概要. 行列

はSylvester 方程式を解くことに利用できる行列関数であり，その数値計算手法としてこれまでにはSchur 法やNewton 法のようなアルゴリズムが考えられてきた．本論文では新たなアプローチとして行列を二重指数関数型数値積分公式で数値計算する手法を提案し，その性能を理論的に評価する．提案法は並列計算によって従来の手法では計算困難な大規模行列に対しても適用できる可能性がある．

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概要. 行列

は，代数的リッカチ方程式の求解や固有値計算など多くの応用を持つ．最近，行列を積分表示して二重指数関数型数値積分公式により計算を行う新しい数値計算法が提案され，その大粒度並列性から注目を集めている．本論文では，この手法に対し，行列が対角化可能な場合について新たな理論誤差上界を与えるとともに，収束性向上と丸め誤差低減のための改良法を提案する．また，数値実験により並列性能を評価する．

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今日, プリント配線板 (PWB) や大規模集積回路 (LSI) におけるディジタルシステムは高機能化, 複雑化および多品種化がますます進展している。それに伴いディジタルシステムの設計もコンピュータ支援のCAD/CAMやHDLなどが広く利用されている。このような高度な設計手法の開発の反面, ディジタルシステムの重要部分である論理回路設計の基礎的な理論や技術の開発も要求されてきている。これらの状況から本論文は, あまり議論がなされていない可変順序回路の設計についての基礎的考察とHDLを用いた自動合成について述べる。複数の順序回路に可変できる論理回路はしばしば利用されており, マルチプレクサを用いた方法が使われているが, いまだに効率的な構成法は確立されていない。本論では, 可変順序回路の基本的構成を述べ, そして順序回路設計における状態割当てと可変するための制御割当てとの関係において, 共通項を多く生成することにより簡単化が行えることを示す。これらの有効性を証明するための比較実験の結果を述べる。また, これらの結果を用いてHDLによる可変順序回路の自動合成について述べる。

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In this paper, we propose a method to compensate for nonlinear friction in linear dc motors (LDM) using a neural network controller that is added to the conventional controller. The output of the neural network controller is multiplied by sign function of the velocity reference, because it learns rapidly the nonlinear friction which is related to signs of the velocity. We applied the new method to positioning control of an LDM. The validity of the new method was verified by the experimental results.

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This paper studies the controller design problem for linear time-invariant systems that have on-off type actuators. Although phase-plane analysis, the describing function approach and pulse-modulation technologies have been studied in the classical literature, such approaches do not permit the direct application of optimal controller design techniques including non-linear effects. In this paper, we propose the application of input-state linearization theory to the general class of single on-off input plants. The linearized space resulting from this method allows the application of any linear controller design tool. The method is also extended to be applicable to on-off controllers with a dead-band. To demonstrate the effectiveness of this approach, some numerical studies are presented including the lunar landing problem, and the results are evaluated and compared with numerical optimal solutions.

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In this paper, a parameterizaton of output feedback dynamic sliding mode controller is proposed and the BIBO stability problem of generalized plant is studied. It is shown that by the proposed controller, the sliding mode is achieved in finite time, and thereafter, the ideal sliding mode controller stabilizes the generalized plant in the sense that the slightly modified BIBO stability is assured. Also, the model matching problem is formulated for this controller and the difference between linear dynamic controller and sliding mode controller is highlighted.

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This note proposes a design method of quasi Sliding Mode Control (SMC) for Linear Parameter-Varying (LPV) systems as the combination of Linear State-Feedback Control (LSFC) and additional internal saturation by extending an LSFC gain parametrization for LTI systems in the literature. A numerical example well illustrates the advantage of our controller.

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The conventional sliding mode control (SMC) theory assumes the discontinuous control law, therefore the dynamical system describing the closed loop doesn't satisfy the Lipschitz condition. In this note, we consider the SMC system assuming the continuous control law, and analyze the stability and the robustness from new viewpoints.

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This paper deals with the response reduction effect by friction under 2-dof system. The friction behaviour is effective for dissipating seismic energy. Therefore, in recent years, the installation of an isolator and a damper with frictional element in industrial facilities has been investigated. In addition, the seismic response is reduced by the frictional vibration occurring between piping and support system. However, the seismic response of a 2-dof friction system depends on system parameters such as natural frequencies and the mass ratio of the structure by support. A great deal of time is required for non-linear analysis to obtain optimum system parameters. The present study deals with the “Response Reduction Map” for a 2-dof friction system. This map shows the area that the response magnification is less than 1 and less than the response of a linear system. Firstly, the response reduction map by actual seismic wave is shown. Secondly, the response reduction map by the artificial seismic wave calculated from the design spectrum is shown. Optimum friction forces for reducing the seismic response of 2-dof friction system can be easily obtained by this map without non-linear time history analysis.

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A new algorithm is proposed to compute complex stability radius for perturbed state space models using matrix sign function. The algorithm is motivated by H_∞ norm computation of transfer function matrices. The idea behind the proposed method is to combine the bisection method with a fast algorithm for H_∞ norm computation. Numerical examples are provided.

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This paper deals with a control strategy to attenuate the rotational motion of a target satellite with a manipulator mounted on a free-flying space robot. First, we approximate an impact force and a friction force between the manipulator and the target satellite with smooth functions. Then, the motions of the space robot and the target satellite are given by equations of motion. Next, we design a feedback control law of joint torques with nonlinear model predictive control. We also propose a performance index for determining the pushing and pulling of the manipulator according to the angular velocity of the target satellite. Finally, numerical simulation shows the effectiveness of this control law.

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Sliding mode control is a nonlinear control strategy that is well known for its robustness characteristics. However, the discontinuous control signal causes a significant problem of chattering. In this paper, a synergistic combination of neural networks with sliding mode control methodology for magnetic levitation systems is proposed. In the present approach, a neural network is utilized to estimate the equivalent control. Moreover, a new and simple approach is utilized to construct switching control term for overcome the chattering problem. As a result, the chattering is eliminated. The reduction of the chattering of sliding mode control is achieved by using a defined distance function as the switching control term which only measure the distance between the trajectory of state errors and the sliding surface. Experimental study carried out on the magnetic levitation system is presented. Experiments verified that the proposed control has the advantage of less chattering in sliding mode control.

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本研究では非線形系の制御法、スライディングモード制御（SMC)による磁気浮上制御について検討する。SMCを用いるとき、チャタリングが発生してしまうという欠点がある。そこで、新たにチャタリングを防ぐ制御器を提案する。この提案法は、まず制御誤差の軌道と切換面との間の距離を測る距離関数を定義し、その距離関数を本来のに代わって切換制御入力として使用することによりチャタリング防止が実現される。一方SMCの等価入力を構築するには、系に関する情報が必要とする。本研究では、この等価入力をニューラルネットワークで推定する。そのため、系の情報が未知でよい。最後に提案した手法の有効性を実験により確認した。

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A new calculation technique is proposed for getting symmetric fundamental harmonic solution of the lumped mass system to discontinuous impact excitation. This system is adopted as a typical piecewise linear oscillator haveing no stiffness. First, it is pointed out that the feedback superposition method which was formerly proposed can not be applied to this particular oscillator. Then, an improved calculation technique for getting the periodic pseudo-feedback response is newly proposed whereby converged infinite series and unconverged infinite series can be separated. According to this improvement, even unconverged series of the periodic pseudo-feedback response become to be evaluated by the Cesaro's (C.2) summation to viscous damped system and those (C.3) summation to undamped system, respectively.

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