Yasuhiko Mutoh

Interactor structure estimation for adaptive control of discrete-time multivariable nondecouplable systems

Abstract We are interested in this paper in adaptively controlling nondecouplable discrete-time multivariable systems with controllers of reduced complexity and without introducing additional delays in the loop. We provide a solution to the following problems: first, give a procedure to incorporate plant prior information to reduce the number of adjustable parameters. To this end, we propose an algorithm for the estimation of the interactor structure from generic knowledge of the plant Markov parameters. Second, present a globally convergent adaptive controller for minimum phase systems with nontrivial delay structure. Also, we give a self-contained elementary derivation of the delay structure of multivariable systems in terms of matchable models and the plant Markov parameters.

Inverse interactorizing and triangularizing with an arbitrary pole assignment using the state feedback

A simple method is presented on how to generate the state feedback which makes the closed-loop transfer matrix the inverse of the interactor matrix. This can be regarded as a generalization of decoupling control using state feedback. An arbitrary pole assignment which preserves the lower left triangular form of the inverse of the interactor matrix is also considered. >

A simple derivation of the interactor matrix and its applications

An interactor matrix plays several important roles in the control system theory. In this article, we present a simple method to derive a special interactor matrix using Moore–Penrose pseudoinverse. The interactor by the proposed method has all its zeros at the origin, and has the all-pass property in the discrete-time. A systematic procedure to obtain an identity interactor, which has an lower triangular structure or has arbitrarily prespecified zeros, is also shown.

Suboptimal exact model matching for multivariable systems with measurement noise

This paper describes a method for the design of discrete-time model matching control systems for a multivariable plant with measurement noise. This method uses a new parametrization for model matching controllers. Simulation results are presented which confirm the validity of the design method.

Suboptimal perfect model matching for a plant with measurement noise and its application to MRACS

This note describes a method for the design of discrete time model matching control systems for a plant with measurement noise, and the application of this method to model reference adaptive control systems. This method uses the free parameters of the controller. Simulation results are presented which confirm the validity of the design method. >

Observer-based pole placement for non-lexicographically-fixed linear time-varying systems

In this paper, the observer based pole placement control for non-lexicographically-fixed linear time-varying MIMO systems is considered. Using the concept of the relative degrees of a MIMO system, Ackerman-like design algorithm for pole placement state feedback control is directly derived. This makes the calculation procedure to obtain the pole placement state feedback very simple, especially for MIMO systems. The separation principle is also shown in the case where both of the controllability indices and the observability indices are not lexicographically-fixed.

A New Design Procedure of the Pole-Placement and the State Observer for Linear Time-Varying Discrete Systems

This paper presents a new design procedure of the pole placement and the Luenberger observer for linear time-varying discrete systems. First, a simple calculation method to derive the pole placement state feedback gain for linear time-varying discrete systems is proposed. It is shown that the pole placement controller can be derived simply by finding some particular “output signal” such that the relative degree from the input to this new output is equal to the order of the system. Using this fact, the feedback gain vector can be calculated directly from plant parameters without transforming the system into any standard form. In general, the equivalent transformation of the time-varying linear system does not preserve the stability. The paper also shows the condition of the stability of the closed loop system. Then, this method is applied to the design of the observer. For this purpose, the anti-causal system is introduced. Using the dual property of this system, the observer gain vector is calculated by the proposed simple design technique of the pole placement control.

A method for verifying sector conditions in nonlinear discrete-time control systems

The stability of a discrete feedback system with a continuous broken-line nonlinearity is considered. Many nonlinearities in practice are included in this class. Sufficient conditions for this type of nonlinear feedback system to be asymptotically stable in the large are developed using the contraction mapping theory. It is then shown that Kalmans conjecture (1957) for a feedback system with a sector nonlinearity also applies to discrete systems under a restricted sector condition. A method for obtaining this restricted sector by solving a quadratic equation is presented. >

A simple derivation of right interactor for tall plant and its application to inner-outer factorization

An interactor matrix plays several important roles in the control system theory. In this paper, we present a simple method to derive the right interactor for tall transfer function matrix using Moore-Penrose pseudoinverse. By the presented method, all zeros of the interactor lie at the origin. Moreover, the interactor by the proposed method has all-pass property in discrete-time. The method will be applied to the inner-outer factorization. It will be shown that the choice of interactor does not influence the result of the factorization.

A Design of Indirect Model Reference Adaptive Control for Discrete-Time Multivariable Plant

Exact model matching (EMM) is not only a useful design strategy itself, but also an important one since it gives the elementary structure of an adaptive control systems. It is reported that EMM system is designed by deriving an interactor matrix of the plant, and then solving the design equation. In this paper, it will be given a new procedure for the EMM design based on an idea of polynomial basis. By this method, it can be obtained the interactor and feedback controllers at the same time. It will be extended to a design of model reference adaptive control systems