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Kanticha Kittipeerachon,Noriyuki Hori 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
An exact discrete-time model of a matrix differential Riccati equation that has recently been proposed is applied to a finite-horizon optimal control problem. This discretization method can always be used for a usual backward-in-time computation of a time-varying feedback control gain, which can be stored then in a memory for later use. Unlike existing methods that involve errors, the proposed algorithm yields gain values that are exact to those of the continuous-time case at discrete-time instants for any discrete-time period. Furthermore, an approach is suggested for extending this method to an on-line computation of the optimal gain, by converting the boundary value condition into an initial value condition using the backward differential Riccati equation. It was found from simulation studies that the proposed on-line algorithm can yield the correct gain sequence under a certain condition, eliminating the need to prepare the gain sequence a priori. However, a further investigation is needed to clarify this condition.
Numerical Exact Discrete-Time-Model of Linear Time-Varying Systems
Hiroaki Shiobara,Noriyuki Hori 제어로봇시스템학회 2008 제어로봇시스템학회 국제학술대회 논문집 Vol.2008 No.10
This paper proposes a method of obtaining a numerical, exact discrete-time-model for linear time-varying systems. The method relies on the computation of a transition matrix expressible as the Peano-Baker Series for a given discrete-time interval and system parameters. For time-invariant systems, the proposed discrete-time model reduces to the well known step-invariant-model. As an example, the Euler differential equation is discretized using the standard forward-difference method, the discretization of Euler differential operator, and the proposed method. Simulations show that the proposed discrete-time-model gives exact values at discrete-time instants for any discretization periods, while the other two methods generate errors.
A New Discrete-Time Logistic Equation Having No Overshoot and No Chaos
Yoshiaki Habiro,Noriyuki Hori 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
This paper proposes a new discretization method for logistic differential equations, for which the popular forward difference model causes chaos and overshoot unless the discrete-time period is chosen to be sufficiently small. While the exact discrete-time model gives exact values at discrete-time instants, it is not really a logistic equation anymore and requires an up-date of a complex gain at each discrete-time instant. In contrast, the proposed discrete-time model has no overshoot for any discretization period T, is more accurate than the forward difference model for large T in general, and requires no update of the gain unlike the exact model.
Improved PIM Digital Driver with Dead-Zone Compensation for a Stepping Motor
Takahiro Okada,Noriyuki Hori 제어로봇시스템학회 2009 제어로봇시스템학회 국제학술대회 논문집 Vol.2009 No.8
The present paper is concerned with an improvement of the so-called Plant-Input-Mapping (PIM) discretization??as applied to an analog controller that is used in a high-performance commercial driver for stepping motors. The controller employs a linearizing compensator to cancel out the effect of dead-zone nonlinearity that exists in a pulse-width-modulation circuit of the driver, which has been one of the major limiting factors in the design of linear PIM digital drivers. The experiments show that the proposed digital driver has the performance that is closer to that of the analog one, even at the low sampling rate of 4kHz, than the existing PIM driver which approximates the dead-zone as a simple gain.
Discrete Modeling of Patellar-Tendon-Reflexes As Logistic Phenomena
Takashi Nozawa,Noriyuki Hori,Naotaka Mamizuka 제어로봇시스템학회 2008 제어로봇시스템학회 국제학술대회 논문집 Vol.2008 No.10
The present paper proposes a logistic model to represent patellar-tendon-reflexes (PTR) from the release-angle of the tapping-hammer to the peak angular-speed of the knee joint. The experimental data obtained are discrete in nature and, thus, they are modeled as a discrete system. However, the model is formulated such that parameters of the underlying continuous model are directly obtained so that the discrete results can be related to continuous counterpart with ease. From the observation of PTR data, it was noticed that they resemble well some of the features exhibited by a system whose characteristics are governed by a logistic equation. For these reasons, a technique developed recently for exact time-discretization of nonlinear systems was applied to this non-temporal discrete system. A discrete logistic model was identified from the experimental data obtained from human reflexes. Furthermore, a method is presented to determine an appropriate initial condition to reproduce the data curve using the identified model. The overall scheme was found to give results that were closer to actual data than the popular forward difference method, even with a very large discrete interval. This is important since the modeling can be achieved using a small number of tapping on the patients.
On Linearization of Riccati Differential Equations through Variable Transformations
Tsubasa Kittaka,Noriyuki Hori 제어로봇시스템학회 2008 제어로봇시스템학회 국제학술대회 논문집 Vol.2008 No.10
Exact linearization of a Riccati differential equation, which has a stable equilibrium and an unstable one, is considered using variable transformations. Of particular interests are what happens to equilibrium points of the nonlinear equation when it is linearized and how these points are related to linearizing transformation. The variable transformation is of fractional type and contains four parameters. It is shown that when two parameters are chosen taking the unstable equilibrium into account, the resulting linearized system is stable, while when they are chosen using the stable equilibrium, the linearized system is unstable. Furthermore, when all four parameters are chosen taking both stable and unstable equilibriums into account, the linearized system can be made arbitrarily stable with a simple modification to the transformation.