Design of Digital High-Gain PD Control Systems Using Analytical Approach

Al-Salem, Nabeel; Fanni, Mohamed

doi:10.1299/jsmec.47.792

Cited by 5 publications

(18 citation statements)

References 12 publications

(23 reference statements)

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“…For D > 0, one can obtain the real root of the cubic equation (10) by substitution for z by the one that has real value from the three solutions (z 1 ,z 2 ,z 3 ) in Eq. (14). It is to be noted that this real root can represent root 1 or root 3 .…”

Section: Appendix Imentioning

confidence: 99%

“…In practice, it has been demonstrated that a system may become unstable when the feedback gains are high (12) . It is shown that a stable highgain continuous PD control system (first and second-order systems) may become unstable when implemented digitally (12) - (14) . In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…Section 3 is devoted to review our analytical approach proposed in Ref. (14). Closed-form stability criteria for damped system are derived in section 4.…”

Section: Introductionmentioning

confidence: 99%

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Stability Analysis for Digital PD Control of Flexible Systems Including Damping

Al-Salem

Fanni

2006

JSME Int. J., Ser. C

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In this work we extent our recent results on the stability of single-rigid/single-flexible mode system to cases involving damping. We present closed form analytical expressions that describe the boundaries of the stability regions for digital PD control systems. This is obtained using a newly adopted approach based on the critical stability constraints of Jury test. The considered system simulates many practical systems such as antenna, space shuttle, and robot arm. It is found that, the stability regions for damped flexible systems have three identifiable and distinguished topologies corresponding to three classes of damped system. The three classes are separated from each other by two surfaces in the three-dimension-space of the system-parameters. The stability region for the first class is almost a right triangle in the gain space where the third boundary, the hypotenuse, is described by the lowest root of a cubic equation. The stability region for the second class is clearly larger in size and the three roots of the cubic equation participate in defining the third boundary. In the third class, the stability region is further larger in size and the highest root of the cubic equation defines the third boundary. A peculiar situation is found where a stable system of the second class is possible with negative derivative gain. Numerical simulation is presented to verify this peculiar situation.

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Section: Appendix Imentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability Analysis for Digital PD Control of Flexible Systems Including Damping

Al-Salem

Fanni

2006

JSME Int. J., Ser. C

Self Cite

View full text Add to dashboard Cite

show abstract

“…In practice, it has been demonstrated that a system may become unstable when the feedback gains are high (11) . It is shown that a stable highgain continuous PD control system (first and second-order systems) may become unstable when implemented digitally (11) - (13) . In Refs.…”

Section: Introductionmentioning

confidence: 99%

“…(13) to cases involving flexible systems. We shall show that a collocated PD control of single-rigid/single-flexible mode system which guarantees stability may become unstable when implemented digitally even in cases involving small gains.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis for Digital PD Control of Flexible Systems

Al-Salem

2006

JSME Int. J., Ser. C

Self Cite

View full text Add to dashboard Cite

In this work we extent our recent results on the stability of rigid systems to cases involving flexible ones. We present closed form analytical expressions that describe the boundaries of the stability regions for digital PD control systems. This is obtained using a newly adopted approach based on the critical stability constraints of Jury test. The considered system consists of a single rigid and a single flexible mode. This simulates many practical systems such as antenna, space shuttle, and robot arm. The obtained closed-form stability criterion shows that the stability region is almost a right triangle in the gain space. The right-angle sides of the proposed triangle coincide exactly with two boundaries of the stability region. The hypotenuse of the triangle is found to well approximate the third boundary. An analytical expression is derived for the slope of the hypotenuse. This approximation results in defining the stability region using only two parameters which is convenient for practical applications. Case study is presented to show the practical usefulness of the proposed close-form stability criteria through investigating the control design of high speed flexible robot arm.

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Iterative learning control for robotic manipulators: A bounded‐error algorithm

Delchev

2013

Adaptive Control & Signal

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This paper presents a model-based nonlinear iterative learning control (NILC) for nonlinear multiple-input and multiple-output mechanical systems of robotic manipulators. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory-tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. Both standard and bounded-error learning control laws with feedback controllers attached are considered. The NILC synthesis is based on a dynamic model of a six degrees of freedom robotic manipulator. The dynamic model includes viscous and Coulomb friction and input generalized torques are bounded. With respect to the bounded-error and standard learning processes applied to a virtual PUMA 560 robot (Unimation, Inc. Danburry, CT, USA), simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control.

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Design of Digital High-Gain PD Control Systems Using Analytical Approach

Cited by 5 publications

References 12 publications

Stability Analysis for Digital PD Control of Flexible Systems Including Damping

Stability Analysis for Digital PD Control of Flexible Systems Including Damping

Stability Analysis for Digital PD Control of Flexible Systems

Iterative learning control for robotic manipulators: A bounded‐error algorithm

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