An extension of generalized minimum variance control for multi-input multi-output systems using coprime factorization approach

Abstract

This paper proposes a new generalized minimumvariance controller (GMVC) having new design parameters by using coprime factorization approach for multiinput multi-output (MIMO) case. The method is directly extended from a conventional GMVC and to construct the controller, it needs to solve only one Diophantine equation as in the conventional method. In this paper, by using double-coprime factorization, a simple formula for closed-loop system given by the parametrized controller is obtained and using the formula, it is proved that the closed-loop characteristic from reference signal to plant output is independent of the selection of the design parameters and the poles of the controller can be chosen by the design parameters without changing the closed-loop system.

A design method of strong stability self‐tuning controller based on on‐demand type feedback control

“…Thus, in order to configure on-demand type feedback control rule that can adjust the effect of (t), we propose a new definition of the design parameter U(z −1 ) as a stable rational function, based on previous research in configuration of strongly stable systems. [12][13][14][15]…”

“…With that method, feedback controller's output is treated as an error signal, and feedforward controller is updated according to the inverse model of controlled plant so as to follow target value. Thus in this paper, we use a stable rational function to specify design parameters of on-demand type feedback control rules based on research in configuration of strongly stable systems, [12][13][14][15] and present control results for a strongly stable self-tuning controller. [7][8][9] On the other hand, the present study deals with a control system to follow a target value (control system with closed loop gain of 1); in so doing, design parameters are introduced based on coprime factorization approach, and feedforward and feedback controllers are configured so that steady-state gain of open-loop system also becomes 1 (control system is configured so that steady-state value of feedback signal is 0 when parameters of controller plant are true values, and no disturbance exists).…”

“…However, control systems obtained with such control rules were not sufficiently examined under noisy environments, while design parameters were restricted to constants. Thus in this paper, we use a stable rational function to specify design parameters of on-demand type feedback control rules based on research in configuration of strongly stable systems, [12][13][14][15] and present control results for a strongly stable self-tuning controller.…”

Current Control of Switched Reluctance Motor Based on Generalized Minimum Variance Controller

“…Among other properties, this new algorithm allows the user to tailor the performance of the controller by a proper choice of the optimality criterion [11], and also can deal with nonminimum phase systems. In recent years, the interest on GMVC-type controllers have reappeared mainly by exploiting its characteristics to interact with other control structures [12], extension to multivariable systems [13], its ability to deal with time variant systems [14], and the improvement in robustness [15]. Nowadays, an adequate specification of cost polynomials for GMVC is a major task and it may become critical if an autonomous initialization is required [16].…”

A state-space based design of generalized minimum variance controller equivalent to transfer-function based design

“…First, it may be possible to design a controller with an observer having poles close to 1, which is robust to measurement noise. Second, authors have already proposed a strongly stable GMVC by using polynomial coprime factorization of a controller of GMVC [5] [6]. However, by polynomial approach, it was difficult to obtain a strongly stable GMVC for multivariable systems having different numbers of inputs and outputs.…”