Generalized‐Disturbance Rejection Control for Vibration Suppression of Piezoelectric Laminated Flexible Structures

Zhang, Xiaoyu; Wang, Runxiao; Zhang, Shunqi; Wang, Zhanxi; Qin, Xin; Schmidt, Rüdiger

doi:10.1155/2018/1538936

Cited by 10 publications

(9 citation statements)

References 69 publications

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“…Control derived by the pseudospectral method will be numerically revealed using MATLAB via a general optimization program [27]. By comparison, recall classical compensators and those designed to control flexible systems [28][29][30][31][32][33][34] ubiquitously command maneuvers in the direction of the desired end state. To validate this claim, reviews of classical compensators [35] and frequency domain shaping filters [36] were performed by Wie and Agrawal, respectively.…”

Section: Of 18mentioning

confidence: 99%

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

Sands

2019

Aerospace

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Automatic controls refer to the application of control theory to regulate systems or processes without human intervention, and the notion is often usefully applied to space applications. A key part of controlling flexible space robotics is the control-structures interaction of a light, flexible structure whose first resonant modes lie within the bandwidth of the controller. In this instance, the designed-control excites the problematic resonances of the highly flexible structure. This manuscript reveals a novel compensator capable of minimum-time performance of an in-plane maneuver with zero residual vibration (ZV) and zero residual vibration-derivative (ZVD) at the end of the maneuver. The novel compensator has a whiplash nature of first commanding maneuver states in the opposite direction of the desired end state. For a flexible spacecraft simulator (FSS) free-floating planar robotic arm, this paper will first derive the model of the flexible system in detail from first principles. Hamilton's principle is augmented with the adjoint equation to produce the Euler-Lagrange equation which is manipulated to prove equivalence with Newton's law. Extensive efforts are expended modeling the free-free vibration equations of the flexible system, and this extensive modeling yields an unexpected control profile-a whiplash compensator. Equations of motion are derived using both the Euler-Lagrange method and Newton's law as validation. Variables are then scaled for efficient computation. Next, general purposed pseudospectral optimization software is used to seek an optimal control, proceeding afterwards to validate optimality via six theoretical optimization necessary conditions: (1) Hamiltonian minimization condition; (2) adjoint equations; (3) terminal transversality condition; (4) Hamiltonian final value condition; (5) Hamiltonian evolution equation; and lastly (6) Bellman's principle. The results are novel and unique in that they initially command full control in the opposite direction from the desired end state, while no such results are seen using classical control methods including classical methods augmented with structural filters typically employed for controlling highly flexible multi-body systems. The manuscript also opens an interesting question of what to declare when the six optimality necessary conditions are not necessarily in agreement (we choose here not to declare finding the optimal control, instead calling it suboptimal).Aerospace 2019, 6, 93 2 of 18 highly flexible structure. In order to optimize the control of such challenging systems, a brief review of mechanics and ubiquitous control techniques is warranted.Mechanical motion of mass in six degrees of freedom is completely described by separate treatment of three degrees of freedom of translation plus three additional degrees of freedom of rotation as articulated in the year 1830 [1] and expanded and modernized over the following two centuries [2][3][4][5][6][7][8][9][10][11][12][13]. Translational degrees of freedom are governed by Newton's law, whil...

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Section: Of 18mentioning

confidence: 99%

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

Sands

2019

Aerospace

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“…As e is the high-frequency noise and e ¼ 0 in the low-frequency domain ðx < x 0 Þ; jeQj ¼ 0. Finally, equation ( 10) transforms to equation (11).…”

Section: Drive Chain Modelmentioning

confidence: 99%

“…18,19,[21][22][23] In fact, the focus has been more on the low-frequency performance of the system. Equation (11) shows that the DOB can well suppress disturbance d and sensor measurement signal noise e.…”

Section: Drive Chain Modelmentioning

confidence: 99%

“…In the inertia phase, the drive chain can be simplified as a dual-inertia system, which includes generalized disturbances comprising random disturbance load, model error, and model uncertainty. 10,11 The random disturbance load exhibits high amplitude, high variance, low frequency, and high energy, which can severely affect the shift smoothness. Owing to the simplification of the non-linear components in the drive chain, modelling errors between the established system model and the existing controlled object will adversely affect the designed controller and cause shift shock.…”

Section: Introductionmentioning

confidence: 99%

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Robust tracking control in the inertia phase for generalised disturbance

Guoxiang

Wang

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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To solve the problem of shift shock during the inertia phase caused by generalized disturbances in wheel loaders and other construction instruments, a robust double closed-loop tracking control method based on an improved disturbance observer (DOB) has been proposed. In this method, the inner loop robustly suppresses disturbance and the outer loop realizes trajectory tracking. The improved DOB based on a nominal disturbance value (NDV) can enhance the disturbance suppression ability of the inner loop when a large part of the generalized disturbance is determinable. The model matching method transforms the outer loop into a transfer function to meet the expected performance. A disturbance compensation controller eliminates the nominal disturbance in the system. A feedforward compensation controller eliminates the influence of reference inputs in the system. Considering the inertia phase of a fixed-axis automatic transmission of a wheel loader, the proposed method was applied to the driveline simulation platform of a specific type of wheel loader. Random loads under actual working conditions were considered as the input load of the simulation platform. The simulation results indicated that the DOB based on the NDV method has better disturbance suppression capability, more accurate tracking capability and smaller shift shock than the conventional DOB method. The proposed control method exhibits robustness under 10%, 50% and 90% of the maximum load. The highest shift shock is 4.94% of the manual shift shock and it is effectively reduced. Thus, robust and smooth inertia phase shift control of the automatic transmission can be realized. This study presents an effective method for solving robust disturbance suppression control problems and tracking control problem under large generalized disturbances.

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“…A highly flexible beam using piezoelectric patches was actively controlled for the first three vibration modes (Wu et al., 2014). In a recent study, the piezoelectric material adhered to a steel beam element and the disturbance rejection control was studied using three different controllers to suppress vibrations against an unknown distortion signal input (Zhang et al., 2018). Moreover, a multi-walled carbon nanotube (MWCNT)/epoxy nanocomposite strain sensor and piezoelectric actuator pair were used in active vibration control of a smart cantilevered beam (Sapra et al., 2018).…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of a blade element with uncertainty modeling in PZT actuator force

Sivrioğlu

Bolat

Ertürk

2019

Journal of Vibration and Control

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The aim of this research is to attenuate the vibrations of a blade structure with an attached piezoelectric actuator using robust multi-objective control. The force obtained from a piezoelectric patch loading has uncertainties due to the complicated shape (airfoil) of the blade element. A parameter-dependent model of the force equation is developed to understand the possible variation range of the actuation force. The modal analysis of the blade is performed to find vibration mode frequencies, and an aerodynamic load is generated experimentally to create steady-state vibration on the blade. A state-space model is obtained by considering certain vibration modes and the parameter-dependent part of the force in the input vector is taken outside of the plant model. The robust stability filter is modified with parameter dependency to have a cluster of the filter. Two different multi-objective controllers are designed with different design objectives. The designed controllers are implemented in experiments and performances of the controllers are compared using frequency and time domain responses. It is shown that the flexible blade vibrations are successfully suppressed with the proposed mixed norm robust controllers under the effect of steady-state aerodynamic disturbance with different air speeds. It is observed in experimental results that the performances of the [Formula: see text] controller are better than the [Formula: see text] controller.

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Generalized‐Disturbance Rejection Control for Vibration Suppression of Piezoelectric Laminated Flexible Structures

Cited by 10 publications

References 69 publications

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

Optimization Provenance of Whiplash Compensation for Flexible Space Robotics

Robust tracking control in the inertia phase for generalised disturbance

Active vibration control of a blade element with uncertainty modeling in PZT actuator force

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