

normalΔ goodbreak= (||, \begin{array}{c} Re ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & Re ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \\ Im ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & Im ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \end{array}), Δ_{1} goodbreak= (||, \begin{array}{c} goodbreak- Re ((), B ((),, b_{i}^{V}, s ((), β))) & Re ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \\ goodbreak- Im ((), B ((),, b_{i}^{V}, s ((), β))) & Im ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \end{array}), Δ_{2} goodbreak= (||, \begin{array}{c} Re ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & goodbreak- Re ((), B ((),, b_{i}^{V}, s ((), β))) \\ Im ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & goodbreak- Im ((), B ((),, b_{i}^{V}, s ((), β))) \end{array}) .

For further construction of the boundary of the vertex D‐partition and particular lines, one should use the well‐known rules [2,5]. …”

Section: Design Of Linear Robust Controller Parameters Based On Verte...mentioning

confidence: 99%

“…For further construction of the boundary of the vertex Dpartition and particular lines, one should use the wellknown rules [2,5].…”

Section: Technique For Determining Two Controller Parametersmentioning

confidence: 99%

“…The main goal in the IDS design is to ensure the desired control quality. There are a lot of studies which deal with the methodology for parametric design of linear robust controllers based on the ICP [1–27]. One should single out root methods that differ from others by their simplicity and visualization [3–6,9,11,13,14,16,17,20,22–25,27].…”

Section: Introductionmentioning

confidence: 99%

“…To determine the linear controller parameters that ensure allowable root quality indices in the control system at any values of the ICP coefficients, it is proposed to use the D-partition method [2,4,5,7,8,10,12,14,18,20,23,25]; the interval extension of this methodology is carried out in terms of the ICP. The disadvantage of the proposed solution is in the necessity to apply the D-partition method for all 2 m vertices of the coefficient polyhedron (m is the number of the interval ICP coefficients), which is a rather laborious procedure.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Synthesis of a linear controller for a control system with interval parameters on a base of D‐partition in vertices of a coefficient's polyhedron of characteristic polynomial

Gayvoronskiy

Ezangina

2022

Asian Journal of Control

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The article deals with the technique developed for the parametric design of a robust controller which ensures the desired robust quality indicators in the system with interval parameters. This technique is based on the construction of the D‐partition in the space of controller parameters at vertices of the coefficient polyhedron of a characteristic polynomial. Grounds for this are the fact that the interval system has its minimum degree of stability and maximum degree of oscillation at certain vertices of the specified polyhedron. To determine the minimum sets of those vertices, a new technique has been developed. The developed technique is based on inequalities obtained for outlet angles of the edge branches coming out from system poles, which determine the root indices of robust quality. Applying the developed technique for the vertex D‐partition, the design of the PI controller of the stabilization system for a tethered underwater vehicle has been carried out. The results of the design confirm the efficiency of the developed approach.

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“…In this case, the region of the vertex D‐partition for boundaries and can be constructed employing the following expression:

k_{0} ((), β) goodbreak= Δ_{1} / normalΔ, k_{1} ((), β) goodbreak= Δ_{2} / normalΔ,

where

normalΔ goodbreak= (||, \begin{array}{c} Re ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & Re ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \\ Im ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & Im ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \end{array}), Δ_{1} goodbreak= (||, \begin{array}{c} goodbreak- Re ((), B ((),, b_{i}^{V}, s ((), β))) & Re ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \\ goodbreak- Im ((), B ((),, b_{i}^{V}, s ((), β))) & Im ((), A_{2} ((),, a_{j}^{V}, s ((), β))) \end{array}), Δ_{2} goodbreak= (||, \begin{array}{c} Re ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & goodbreak- Re ((), B ((),, b_{i}^{V}, s ((), β))) \\ Im ((), A_{1} ((),, a_{j}^{V}, s ((), β))) & goodbreak- Im ((), B ((),, b_{i}^{V}, s ((), β))) \end{array}) .

For further construction of the boundary of the vertex D‐partition and particular lines, one should use the well‐known rules [2,5]. …”

Section: Design Of Linear Robust Controller Parameters Based On Verte...mentioning

confidence: 99%

“…For further construction of the boundary of the vertex Dpartition and particular lines, one should use the wellknown rules [2,5].…”

Section: Technique For Determining Two Controller Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synthesis of a linear controller for a control system with interval parameters on a base of D‐partition in vertices of a coefficient's polyhedron of characteristic polynomial

Gayvoronskiy

Ezangina

2022

Asian Journal of Control

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show abstract

“…Additionally, there are many effective algorithms in other fields that are worth investigating and implementing in the field of structure and robotic control. For example, control algorithms in chemical, electrical, and biological [23,24,25] fields have shown very effective results within their applications 5 in these fields, but researchers have shown little attention to these applications.…”

Section: Motivationmentioning

confidence: 99%

Dynamics and control of mechanical and biomechanical systems

Liu¹

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With the advances in mechanical and robotic systems in terms of light weights, high speeds, and precision comes a great demand for more effective vibration suppression and control schemes. This work presents a novel algorithm, called Optimal-SNC/Optimal-SNC-PID, for vibration suppression and control of mechanical and robotic systems for better accuracy. The proposed method has been tested and compared with traditional control algorithms on several multi-degree-of-freedom systems and a robotic arm under simulated random vibration signals in the vertical and horizontal directions. The proposed control scheme has the potential to be applied for high precision surgical and fabrication applications. Transmitted vibrations can affect human performance and comfort and can be a potential risk for injuries. According to the literature, vibration transmitted to seated humans would mostly affect their lumbar and cervical spine regions. Based on the structure of the proposed Optimal-SNC control algorithm, a human head-neck model is developed in this work to resemble the head-neck biodynamic response due to fore-aft whole-body vibration. The proposed model has the potential to be used for investigating head-neck discomfort and injury. It also has the potential to be used for the development of more effective seats in whole-body applications. iii

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An Overview of Tuning Rules for the PI and PID Continuous-Time Control of Time-Delayed Single-Input, Single-Output (SISO) Processes

O’Dwyer¹

2012

Advances in Industrial Control

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Pid And Pid‐Like Controller Design By Pole Assignment Within D‐Stable Regions

Cited by 21 publications

References 19 publications

Synthesis of a linear controller for a control system with interval parameters on a base of D‐partition in vertices of a coefficient's polyhedron of characteristic polynomial

Synthesis of a linear controller for a control system with interval parameters on a base of D‐partition in vertices of a coefficient's polyhedron of characteristic polynomial

Dynamics and control of mechanical and biomechanical systems

An Overview of Tuning Rules for the PI and PID Continuous-Time Control of Time-Delayed Single-Input, Single-Output (SISO) Processes

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