Tetsuo Iwazumi

Stabilizing feedback controllers for singularly perturbed discrete systems

Stabilizing problems for singularly perturbed discrete systems are considered. First, systematic approaches to designing feedback controllers are discussed. Second, stability results for singularly perturbed discrete systems are given, and these results are used to investigate stabilizing problems for state feedback-controlled systems.

Sub-optimal control of discrete regulator problems via time-scale decomposition

The paper investigates an infinite-time discrete regulator problem with a two-time-scale property. Sufficient conditions are given for the existence of a suboptimal solution, and a near-optimum design method is proposed via the time-scale decomposition approach. The method reduces the system order and has a mode-decoupling property.

Initial value problems of singularly perturbed discrete systems via time-scale decomposition

In this paper, we investigate the iteration scheme of the mode decoupling transformation in the discrete system, and by using these results, we formulate the boundary layer method in the discrete system. The main purpose of this method is the systematic treatment of obtaining approximate solutions of the singularly perturbed initial value problem. Finally, we give an illustrative example of a seventh order power system.

Multirate observer design via singular perturbation theory

Abstract In this paper multirate observer design is considered via singular perturbation theory. Following a discussion of the design of single-rate observers, i.e. fast- and slow-sampling observers, multirate observer design is developed within the framework of a decomposition-coordination principle. Problems of asymptotic stability and the responses of an error system are investigated, and the relation between single-rate and multirate observers is clarified.

General servomechanism problems for distributed parameter systems

Abstract This paper investigates a general servomechanism problem for distributed parameter systems. The systems are described by linear differential equations in a Banach space applicable to both parabolic and hyperbolic equations. A feedback control law is determined in order to stabilize the resultant controlled system exponentially or strongly, and regulate output to reference outputs asymptotically in spite of un-measurable arbitrary disturbances. It is noted that the disturbances and the reference outputs treated here both belong to general classes.

Design of servo systems for distributed parameter systems by finite dimensional dynamic compensator

The design problem of servo systems for distributed parameter systems is investigated. The output regulator of integral type is designed in order to guarantee internal stability and output regulation. The design procedure based on a dynamic stabilizing compensator is discussed. The output regulation of a wide class of distributed parameter systems is proved under the condition that a closed-loop system is stabilized by a dynamic compensator of general type. Then a closed-loop system can be stabilized by a finite dimensional dynamic compensator under some additional conditions. The reducabitity of the design procedure to a purely finite dimensional one is discussed.

Singular perturbation modelling of large-scale systems with multi-time-scale property

The problem is investigated of singular perturbation modelling, which plays an important role in cases of the application of the singular perturbation method to the design and analysis of large-scale systems. In both continuous- and discrete-time versions, modelling concepts based on structural properties are studied, and computer-oriented algorithms are developed. The results of two-time-scale systems are extended to multi-time-scale cases. Furthermore, in order to verify the validity of these studies, some numerical examples are given.

A new approach to control of xenon spatial oscillation during load follow operation via robust servo systems

The control problem of xenon-induced spatial oscillations of a PWR in the axial direction during a load following operation is investigated. The system models are described by a one-group diffusion equation with xenon and temperature feedbacks, iodine and xenon dynamic equations, and heat conduction processes. Control is implemented by full-length and part-length control rods and the boron concentration. In order to achieve the control purpose, control models are formulated as the design problem of robust servo systems for distributed parameter reactor systems. The total thermal power and the axial offset are chosen as outputs to be controlled. The control systems consist of servo compensators and stabilizing compensators. They are designed based on finite-dimensional systems which are constructed by linearizing around steady states, approximating by the Galerkin method, and reducing dimensions via the singular perturbation method. A new and simple computational algorithm to obtain an approximate solution of steady-state neutron balance is developed via the perturbation method. Some results of numerical simulations are shown in order to discuss the effectiveness of the theory developed in this paper. In particular, it is shown that the designed servo systems are robust against model errors with linearization and modal truncation. >

State feedback controller design of two-time-scale discrete systems via singular perturbation approach

The design of a state feedback controller for a two-time-scale discrete-time system is considered via a two-stage design approach. After discrete-time modelling via slow and fast sampling rates has been discussed, state feedback design approaches for the fast sampling model (i.e. the two-stage design approach and the direct approach) are studied, and the relation between them is clarified. Following these results, the eigenvalue assignment and the stabilizing problems are investigated.

Trajectory control of multi-link elastic robot manipulators via a nonlinear feedback controller and a robust servo controller

This paper investigates the control problem for multi-link elastic robot manipulators tracking desired trajectories with suppressed vibrations due to the elasticity of links. By using the virtual rigid link coordinate system, the finite-dimensional model is obtained. Then the controller is constructed by the nonlinear feedback controller and the robust servo controller. The nonlinear feedback controller compensating for the nonlinear terms contains not only rigid modes but also elastic modes estimated on the basis of the asymptotic perturbation techniques. The robust servo controller is designed for the low-dimensional model as it suppresses the elastic vibrations and eliminates the control and observation spillover. Some results of numerical simulations are presented to show the effectiveness of the design procedure proposed in this paper. In particular, it is shown that the proposed controller is robust against the model errors with the linearization, the modal truncation, and the parameter uncertainties.