A Negative Imaginary Approach to Modeling and Control of a Collocated Structure

Bhikkaji, Bharath; Moheimani, S. O. Reza; Petersen, Ian R.

doi:10.1109/tmech.2011.2123909

Cited by 140 publications

(98 citation statements)

References 44 publications

(56 reference statements)

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“…It is worth mentioning that IRC's are defined for negative imaginary systems, i.e., systems with transfer function G(s), satisfying the inequality i(G(iω) − G(−iω)) ≥ 0, ∀ ω ≥ 0, [47]. It can be checked that G X X (s), (10), and G Y Y (s), (11), satisfy the negative-imaginary property, while G X X (s)T (s) and G Y Y (s)T (s) do not.…”

Section: A Irc Design and Fpaa Implementationmentioning

confidence: 99%

“…Here, the IRC has been extended to accommodate the time delay. A complete stability proof, of the type give in [47], for a general negative-imaginary system with time delay is beyond the scope of this paper. However, it suffices to say that the root locus procedure presented in [14], [48] for constructing IRCs for negative-imaginary systems can be used in the current context [i.e., for G X X (s)T (s) and G Y Y (s)T (s)].…”

Section: A Irc Design and Fpaa Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner

Yong

Bhikkaji

Moheimani

2013

IEEE/ASME Trans. Mechatron.

124

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Abstract-An XYZ nanopositioner is designed for fast the atomic force microscopy. The first resonant modes of the device are measured at 8.8, 8.9, and 48.4 kHz along the X-, Y-, and Z-axes, respectively, which are in close agreement to the finite-element simulations. The measured travel ranges of the lateral and vertical axes are 6.5 μm × 6.6 μm and 4.2 μm, respectively. Actuating the nanopositioner at frequencies beyond 1% of the first resonance of the lateral axes causes mechanical vibrations that result in degradation of the images generated. In order to improve the lateral scanning bandwidth, controllers are designed using the integral resonant control methodology to damp the resonant modes of the nanopositioner and to enable fast actuation. Due to the large bandwidth of the designed nanopositioner, a field programmable analog array is used for analog implementation of the controllers. Highresolution images are successfully generated at 200-Hz line rate with 200×200 pixel resolution in closed loop.Index Terms-Field-programmable analog array (FPAA), flexure-guided positioners, high-speed atomic force microscope (AFM), integral resonant control (IRC), nanopositioner, piezoelectric actuators.

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Section: A Irc Design and Fpaa Implementationmentioning

confidence: 99%

Section: A Irc Design and Fpaa Implementationmentioning

confidence: 99%

Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner

Yong

Bhikkaji

Moheimani

2013

IEEE/ASME Trans. Mechatron.

124

View full text Add to dashboard Cite

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“…Therefore, some form of mode truncation for the higher modes is needed. A common reduced order model used by Bhikkaji et al [15] Orszulik and shan [17] is given as…”

Section: System Identificationmentioning

confidence: 99%

“…Qiu et al [14] conducted an acceleration sensor based identification of modal frequencies for plate structures, including the first two bending and torsional modes. In order to estimate the model parameters of a flexible structure with collocated sensors/actuators, Bhikkaji et al [15] proposed a novel frequency domain subspace identification scheme using the negative imaginary approach. To obtain the experimental model of a flexible plate, several frequency domain subspace identification algorithms with the instrumental variable idea were addressed by Ahmadizadeh et al [16].…”

Section: Introductionmentioning

confidence: 99%

Experimental Identification and Vibration Control of A Non-Collocated Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

Lou

Liao

Yang

et al. 2017

Preprint

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This paper presents experimental identification and vibration suppression of a flexible manipulator with non-collocated piezoelectric actuators and strain sensors using optimal multipoles placement control. To precisely identify the system model, a reduced order transfer function with relocated zeros is proposed, and a first-order inertia element is added to the model to compensate the non-collocation. Comparisons show the identified model match closely with the experimental results both in the time and frequency domains, and a fit of 97.2% is achieved. Based on the identified model, a full-state multi-poles placement controller is designed, and the optimal locations of the closed loop poles are determined. The feasibility of the proposed controller is validated by simulations. Moreover, the controller is tested for different locations of the closed loop poles, and an excellent performance of the optimal locations of the closed loop poles is shown. Finally, the effectiveness of the proposed controller is demonstrated by experiments. Results show that the vibrations of the expected modes are significantly diminished. Besides, vibrations of the higher modes are also slightly suppressed. Accordingly, multi-mode vibrations of the manipulator are well attenuated, and the tip displacement converges quickly with the proposed method.

show abstract

Section: Introductionmentioning

confidence: 99%

Experimental Identification and Vibration Control of A Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

et al. 2017

View full text Add to dashboard Cite

This paper presents experimental identification and vibration suppression of a flexible manipulator with piezoelectric actuators and strain sensors using optimal multi-poles placement control. To precisely identify the system model, a reduced order transfer function with relocated zeros is proposed, and a first-order inertia element is added to the model. Comparisons show the identified model match closely with the experimental results both in the time and frequency domains, and a fit of 97.2% is achieved. Based on the identified model, a full-state multi-poles placement controller is designed, and the optimal locations of the closed loop poles are determined where the move distance of the closed loop poles is the shortest. The feasibility of the proposed controller is validated by simulations. Moreover, the controller is tested for different locations of the closed loop poles, and an excellent performance of the optimal locations of the closed loop poles is shown. Finally, the effectiveness of the proposed controller is demonstrated by experiments. Results show that the vibrations of the expected modes are significantly diminished. Accordingly, multi-mode vibrations of the manipulator are well attenuated.

show abstract

A Negative Imaginary Approach to Modeling and Control of a Collocated Structure

Cited by 140 publications

References 44 publications

Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner

Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner

Experimental Identification and Vibration Control of A Non-Collocated Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

Experimental Identification and Vibration Control of A Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

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