Yasuyuki Funahashi

Design of discrete-time repetitive control system for pole placement and application

A new repetitive control system is proposed from the viewpoint of pole placement. First, the proposed repetitive controller can assign all poles of the closed-loop system on a disk with a given radius and the center at the origin. As a result, faster convergence of the controlled error to zero than the previous ones is obtained. Next, the proposed controller is obtained explicitly, and the design method does not require an equation to be solved. The design effort is independent of the period of the repetitive signals to be tracked or rejected. In other words, the design effort is very small, even if the period is very large. Then, the robustness of the control system is improved by introducing a low-pass finite-duration impulse-response filter in the controller. Finally, the proposed scheme is applied to a DC servomotor system, and the effectiveness is demonstrated by both simulations and experiments.

Grasp stability analysis considering the curvatures at contact points

Proposes a method for analyzing the stability of grasps. The characteristic points in this paper are to consider the curvature of both hand and object at contact points and the grasp with friction and frictionless contact. From this analysis, it is shown that the grasp using round fingers is more stable than using sharp fingers. Moreover, we establish the condition on the fingers stiffness to stabilize the grasp with friction. It is proved that the required stiffness of fingers are decreased by considering the curvature. The stability analysis is greatly simplified by using potential energy of the grasp system and is of practical use.

The role of retinal bipolar cell in early vision: an implication with analogue networks and regularization theory.

Abstract. A linear analogue network model is proposed to describe the neuronal circuit of the outer retina consisting of cones, horizontal cells, and bipolar cells. The model reflects previous physiological findings on the spatial response properties of these neurons to dim illumination and is expressed by physiological mechanisms, i.e., membrane conductances, gap-junctional conductances, and strengths of chemical synaptic interactions. Using the model, we characterized the spatial filtering properties of the bipolar cell receptive field with the standard regularization theory, in which the early vision problems are attributed to minimization of a cost function. The cost function accompanying the present characterization is derived from the linear analogue network model, and one can gain intuitive insights on how physiological mechanisms contribute to the spatial filtering properties of the bipolar cell receptive field. We also elucidated a quantitative relation between the Laplacian of Gaussian operator and the bipolar cell receptive field. From the computational point of view, the dopaminergic modulation of the gap-junctional conductance between horizontal cells is inferred to be a suitable neural adaptation mechanism for transition between photopic and mesopic vision.

Design of robust repetitive control system for multiple periods

An approach to regulating quickly any periodic signals with multiple periods is proposed. The contributions are as follows. First, the proposed multiple repetitive controller not only can be implemented with much fewer memory elements than previous ones but also can provide much faster convergence of the controlled error to zero. Secondly, the proposed repetitive controller can assign all poles of the system on a disk with a given radius whose center is the origin. Thirdly, the proposed controller is obtained in an explicit form and the design method requires no equation to be solved. Fourthly, the robustness of the system is improved by introducing a low pass zero phase filter.

Stability analysis of 3D grasps by a multifingered hand

We discuss stability of 3D grasps by using a three-dimensional spring model (3D spring model). Many works have described stability of a frictionless grasp. These works used a one-dimensional spring model (1D spring model) for representation of frictionless contact as a matter of course. However, a 1D spring model involves the following problems: (i) displacement of a finger is restricted to one dimension along the initial normal at contact point; and (ii) it is not clearly considered that a finger generates contact force to the object along the normal direction only. To overcome the problems and provide accurate grasp stability, we introduce a 3D spring model. Then a fingers displacement is relaxed and a fingers contact force is precisely formulated. We analyze grasp stability from the viewpoint of the potential energy method. From numerical examples, we show that there exists an optimum contact force for stable grasp. Moreover, we also analyze a frictional grasp by using contact kinematics of pure rolling. By comparing frictional grasp stability with a frictionless one, we prove that friction enhances stability of a grasp.

Computational Studies on the Interaction Between Red Cone and H1 Horizontal Cell

We propose an equivalent circuit model of a discrete formulation to describe the interaction between the red cone syncytium and the H1 horizontal cell syncytium in lower vertebrate retinas. Analytical solutions of the model provide intuitive understandings of spatio-temporal properties of light-induced responses in reference to membrane impedance, strength of chemical synapse and coupling resistance connecting neighbouring cells. Physiologically plausible values of these parameters are estimated using the solutions. Quantitative studies are made to elucidate the function of (1) the negative feedback from the H1 horizontal cell to the red cone, and (2) the resistance increase of H1 horizontal cell coupling by dopamine.

Stability robustness for linear state space models—a Lyapunov mapping approach

Some Pythagorean-like conditions for the existence of a common Lyapunov solution for two given matrices are presented. These conditions are set on the Lyapunov mappings associated with given matrices. The key is the semipositiveness of linear mappings defined on symmetric matrices. From the viewpoint of the existence of a common Lyapunov solution, some known stability robustness results are reviewed and refined.

Discrete-time repetitive control system with multiple periods

In this paper, a new approach to regulate any periodic signals with multiple periods is proposed and a useful discrete-time controller called multiple repetitive controller is presented. The contributions are as follows. First, the proposed multiple repetitive controller not only can be implemented with much less memory elements than the previous ones but also can provide much faster convergence of the controlled error to zero. Secondly, the proposed repetitive controller not only can assure the stability of the closed loop system but also can assign all poles of the system on a disk with a given radius whose center is the origin. Thirdly, the proposed controller is obtained in an explicit form and the design method requires to solve no equation. The design effort is very small even if the periods are very large. Finally, the proposed scheme is applied to DC servo motor system, and the effectiveness is demonstrated by simulation.

Robust-tracking deadbeat control

We derive the parametrization of all controllers that achieve both the robust-tracking and the deadbeat control. We also give the parametrization of all reference functions for which the robust tracking and designed deadbeat property is guaranteed by all robust-tracking deadbeat controllers for one reference. The solution to the robust-tracking deadbeat problem for more than two reference functions is also given. We use the H ∞-norm of the sensitivity function as the robustness index of the system. By using two-degree-of-freedom control systems, we can achieve both minimal-time deadbeat control and optimal robustness with only one controller.

On the simultaneous diagonal stability of linear discrete-time systems

Abstract This paper studies the set of time-invariant linear discrete-time systems in which each system has a diagonal quadratic Lyapunov function. First, it is shown that there is generally no common diagonal quadratic Lyapunov function for such a set of systems even if the set is assumed to be commutative. It is also shown that the commutativity assures the existence of a common diagonal quadratic Lyapunov function inside the set of 2×2 systems or the set of nonnegative systems. Then, two simple topological results are presented concerning the simultaneous diagonal stability on the set of nonnegative systems. The first is a measure of the difference of matrices that assures the simultaneous diagonal stability. The second is a measure of the commutativity of matrices.