Separation Principle for a Class of Nonlinear Systems

Голубев, А. Е.; Крищенко, А. П.; Tkachev, Sergei B.

doi:10.3182/20020721-6-es-1901.00236

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Substituting (41) and (42) into (38), multiplying both sides by ϕ x¯, and integrating the obtained equation over the beam length (x¯= 0 to x¯= 1), the following dimensionless ordinary differential equation is achieved as…”

Section: Non-local Strain Gradient Nanobeammentioning

confidence: 99%

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

Vahidi-Moghaddam

Rajaei

Ayati

et al. 2020

IET Control Theory & Appl

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In this study, adaptive prescribed finite-time stabilisation of uncertain single-input and single-output non-linear systems is considered in the presence of unknown states, unknown parameters, external load disturbance, and non-symmetric input saturation. A prescribed finite time disturbance observer is designed to approximate the unmeasured external disturbance. Also, a non-singular prescribed finite time terminal sliding mode control is proposed for the closed-loop control of the system with the non-symmetric input saturation. Extended Kalman filter algorithm is employed for the real-time estimations of the states and unknown parameters of the system. Moreover, a particle swarm optimisation algorithm is used to obtain the design parameters of the proposed disturbance observer and controller. To show the performance of designed control scheme, the proposed approach is employed to guarantee prescribed finite time stabilisation of non-linear vibration of a non-local strain gradient nanobeam. The Galerkin projection method is used to reduce the non-dimensional form of the governing non-linear partial differential equation of Euler-Bernoulli nanobeam to the ordinary differential equation. Finally, numerical simulations are performed to illustrate the effectiveness and performance of the developed adaptive control scheme for the vibration control of nanobeam in comparison with the conventional sliding mode control.

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Section: Non-local Strain Gradient Nanobeammentioning

confidence: 99%

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

Vahidi-Moghaddam

Rajaei

Ayati

et al. 2020

IET Control Theory & Appl

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“…The results are fed to a controller, which naturally calls for the application of the separation principle. Unfortunately, the application this principle to nonlinear systems is still an active topic of theoretical research with sparse results that apply to restricted classes of systems [18,19]. In the following, the separation principle is considered and the controller and observer designs is carried out for a system linearized around an equilibrium.…”

Section: Modeling Head Stabilizationmentioning

confidence: 99%

Idiothetic Verticality Estimation Through Head Stabilization Strategy

Farkhatdinov

Michalska

Berthoz

et al. 2019

IEEE Robot. Autom. Lett.

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The knowledge of the gravitational vertical is fundamental for the autonomous control of humanoids and other freemoving robotic systems such as rovers and drones. This article deals with the hypothesis that the so-called 'head stabilization strategy' observed in humans and animals facilitates the estimation of the true vertical from inertial sensing only. This problem is difficult because inertial measurements respond to a combination of gravity and fictitious forces that are hard to disentangle. From simulations and experiments, we found that the angular stabilization of a platform bearing inertial sensors enables the application of the separation principle. This principle, which permits one to design estimators and controllers independently from each other, typically applies to linear systems, but rarely to nonlinear systems. We found empirically that, given inertial measurements, the angular regulation of a platform results in a system that is stable and robust and which provides true vertical estimates as a byproduct of the feedback. We conclude that angularly stabilized inertial measurement platforms could liberate robots from ground-based measurements for postural control, locomotion, and other functions, leading to a true idiothetic sensing modality, that is, not based on any external reference but the gravity field. Index Terms-Biologically-Inspired Robots; Biomimetics; Sensor-based Control I. INTRODUCTION F OR humans, as for other living creatures, it is substantial to know the spatial orientation of our body with respect to the external world. Most of our sensory systems can contribute to this task. Interestingly, visual, auditory, tactile, proprioceptive, or olfactory sensory inputs can be easily put out of action, but the vestibular inputs are always available, even in the absence of gravity [1]. In artificial systems, robots in particular, inertial measurement units (IMUs) often play the role of a 'robotic vestibular system'. These IMUs sense the movements of the robot and provide its control system Manuscript

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“…The application of the separation principle to nonlinear systems is currently an active theoretical research topic and the results are rare and apply to only certain restricted classes of systems [81,155,66]. In our case, the separation principle may be considered valid if we carry out the controller and the observer designs for a system linearized around an equilibrium.…”

Section: Head Stabilization and The Separation Principle 441 Linearmentioning

confidence: 99%

Modeling Verticality Estimation During Locomotion

Farkhatdinov

Michalska

Berthoz

et al. 2013

Romansy 19 – Robot Design, Dynamics and Control

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In this thesis, a nonlinear model of the vestibular system is proposed, with special reference to humans and other locomoting animals. The vestibular system is essential for stable locomotion since it provides idiothetic measurements of spatial orientation that are needed for postural control. The model was constructed from general considerations regarding the Newton-Euler dynamics governing the three-dimensional movements of bodies constrained to oscillate in non-inertial frames, such as the otoliths, which were modeled as spherical damped pendula. Two configurations were considered. The medial model considered only one inner ear located in the center of a head. The lateral model considered two inner ears located laterally with respect to the center of rotation of the head. The differences between these two models were analyzed and the importance of having two vestibular organs discussed. To this end, a nonlinear algebraic observability test was used to verify whether the reconstruction of the head orientation with respect to the gravitational vertical was possible from otoliths measurements only. It could be shown that in order for the head vertical orientation to be observable, the head had to be stabilized during locomotion. Moreover, it was shown that the gravitoinertial ambiguity inherent to inertial idiothetic sensing could be resolved if the head was horizontally stabilized. These results were applied to solve the head vertical orientation estimation problem in the linearized case (Luenberger observer, Kalman filter) as well as in the nonlinear case (Extended Kalman filter, Newton method based observation). These observers were designed and tested in simulations. The simulations indicated that the estimation errors were smaller and the observers converged faster when head was stabilized during locomotion, leading to a nonlinear, combined observation-control system that could be stabilized with respect to the gravitational vertical based on no other information than the prior knowledge of the Newton-Euler dynamics. The results were further tested with a specifically designed experimental setup that comprised an actuated gimbal mechanism to represent the head-neck articulation and a liquid-based inclinometer that represented the otoliths organs. The findings derived from this research would be helpful for analyzing spatial perception in humans and animals, and for improving the perceptual capabilities of robotic systems, such as humanoid robots, rough terrain vehicles, or free-moving drones.Keywords: vestibular system, head-neck system, nonlinear system, observation, estimation, verticality, spatial perception, locomotion, humanoid robot. 3 RésuméDans cette thèse, nous proposons un modèle non-linéaire du système vestibulaire, en particulier chez l'humain et autres animaux mobiles. Le système vestibulaire est essentiel pour une locomotion stable dans la mesure où il fournit des mesures idiothétiques d'orientation spatiale nécessairesà la stabilité posturale. Le développement du modèle est basé sur l...

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Separation Principle for a Class of Nonlinear Systems

Cited by 9 publications

References 12 publications

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

Adaptive prescribed‐time disturbance observer using nonsingular terminal sliding mode control: Extended Kalman filter and particle swarm optimization

Idiothetic Verticality Estimation Through Head Stabilization Strategy

Modeling Verticality Estimation During Locomotion

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