Katsutoshi Yoshida

Characterization of reverse rotation in chaotic response of mechanical pendulum

Characterization of reverse rotation in chaotic responses of a parametrically excited damped pendulum is experimentally investigated. For this purpose, a statistical mechanical analysis by dynamical structure functions is used. The results showed that the difference of the two chaotic responses of the pendulum, one stably keeping a direction of rotation and the other having the possibility of reverse rotations that randomly arise in the response, can be characterized by a peak at negative q in q-weighted variance, and that the peak may act as an identifier of the possibility of the reverse rotation in the chaotic response of the pendulum.

PSO-based model identification of a full-scale CVT drivetrain

Torque transfer characteristics of the drivetrain of a production continuously variable transmission (CVT) vehicle is identified based on a particle swarm optimization (PSO) technique. The torque transfer characteristics from the CVT input shaft to the driveshaft is described by a simple nonlinear model: a single degree-of-freedom vibration model with a clearance. Based on the full-scale experimental data, the model parameters are identified by a data correction method and PSO. The simulated driveshaft torque shows good agreement with the measured torque from the experiment.

Characterization of chaotic vibration without system equations

Abstract This paper studies a method that enables us to get information about how a chaotic system behaves as its parameters are changed. This method is an application of theory based on statistical mechanics developed by Tomita and others. In a previous paper, in order to apply the theory to time series analysis, we proposed a method that can calculate quantities based on statistical mechanics, rather than on system equations. The results showed that our method is effective for characterization of non-linear systems whose equations are not known. This paper focuses on effect of instrumental noise on our method because it is a significant problem if our method is used for time series analysis. The results showed that a q β -phase transition may become invalid as an identifier of chaos or disappears altogether.

Nonlinear analysis on purely mechanical stabilization of a wheeled inverted pendulum on a slope

This paper investigates the potential for stabilizing an inverted pendulum without electric devices, using gravitational potential energy. We propose a wheeled mechanism on a slope, specifically, a wheeled double pendulum, whose second pendulum transforms gravity force into braking force that acts on the wheel. In this paper, we derive steady-state equations of this system and conduct nonlinear analysis to obtain parameter conditions under which the standing position of the first pendulum becomes asymptotically stable. In this asymptotically stable condition, the proposed mechanism descends the slope in a stable standing position, while dissipating gravitational potential energy via the brake mechanism. By numerically continuing the stability limits in the parameter space, we find that the stable parameter region is simply connected. This implies that the proposed mechanism can be robust against errors in parameter setting.

Parametric identification of stochastic dynamic model of human visuomotor tracking control

We conducted an experiment on a visuomotor tracking task using human participants and compared it with numerical simulations on a stochastic dynamic model of the same task. Our numerical model comprises additive and multiplicative white Gaussian noises and a state feedback term. The parameters of the numerical model were identified using particle swarm optimization. To examine the stochastic behavior of the tracking task, we experimentally estimated the probability density functions (PDFs) of the state variables. Three of the four experimentally obtained PDFs show good agreement with those numerically obtained by the proposed model.

Moment stability analysis of linear stochastic human controller model in visuomotor tracking task

AbstractWe investigate the stability limits of linear stochastic human controller model. In our previous study, we had proposed a model by which the probability distributions of human visuomotor tracking data can be accurately reproduced. In this study, we conduct a stochastic analysis on our model by deriving a system of moment differential equations with respect to random state variables of this model. We evaluate the stability limits of our model by detecting zero-eigenvalue conditions of the Jacobian matrix of the moment differential equations. The resulting stability limits make it possible to characterize the human parameter values that were experimentally identified from the human participants in our previous study; this shows that during the visuomotor tracking experiments, the human participants generated huge fluctuations far from the stability limits while applying almost neutrally stable proportional gain.

Improvement of an LUT-based intelligent motion controller by underestimation of reachable sets

We develop a preprocessing method to improve the performance of an intelligent motion controller. Our method addresses the competitive problems that have been observed in the coupled inverted pendula model, in which a controller outputs impulsive forces to produce the desired final states based on a look-up table (LUT) that stores dynamical correspondences from the initial to the final states. However, the degradation in performance due to misclassifications in the LUT occurs near the boundary points of the reachable sets of the model. The proposed algorithm removes the boundary points from the LUT. The resulting controller successfully reduces misclassification errors and improves overall control performance.

An Experimental Study on Balancing Tasks of Human Subjects in Cooperation With Invisible Artificial Partners

This paper studies coupled balancing tasks based on coupled inverted pendula (CIP) framework. We experimentally investigate the cooperative balancing task on a virtual CIP model, performed by a pair of an invisible artificial controller and a human subject, where experimental participants were not allowed to watch the movement of the artificial partner during experiments. The experimental result on Lyapunov exponents implies that the human subject seems to try to make the artificial controller neutrally stable as well as the visible case in our previous study. Therefore, the result implies that the visual feedback from the balancing state of the artificial partner may not be related to the dynamical property of human.Copyright

Identification of Nonlinear Systems by Synchronization in Chaotic Systems. Parametric Identification by Autosynchronization.

This paper studies a practical method for parametric identification of one degree of freedom forced Duffing system by the chaotic autosynchronization. Our previous paper discussed a method evaluating modeling errors of a chaotic system by the chaotic synchronization and showed that the proposed index approaches its minimal value as a modeling error reaches zero. The next step of our approach is to develop a practical method to obtain a model which synchronizes with a target chaotic system (consequently becomes identical to the target system). To achieve this, we develop an application of an autosynchronizing chaotic system. The basic theory of our method have been developed by Parlitz. However, his work dealt only with an autonomous system such as Lorenz system, which rarely arises in mechanical vibration problems. First, we develop a method constructing an autosynchronizing system for a parametric identification of mechanical vibration systems. We then perform a parametric identification of the forced Duffing system by the autosynchronizing system. The precise values of system parameters of the forced Duffing system are dynamically estimated even if these parameters are time-varying.

Characterization of Chaotic Behaviors in Nonlinear Systems. Experiment.

This paper shows experimental results of a method determining what kind of chaotic bifurcations occur. The method is an application of statistical mechanics. In the previous paper, in order to apply the statistical mechnics to time series analysis in practical situations, we proposed a method of calculating statistical mechanical quantities without system equations. The results showed that the method is effective for characterization of unknown systems whose equations are not known. The next step is to investigate whether the method is also effective for experimental chaos. For this purpose, we analyze chaotic motions in an experiment on a parametrically forced pendulum by our method. The results are in good agreement with our previous numerical results. This means that the method will be useful to identify physical chaos near burst bifurcation.