Minimal Dimension Realization for Stochastic Discrete Time Systems

This paper is concerned with the problem of minimal dimension realization for stochastic systems. The innovation representation is adopted as the model of the system. Two algorithms are presented which yield the minimal dimension realization from the given finite length of output covariance data. One is for the scalar output system, the other is for the vector output system

State Estimation of Jump Parameter Systems with State-Dependent Observation Noise

A least-squares state estimation algorithm is obtained for a general class of stochastic systems having 1) system nonlinearity ; 2) an unknown jump parameter and 3) state-dependent observation noise. The algorithm developed is consistent in the sense that for each special case with the properties 1) and 2) or 3), it reduces to the algorithm the authors have already developed. Illustrative examples of numerical computation are given for better understanding of the result

Design of Dynamic Deadbeat Controllers Using an Observer or a Dual Observer in Discrete Time Linear Multivariable Systems

This paper considers the problem of designing the minimum time dynamic deadbeat controllers, using an observer or a dual observer. As a preliminary, optimal controller and observer are defined and obtained. Then, the existence of a dynamic deadbeat controller is examined, and a separation theorem is proved. This theorem states that the minimum time dynamic deadbeat controller is given by the optimal controller combined with the optimal observer. These results are dualized to yield the corresponding result in the case of using the dual observer, i.e., the result on the minimum time dual deadbeat controller. Finally, a method is presented for finding reduced order controllers by applying the results on linear function observers

Parameter Identification of Systems with Noise in Input and Output

In the problem of system parameters identification, most treatments made previously have assumed that the input to the system was free from noise. However, there would be many instances, where it would be more practical to assume the input to be accompanied with additive noise. Such a case is considered in the present paper, and the asymptotic unbiased estimate is obtained under certain conditions. The extended matrix approach with the ordinary least square method is used for the estimation of the parameters of the systems and the noise filter. Order identification is also discussed for this system with input noise. An application of the obtained solution to a numerical example shows that it gives a satisfactory result, both in parameter identification and in order identification

The Monte Carlo Approach to State Estimation for Linear Dynamical Systems with State-Dependent Measurement Noise

This paper is concerned with the state estimation of linear dynamical systems with state-dependent measurement noise. The minimum variance estimate of the state is obtained as the weighted mean of the outputs of Kalman filters parameterized by the state-dependent measurement noise sequences. The usual calculation for this estimate, however, becomes impractical since a very large amount of outputs of Kalman filters is required. Therefore, we regard the set of all the state-dependent measurement noise sequences as a population. Then, we evaluate the minimum variance estimate on the basis of a relatively small number of outputs of Kalman filters, parameterized by the state-dependent measurement noise sequences sampled at random from the population. The convergence of the algorithm is established. Then, by an approximation of a sampling procedure with a fast convergence property, a feasible sampling procedure is determined and a practical algorithm is designed. This policy of design leads to an efficient algorithm. Digital simulation results show a good performance of the proposed algorithm

State Estimation for Linear Discrete-Time Systems with State-Dependent Noise

In this paper, the state estimation problem is considered for a class of linear systems with state-dependent noise. The optimal nonlinear estimator in the mean square sense is first derived on the basis of the Bayesian approach. Then a sub-optimal estimator is proposed, in which the estimate is still nonlinear in the observation data, and the covariances are obtained recursively using the observation data. The case where the state-dependent noise is white is treated specifically. Some simulations for this case are made in order to examine the practicability of the proposed sub-optimal estimator, and the result is compared with that of the linear estimator by McLane

Parameter and Order Estimation in A Class of Multivariate Stochastic Systems

The problem of estimating the parameters and order of a class of multivariate systems is treated. The considered systems are described by a stochastic time invariant linear difference equation. We will introduce the so called canonical form III as a possible unique representation of the system. We will show that by using this canonical form, the computational effort compared with other canonical forms can be reduced. Further, we will show that the pole-zero cancellation, which is one of the methods used in identifying the order of single input-single output systems, can be extended to the multivariate systems in canonical form III

On Pole Assignment and Stabilization for the Heat Equation

For one type of infinite dimensional linear systems, specifically the heat equation, the possibility of assigning the infinite set of poles of a closed loop system formed by means of a suitable linear state feedback operator is discussed. Necessary and sufficient conditions are derived for the existence of a feedback opeartor to shift all the eigenvalues of the controllable system, and to assign an arbitrary finite set of poles of the closed loop system. As an application of this result, it is shown that an open loop controllable system can be stabilized in a desired order of convergence by a suitable choice of the feedback operator

Nonlinear Compensation of Two-Dimensional Contouring Servomechanism

This paper gives a method of nonlinear compensation for a two-dimensional contouring servomechanism, by which the cornering error, or the transient error at the corner of a figure being traced, is held within given tolerance. The effect of compensation is analyzed by graphical means, using the result of model experiment and the parameters are determined so as to obtain the desirable performance. Stability analysis of the system is also given utilizing the describing function method. The result is applied to an actual automatic flame cutting machine and the practicability is proved

Analysis of the High-Speed Servo-System with an SCR Servo-Amplifier

In this paper we will analyze the high-speed servo-system with an SCR servo-amplifier. The improvement of the system performance is made by stabilizing the system and obtaining a fast response. For these purposes, two nonlinear compensation networks, a nonlinear lowpass filter and a nonlinear compensation with a Zenor diode, are inserted into the feedback loop. The effects of such compensations are investigated by the model experiments and are discussed, considering them as a nonlinear gain adjustment