Yoichi Hirashima

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

This paper proposes a new generalized minimum-variance controller (GMVC) having new design parameters by using the coprime factorization approach for a multi-input multi-output (MIMO) case. The method is directly extended from a conventional GMVC and used 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 the closed-loop system given by the parametrized controller is obtained; and using the formula, it is proved that the closed-loop characteristic from the 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 of a strongly stable self-tuning controller using coprime factorization approach

Abstract This paper proposes a new self-tuning controller having new design parameters. In selecting the design parameters, the controller gives a strongly stable self-tuning controller, that is, the closed-loop system is not only stable, but also the controller itself is stable. The controller consists of an extended minimum variance controller and a parameter identification law. The extended minimum variance controller is extended by including newly introduced design parameters into the generalized minimum variance controller given by Clarke and others. The parameters are introduced by applying the coprime factorization approach and comparing Youla parametrization of stabilizing compensators with the minimum variance controller.

Self-tuning two-degree-of-freedom PID controller reducing the effect of disturbances

This paper proposes a new design scheme for a self-tuning PID controller. To improve the transient property for a reference signal and the robustness to disturbance, the proposed controller is designed in the form of two-degree-of-freedom. Expressions to calculate PID parameters from the identified plant coefficients are given. These expressions are derived by approximating the PID controller to an extended generalized minimum variance control (GMVC) law, which can adjust both of reference response and disturbance response independently. Using a numerical example, the control performance of the proposed method is compared with those of PID controllers designed by other schemes.

Continuous-time anti-windup generalized predictive control of non-minimum phase processes with input constraints

This paper deals with a design problem of a continuous-time anti-windup generalized predictive control system using coprime factorization approach for non-minimum phase processes with input constraints. Based on the proposed design scheme, a condition for stability of the closed-loop system with input constraints and a straightforward method to improve the output response of the system with input constraints are given. Simulation results are presented to support the theoretical analysis.

Adaptive vibration control of flexible structure with unknown and unmeasurable disturbances

Abstract In real robotic systems, when external disturbances (forces and including gravity of the robot) are applied, the vibration effect due to the inherent elastic deformation has to be taken into account in some cases. This paper presents an adaptive compensator by piezoelectric elements to cancel the vibration effect. First, the disturbance model of the external disturbance and the vibrational arm mode is derived. Second, by using coprime factorization, the adaptive compensator is designed to estimate the parameters of the disturbance model. Using the norm bound given by small gain theorem(SGT), robustness of the proposed control system is evaluated. Simulation results support the above proposals.

An extension of discrete-time model reference adaptive control by using coprime factorization approach

This paper proposes a new discrete-time model reference adaptive controller(MRAC) having new design parameters. In selecting the design parameters, the controller becomes a strongly stable MRAC except the zeros of the plant, that is, the closed-loop system is not only stable, but also the controller itself is stable. The extended MRAC is obtained by including newly introduced design parameters into the controller designed by standard MRAC. The parameters are introduced by applying the coprime factorization approach and comparing Youla-Kucera parametrization of stabilizing compensators to the controller by the standard MRAC.

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

Proposes a generalized minimum variance controller (GMVC) using a state-space approach. The controller consists of a state feedback and a reduced-order observer with poles at z=0. A coprime factorization of the state-space based controller is also obtained. It is shown that the GMVC designed by state-space approach is equivalent to the GMVC given by solving Diophantine equations and a polynomial approach. The equivalence is proved by comparing coprime factorizations of the two controllers. From the results of the paper, it may be possible to apply advanced design schemes given by state-space control theory to the design of GMVC.

Continuous-time anti-windup generalized predictive control of uncertain processes with input constraints and time delays

In this paper, a design problem of a continuous-time anti-windup generalized predictive control (CAGPC) system using coprime factorization approach for uncertain processes with input constraints and time delays is considered. The uncertainty of the process is considered as an uncertain time delay. To reduce the effect of the input constraint and uncertain delay, controller for strong stability of the closed-loop system is designed. As a practical appeal, the effectiveness of the proposed design scheme is confirmed by a simulated application to an industrial process with input constraint and uncertain time delay.

Self-Tuning Two-Degree-of-Freedom PID Compensator Based on Two-Degree-of-Freedom Generalized Minimum Variance Control

Abstract This paper proposes a new design scheme for a self-tuning PID controller. Expressions to calculate PID parameters from the identified plant coefficients are given. These expressions are derived by approximating the Two-Degree-of-Freedom PID controller to the Two-Degree-of-Freedom generalized minimum variance control (GMVC) law. Since the proposed self-tuning PID control law is Two-Degree-of-Freedom, reference response and disturbance response can be designed independently. Using a numerical example, the control performance of the proposed method is compared with that of another self-tuning PID controller

Intersample Performance Improvement in Generalized Predictive Control

Abstract The standard GPC is designed so that a discrete-time cost function is optimized. However, rather poor intersample performance may occur because the cost function in the discrete-time form cannot account for intersample behavior. Therefore, in this paper, a GPC design which can optimize the continuous response using a discrete-time control law with a Zero Order Hold (ZOH) is proposed. To this end, the discrete equivalent plant model and cost function are derived and the modified discrete-time GPC is solved. Finally, a numerical example is illustrated to show the effectiveness of the proposed method.