The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is ‘off’ when the state vector is near the stable manifold of the saddle and is ‘on’ otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.

This paper mentions about the permanentmagnet synchronous motor (PMSM) propulsion system and its energy-saving performance confirmed through running tests on the Ginza Line of Tokyo Metro Co., Ltd. Comparing the conventional IM system installed Ginza Line with the PMSM system, the PMSM propulsion system has achieved 12.5% power consumption reduction in powering. In this paper, we describe the outline of the PMSM propulsion system and show results of the energy-saving performance evaluation tests carried out for more than 1.5 years.

Tokyo Metro Co., Ltd. (Hereunder;, Tokyo Metro) and Toshiba Corporation (Hereunder; Toshiba) successfully developed and introduced PMSM (Permanent Magnet Synchronous Motor) propulsion system for Tokyo Metro Line in Tokyo Japan. It has been past four (4) years without problems since the first revenue service was started.This paper explains the background and evolution of the system and reports the confirmed productive results in view of "Energy savings", "Low noise emission" and "Less maintenance".