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State estimation in multibody systems with rigid or flexible links
Full text linkIn the multibody field the design of state observers proves useful for several tasks, ranging from the synthesis of control schemes and fault detection strategies, to the identication of uncertain parameters. State observers are designed to obtain accurate estimates of unmeasurable or unmeasured variables. Their accuracy and performance depend on both the estimation
algorithms and the system models. Indeed, on the one hand the estimation algorithms should be able to cope with multibody system (MBS) nonlinearities. On the other, MB models should be suitable to state estimation, i.e. accurate and computationally efficient.
In order to obtain the best results, it has been necessary to develop dierent approaches for rigid-link and flexible-link MBSs.
In the case of rigid-link MBSs, state observers based on nonlinear kinematic models (i.e. kinematic constraint equations) have been developed. When compared to dynamic models, kinematic models present some relevant advantages. In particular, they are less complex and much less aected
by uncertainty. Additionally, though kinematics-based observers do not require force and torque measurements (often dicult to gather) as inputs, they can be successfully employed for estimating unknown forces: to this purpose a novel two-stage approach is proposed in this dissertation.
As far as modeling flexible-link MBSs is concerned, it is more complicated and makes the implementation of kinematics-based observers impossible, since it is not possible to decouple kinematics from dynamics easily. Furthermore, the so called ne motion of such systems is typically described through a large number of elastic coordinates, which in turns leads to high
model dimensions, and to very inefficient, if not impossible to synthesize, state observers. In order to address this issue, firstly, a new strategy has been developed to keep model dimensions to a minimum. Such a strategy leads to a signicant reduction in the size of the models, which, in turns, provide an appropriate representation of the system dynamics in a frequency range of interest. The availability of reduced-dimension but accurate models for flexible-link MBSs poses the way to the synthesis of more efficient observers provided that a suitable estimation algorithm is chosen.
This thesis also collects results from a large number of numerical and experimental tests carried out to validate the intermediate and nal outcomes of the theoretical investigations
Kinematic state estimation for rigid-link multibody systems by means of nonlinear constraint equations
Full text linkIn the multibody field the design of state observers proves useful for several tasks, ranging from the synthesis of control schemes and fault detection strategies, to the identification of uncertain parameters. State observers are designed to obtain accurate estimates of unmeasurable or unmeasured variables. Their accuracy and performance depend on both the models used and the measurement sets. In multibody systems, if it is reasonable to neglect joint clearance and to assume that links are rigid, the estimates of kinematic variables (i.e. position, velocity and acceleration) can be carried out very effectively using kinematic models, i.e. models based on kinematic constraint nonlinear equations, which provide much less uncertain models than dynamic equations. Under the aforementioned assumptions, this paper proposes a general theory, valid for both open-chain and closed-chain multibody systems, to design observers based on nonlinear kinematic models. The concurrent use of kinematic models and nonlinear estimators is original in the multibody field and represents the chief contribution of the paper. The soundness of the proposed theory is proved through numerical and experimental tests on both open-chain and closed-chain multibody systems. Finally, a comparison is given between the kinematic estimations computed through two nonlinear observers (the extended Kalman filter, EKF, and the spherical simplex unscented Kalman filter, SS-UKF), in order to demonstrate the benefits of the SS-UKF in nonlinear estimation
Two-stage approach to state and force estimation in rigid-link multibody systems
Full text linkA novel two-stage approach is presented for improving the estimates of both the kinematic state and the unknown external forces in rigid-link multibody systems with negligible joint clearance. The approach is said to be a two-stage one because the estimation process is carried out by two observers running simultaneously and only partially coupled in order to reduce model uncertainties. Nonlinear Kalman filters are employed at both stages. In the first stage, a kinematic observer estimates an augmented system state (i.e., positions, velocities and accelerations) by employing the kinematic constraint equations and some measurements of kinematic quantities as inputs and outputs. Therefore, it is unbiased by external forces and uncertainties on any dynamic parameters. In the second stage, a force observer estimates the external forces by employing dynamic models. The input of the force observer is the kinematic state, while the correction is performed through some direct or indirect measurements of the known forces. Numerical assessment of the theory developed is provided through a slider–crank mechanism. The results achieved through the proposed approach are compared with those yielded by traditional unknown input observers based on a single-stage dynamic estimation. An extensive statistical analysis is carried out at varying levels of measurement noise. Two different strategies are followed in the synthesis of the non-linear Kalman filters. The comparison clearly shows the advantages and the effectiveness of the new two-stage approach
Mode selection for reduced order modeling of mechanical systems excited at resonance
No full textWelding, food cutting, atomizing, cleaning and deagglomerating are just a few common uses for ultrasonic resonators, which are carefully designed to operate excited in resonance. Finite element analysis is nearly always adopted for predicting and improving resonator performances. Large number of small elements are usually needed to guarantee accuracy. As a consequence, models have typically very large dimensions, and hence considerable computational and ill conditioning problems arise. Model reduction techniques can be extremely useful to keep model dimensions to a minimum. In this paper a new ranking method, called Interior Mode Ranking (IMR), is introduced for the selection of the interior normal modes in the Craig Bampton reduction technique, which is one of the most popular model reduction methods, often available in commercial finite element software packages. The IMR method allows ranking the interior modes analytically by comparing the contributions provided by the interior modes of the subsystem with constrained boundary conditions to the dynamics of interest of the complete system (with actual boundary conditions). The method is general and can be applied to any resonator in the reduction at the system level. Here it is employed to obtain an accurate reduced-order model of an ultrasonic welding bar horn. The results achieved by the method are compared with those yielded by other ranking techniques. The comparison shows that the IMR method outperforms the other ranking techniques and leads to accurate representations of the excited modes
Simultaneous estimation of kinematic state and unknown input forces in rigid-link multibody systems
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Nonlinear kinematic state estimation in rigid-link multibody systems by spherical simplex sigma point unscented Kalman filters
No full textThe design of state observers for multibody systems usually relies on dynamic models. Whenever the system links can be assumed rigid, a great improvement in the estimation accuracy can be achieved by employing kinematic constraint equations as the system model. Indeed, such geometrical equations do not involve forces and inertia characteristics and also the observer synthesis does not impose the knowledge of the external forces. These features reduce the overall uncertainty and noise. To this purpose, this paper proposes the general theory for the development of kinematic Kalman filters (KKFs) in multibody systems, suitable for both open and closed chain mechanisms and manipulators. Particular interest is paid to the sigma point unscented Kalman filters, which allow a more effective estimation than the Extended Kalman Filter in the presence of system nonlinearities and does not impose the computation of the Jacobian matrices. Experimental assessment of the developed theory is proposed through a planar multibody system
MODE SELECTION IN REDUCED-ORDER MODELS FOR ULTRASONIC HORNS UNDER LONGITUDINAL VIBRATION
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