Hisashi Kando

Multirate digital control design of an optimal regulator via singular perturbation theory

Abstract In this paper a multirate digital control design of an optimal regulator is investigated via singular perturbation theory. It is shown that the singularity perturbed continuous-time regulator leads, under slow and fast sampling rates, to two different discrete-time versions. They are decomposed into slow and fast subsystems, and then these solutions are combined in a proper way. Within the framework of such a decomposition-coordination principle, a multirate control design is developed naturally. Furthermore, the problem of the asymptotic stability of a multirate controlled system is investigated and the relationship between the original continuous-time version and the multirate controlled version is discussed.

Robust Trajectory Tracking Control of Elastic Robot Manipulators

In this paper, a robust control strategy is proposed for the trajectory tracking control of multi-link elastic robot manipulators. The robustness against both of the structured uncertainty caused by the nonlinear mechanical structure and the unstructured one caused by elasticity of links is taken into account in designing controllers. For this purpose the model of elastic robot manipulators is decomposed into the slow model and the fast model by using an integral manifold approach. The slow controller, which is robust against the structured uncertainty, is designed for the slow model on the basis of VSS theory. On the other hand, the fast controller, which is robust against the unstructured uncertainty, is designed for the fast model on the basis of H control theory. Then the composite control is constructed with the slow controller and the fast controller. Some results of numerical simulations are presented to show the effectiveness of this design procedure.

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.

Lyapunov-based force control of a flexible arm considering bending and torsional deformation

Abstract This paper describes the Lyapunov-based force control suppressing the coupled bending and torsional vibrations of a one-link flexible arm with a rigid tip body. On the basis of the distributed parameter model, the output feedback control law is constructed using Lyapunov method, and the asymptotic stability of the closed-loop system is proved. The proposed controller consists of the PD feedback of the motor angle and a feedback of the bending strain at the root of the flexible arm. Some simulations are performed to show the effectiveness of the proposed controller.

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.

Optimal force control of elastic robot with contact motion to environment

This paper presents a control method for the contact motion of the one link flexible arm. Our purpose is to accomplish the smooth transition from the free space to the constraint space without changing control laws at a collision. We design the controller based on the model following servo system with two additional compensators: one is the stabilizing compensation based on a strain feedback, and the other is the approaching velocity compensation based on an angle feedback. In order to improve the force tracking performance, we determine the angle feedback gain so as to minimize the performance index. Some experimental results are presented to show the effectiveness of the proposed controller.

Sliding Mode Servo Control for Electromagnetic Engine Valve

An electromagnetic engine valve (EMV) has received a great deal of attention due to the growing importance of issues such as fuel economy and environmental protection in the automotive. In this paper we propose a new positioning control method for the prototype linear motor developed for the EMV. This linear motor has nonlinear properties due to the detent force, force ripple and the friction. We design a positioning controller using the sliding mode servo control with variable switching hyper plane in order to realize the robust property against the nonlinear properties and the high speed positioning. Moreover, the low valve seating velocity is very important to realize the EMV. For this purpose we modified the reference signal of the displacement of the valve to reduce the valve seating velocity. The effectiveness of the proposed control methods are confirmed by some experiments