Almost Strictly Positive Real Condition Research Articles

Design and Experimental Evaluation of a Discrete‐time ASPR‐based Adaptive Output Feedback Control System Using FRIT

AbstractThis paper describes the design of an adaptive output feedback control system in discrete‐time, based on almost strictly positive real (ASPR)‐ness with a feedforward input. It is well‐known that an adaptive output feedback control system based on ASPR conditions can achieve asymptotic stability via a constant feedback gain. Unfortunately, most realistic systems are not ASPR because of the severe conditions. The introduction of a parallel feedforward compensator (PFC) is an efficient way to alleviate such restrictions. However, the problem remains that there exists a steady state error between the output of the augmented system and the output of the original system. The proposed scheme provides a strategy wherein the feedforward input is utilized such that the steady state error is removed. Furthermore, the fictitious reference iterative tuning (FRIT) approach is employed to determine the control parameters using one‐shot input/output experimental data directly, without prior information about the control system. This paper explains how the FRIT approach is applied in designing an adaptive output feedback control system. The effectiveness of the proposed scheme is confirmed experimentally, by using a motor application.

Performance-Driven Adaptive Output Feedback Control with Direct Design of PFC

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270005/01.jpg"" width=""300"" /> Block diagram of proposed control</div> An adaptive control system is configured simply by output feedback when the controlled system is almost strictly positive real (ASPR). ASPR conditions are, however, very severe restrictions for actual systems. The parallel feedforward compensator (PFC), which is designed for making augmented controlled system ASPR, has been proposed to solve this problem. We propose a performance-driven adaptive output feedback control system with a PFC designed via direct design. Our proposed adaptive control system is to be used for systems whose properties change during operation. Our PFC’s direct design uses the system’s input/output data and readjusts output feedback gain based on a performance index. The effectiveness of the proposed method is confirmed through experiments using liquid level control for the two-tank process system. </span>

Flight Evaluation of Fault-tolerant Control System Using Simple Adaptive Control Method

A flight controller based on Simple Adaptive Control (SAC) method was implemented to multipurpose experimental aircraft MuPAL-α developed by JAXA (Japan Aerospace Exploration Agency) to demonstrate the effectiveness of SAC flight controller in the serious fault case where the longitudinal stability was suddenly reduced in the air. A parallel feed-forward compensator was added to make the whole system meet the ASPR (Almost Strictly Positive Real) condition that is necessary for the plant to be stabilized by the SAC controller. In order to represent the fault case in a real flight test, a “pseudo-fault term” was added to the original controller equipped with MuPAL-α. Through numerical simulations, hardware in the loop tests and flight experiments, it was revealed that the SAC could stabilize the aircraft with such a fatal fault while a conventional PID control system could not stabilize the plane.

A Backstepping Simple Adaptive Control Application to Flexible Space Structures

Although the simple adaptive control (SAC) is widely studied both in theory and application in flexible space structure control and other control problems, it is restricted by the almost strictly positive real (ASPR) conditions. In most practical control problems, the ASPR conditions are not satisfied. Therefore, based on the SAC theory, this paper proposes a backstepping simple adaptive control algorithm which suits the system with arbitrary relative degree with no need of parallel feedforward compensator. The proposed control algorithm consists of decomposition of the arbitrary relative degree system into a known subsystem and an unknown ASPR subsystem which are connected in cascade, design of constant output feedback controller for the known subsystem, and implementation of backstepping method and SAC of the unknown ASPR subsystem. Inheriting the characteristics of the SAC, this method can be adaptive online for the parameter uncertainties. Then, the application of the proposed controller to large flexible space structure with collocated sensors and actuators is studied, and the simulation results validate the proposed controller. It is a new strategy to apply the classical SAC to high relative degree plants.

Simple Adaptive Control with a Parallel Feedforward Compensator for Processes with Time Delay

Abstract This paper deals with a design problem concerning a simple adaptive control (SAC) system for processes with time delays or higher order lag elements. The SAC method, which is a type of direct model reference adaptive control (MRAC) based on the command generator tracker (CGT) theorem, is fundamentally applicable to plants satisfying the so-called almost strictly positive real (ASPR) condition. Most processes with higher order lag elements do not satisfy the ASPR condition. A design method of a parallel feedforward compensator (PFC) for processes with time delays is derived so that the resulting augmented plant with the PFC, which is virtually regarded as a new controlled plant, will be ASPR. As a result, the SAC can be applied to a broader class of controlled plants including processes with higher order lag elements. The effectiveness of the proposed method is confirmed through a numerical simulation.

Simple Adaptive Control for MIMO Plants with Unmodelled Dynamics and its Application to Processes with Higher Order Lag Elements

Abstract This paper deals with a design problem concerning a simple adaptive control (SAC) system for multi-input/multi-output (MIMO) plants with unmodelled dynamics. The SAC method is fundamentally applicable to plants satisfying the so-called almost strictly positive real (ASPR) condition. The ASPR condition, however, imposes severe restrictions on the plant with regard to practical applications. The design schemes of compensators which make the non-ASPR plant virtually ASPR are proposed by taking plant uncertainties into consideration. As a result, the applicable class of the SAC can be expanded to a broader class of MIMO plants with unmodelled dynamics. The effectiveness of the proposed method is confirmed through a numerical simulation by a process with higher order lag elements.

Control of an Inverted Pendulum Using Direct Model Reference Adaptive Control

This paper presents the design of a robust direct model reference adaptive control (DMRAC) algorithm with focus on the satisfaction of an almost strictly positive real (ASPR) condition over the maximal range of parameter variations of the plant, and its application to an inverted pendulum. To alleviate the ASPR condition, the pendulum is augmented with a feedforward compensator optimized for robustness. A DMRAC algorithm ensuring asymptotic model following is then integrated with the feedforward compensator design. These new experimental results validate the algorithm's use and applicability to the control of an inverted pendulum with a variety of parameter uncertainties. On presente la conception d'un algorithme robuste de reglage adaptif a 'reference au modele directe (DMRAC) qui dois satisfaire la condition de realization positive presque partout (PPP) et son application a un pendule renverse. Pour alleger la condition PPP, le pendule est ameliore' par l'ajout d'un compensateur "feed-forward" qui est optimise' pour la robustess. Puis, un algorithme DMRAC qui assure que la modele soit suivi asymptotiquement est integre' dans la realisation du compensateur. Les nouvaux resultats experimentaux verifient l'usage et l'application de l'algorithme pour regler le pendule renverse' avec des incretitudes sur les valeurs des parametres.

Simplified adaptive model output following control for plants with unmodelled dynamics

In this paper, an adaptive model output following control utilizing almost strictly positive real (ASPR) characteristics of the plant is considered. The plant is said to be ASPR if there exists a static output feedback such that the resulting closed-loop transfer function is strictly positive real. A design scheme of an adaptive model output following control system having a simple structure is proposed for the ASPR plant. The ASPR condition imposes severe restrictions on the plant with relation to the practical application. However, we can construct an ASPR augmented plant, which is regarded as a virtually new controlled plant, by implementing a parallel feedforward compensator or pre-compensator on the plant. The design scheme of such compensators that make the non-ASPR plant virtually ASPR is proposed by taking plant uncertainties into consideration. As a result, the applicable class of the proposal can be expanded. The effectiveness of the proposed methods is confirmed through numerical simulations.

Model Output Following Control Based on Output Feedback and Its Robustness Analysis.

This paper deals with the problems of model output following control based on output feedback for the multi-input multi-output systems with additive and/or multiplicative unmodelled dynamics. Existence of an allowable range of unmodelled dynamics, which guarantees the uniform boundedness of all signals in closed-loop with output feedback, is examined for the system of which dominant part satisfies the almost strictly positive real (ASPR) condition. Furthermore, it is verified that the ASPR condition with respect to the dominant part can be relaxed using a precompensator inserted in the feedback path.