Sadaaki Kunimatsu

Stability of zero dynamics of sampled-data nonlinear systems

Abstract One of the approaches to sampled-data controller design for nonlinear continuous-time systems consists of obtaining an appropriate model and then proceeding to design a controller for the model. Hence, it is important to derive a good approximate sampled-data model because the exact sampled-data model for nonlinear systems is often unavailable to the controller designers. Recently, Yuz and Goodwin have proposed an accurate approximate model which includes extra zero dynamics corresponding to the relative degree of the continuous-time nonlinear system. Such extra zero dynamics are called sampling zero dynamics. A more accurate sampled-data model is, however, required when the relative degree of a continuous-time nonlinear plant is two. The reason is that the closed-loop system becomes unstable when the more accurate sampled-data model has unstable sampling zero dynamics and a controller design method based on cancellation of the zero dynamics is applied. This paper derives the sampling zero dynamics of the more accurate sampled-data model and shows a condition which assures the stability of the sampling zero dynamics of the model. Further, it is shown that this extends a well-known result for the stability condition of linear systems to the nonlinear case.

Asymptotic Properties and Stability Criteria of Zeros of Sampled-Data Models for Decouplable MIMO Systems

This note analyzes the zeros of the sampled-data models corresponding to continuous-time decouplable MIMO systems with all relative degrees less than or equal to two and shows approximate expressions of the zeros as power series expansions with respect to a sampling period. Further, stability criteria of the zeros for small sampling periods are given.

Motion planning based on simultaneous perturbation stochastic approximation for mobile auditory robots

In this paper, a motion planning method for mobile auditory robots is proposed based on an optimization technique. Since it is one of the most important abilities for auditory robots to recognize vocal messages correctly, the proposed method is designed to maximize the confidence measure of a speech recognition since the measure is thought to be strongly related to the accuracy of the speech recognition. However, the cost function to optimize is hard to model explicitly, and it is difficult to obtain the gradient that is normally utilized to derive the motion. In order to overcome this difficulty, simultaneous perturbation stochastic approximation(SPSA) that does not require an explicit model of the cost function is applied to generate robot motion. The effectiveness of the approach was verified through real experiments: the robot could get better speech recognition rate after it approached the sound source by measuring the confidence measure.

Asymptotic properties of zeros of sampled-data systems

When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold, at least one of the zeros of the resulting sampled-data model is unstable for small sampling periods. Thus, attention is here focused on continuous-time systems with relative degree less than or equal to two. This paper analyzes the zeros of the sampled-data models corresponding to the continuous-time systems mentioned above and gives approximate expressions of the zeros as power series expansions with respect to a sampling period. Further, the stability of the zeros is discussed for small sampling periods and a new stability condition is derived.

On positive real lemma for non-minimal realization systems

Abstract In this paper, we state the positive real lemma and the strictly positive real lemma (KYP lemma) for non-minimal realization systems. First we show the positive real lemma for stabilizable and observable systems under only the constraint on the regularity of the systems, by using the generalized algebraic Riccati equation. Moreover we show that the solution of the Lyapunov equation in the positive real lemma is positive definite. Next we similarly derive the KYP lemma for stabilizable and observable systems with only the above constraint and show that the corresponding solution in the KYP Lemma is positive definite. Finally, as the duals of these problems, we show that the positive real and KYP lemmas for controllable and detectable systems have both positive definite solutions.

The opening-and-closing speed control of an elevator door by frequency-shaping ILQ design method

In this paper we present a modeling and design for robust speed control of an elevator door using ILQ design method with frequency-shaping. We have applied the design results to actual equipment, and performed experiments. By proper shaping of the frequency response of the closed loop transfer function from noise to output, an unnecessary vibration of speed generated by uncertainty was confirmed to be suppressed. As a result, the proposed method has been verified to show robustness against the change of weight of door panels

Design Method of ILQ Servo System with Tracking Robustness

Abstract A robustness problem of output trajectories is considered here in the design of servo systems. Our purpose is to design a robust servo system with tracking robustness in that its output trajectory remains in a neighborhood of the nominal trajectory when the dynamics of the system is perturbed. For this purpose we propose a control configuration of robust servo system with a conditional feedback. In this configuration the robust servo system is designed by the Inverse Linear Quadratic (ILQ) design method as proposed by the second author, and the conditional feedback is added to achieve tracking robustness of the output response. First, we state the configuration of this servo system, called Model Reference ILQ (MR-ILQ) servo system, and then provide a theoretical basis for parameter tuning. Second, we clarify the relation between these parameters and the closed loop performances such as robust stability and tracking robustness. Finally, we establish a new design method of ILQ servo system with tracking robustness. We also illustrate a numerical example to show the validity of our results.

Generalized algebraic Riccati equations and its application to balanced stochastic truncations

We first study a generalization of algebraic Riccati equations that solve a certain type of spectral factorization problems. We then apply this result to balanced stochastic truncations of a plant without the assumption of nonsingularity of its direct transmission term. Finally, we illustrate a numerical example to show the validity of our results.

Optimal decentralized servo control for systems with diagonal decoupling matrix

Abstract In this paper, we propose an optimal servo design method of decentralized control systems from the inverse linear quadratic problem viewpoint by using the structure of controllers obtained by the ILQ(Inverse Linear Quadratic) design method. Particularly, we propose a decentralized ILQ servo design method for systems with relative degree no more than 2 and diagonal decoupling matrix. We show that the closed loop system can always be stabilized in the framework of the decentralized ILQ design method. Moreover, we show that the optimal decentralized servo controller with the decoupled input/output characteristics is obtained. Finally, we illustrate the effectiveness of our proposed method by simulation.

l ∞ preview control for biped walking pattern generation

In this paper, we propose mixed l<inf>2</inf>/l<inf>∞</inf> preview control for biped walking pattern generation. First, we propose the mixed l<inf>2</inf>/l<inf>∞</inf> preview control via BMI(Bilinear Matrix Inequality) optimization approach for the system representing ZMP of humanoid robots. Next, we derive a method optimizing the mixed l<inf>2</inf>/l<inf>∞</inf> preview controller by transforming the BMI condition into an iterative LMI(Linear Matrix Inequality) condition. Finally, we show the effectiveness of our proposed method by simulation.