Almost Strictly Positive Real Research Articles

Combined simple adaptive and integral terminal sliding mode control for industrial feed drive systems

In the manufacturing industry, feed drive systems are utilized for various applications in industrial machines. These systems are crucial components for ensuring precision in motion control and are, therefore, expected to offer high tracking performance. This study focuses on application of integral terminal sliding mode control (ITSMC) to a feed drive system because of its robustness against disturbances and convergence of the tracking error in finite-time. However, its design requires plant dynamics model. To alleviate this concern, a solution of modifying the original ITSMC law to adaptive ITSMC law based on simple adaptive control (SAC) technique is used. To implement SAC-like adaptive law to a real plant, a property of “almost strictly positive real (ASPR)” is required to be satisfied. ASPR property is satisfied using velocity-based augmented output signal that ensures the stability. In experimental results, the adaptive controller follows the reference trajectory more precisely than conventional methods.

The design method of simple adaptive control system with PFC for MIMO system via DE

This paper deals with a design method of adaptive output feedback control system with parallel feedforward compensator (PFC) for a multiple input multiple output system. An adaptive output feedback control system, which is based on almost strictly positive real (ASPR), requires PFC in most cases. The design method is using one-shot input/output data of the controlled system, and parameter optimization will be done by differential evolution (DE). By using DE, the designer can optimize the design parameters without trial and error, which can be a more practical method.

ASPR-based Output Feedback Control with Virtual PFC for Output Tracking

Nowadays, the output feedback control method based on the Almost Strictly Positive Real (ASPR) property gets many attentions and has been researched widely. ASPR models can be stabilized by applying simple output feedback control; so the designed controllers have a simple structure. However, the systems have to satisfy quite strict conditions in order to obtain ASPR-ness, although almost all practical systems do not have the ASPR property. Therefore, for relaxing those conditions, the introduction of a Parallel Feedforward Compensator (PFC) has been proposed. This method can render the resulting augmented system ASPR. Up to now, several PFC design methods have been proposed, and one of them is an adaptive PFC design scheme. This technique has a feature that it can design a PFC automatically by utilizing online data. Furthermore, for the purpose of output regulation, the control design methods with an adaptive PFC have been proposed. Unfortunately, however, in almost all schemes, the discussion on the convergence of actual errors has not been conducted. Therefore, in this paper, introducing a virtual PFC model and an auxiliary input for ensuring ASPR-ness, a new ASPR-based output feedback control method is proposed, and the stability analysis and convergence of the actual error are discussed. Finally, the effectiveness of the proposed method is confirmed via numerical simulations.

Enhanced Motion Accuracy in Industrial Feed Drive Systems Using Simple Adaptive Control with a Jerk-Based Augmented Signal

In precision motion technology, motion accuracy is crucial to eliminate potential effects of screw compliance and improve the performance of feed drive systems. This study focuses on motion accuracy improvement for feed drive systems using simple adaptive control (SAC) technique. Almost strictly positive real (ASPR) is a key property to implement SAC to a system. The jerk-based augmented output signal is proposed for the ASPR property that includes velocity, acceleration, and jerk signals. The proposed approach allows the controller to achieve high tracking accuracy and faster adaptation by placing zeros of the controlled system at appropriate locations. To verify the feasibility of the proposed approach, control simulations are conducted and the results are compared with a typical parallel feedforward compensation method. Simulation results revealed that the proposed approach reduces tracking error significantly.

Adaptive Trajectory Control of Quadrotor by Output Feedback based Control via Backstepping Strategy

In this paper, a control method of quadrotor is proposed based on the almost strictly positive real (ASPR) based output feedback control and backstepping strategy in order to realize a robust and accurate automatic flight control. By adding parallel feedforward compensators (PFCs) to the considered flight control system so as to render the augmented ASPR control system, output feedback based control is easily designed and the number of steps in backstepping strategy can be reduced. In addition, in order to attain output tracking to arbitrary trajectory of the quadrotor, the ideal attitude angles are utilized to the input design in the backstepping strategy, and a two-degree-of-freedom control system with adaptive feedforward input is designed. The effectiveness of the proposed method will be verified though experiments of quadrotor flight control.

Null-space-based steady-state tracking error compensation of simple adaptive control with parallel feedforward compensator and its application to rotation control

In the design of simple adaptive control (SAC) using almost strictly positive real (ASPR), the feedback control system is stabilized by the output feedback with a high gain. Although ASPR is not, however, generally satisfied, it is achieved by introducing a parallel feedforward compensator (PFC). When SAC is designed for the augmented system which consists of an actual plant and PFC, not the actual plant output but the augmented system output converges to the reference input because of the influence of PFC. To resolve the problem, an extension method of the conventional SAC is proposed. In the proposed method, based on the null-space of an augmented plant, an exogenous input, which is independent of the augmented system output, is newly introduced. Because the exogenous input is designed so that PFC output is to be 0, the actual plant output is the same as the augmented system output in the steady state, and as a result, the actual plant output converges to the reference input. From a practical application point of view, the proposed method can easily improve the control performance of the conventional SAC with a PFC. In the proposed method, an exogenous input generated as the feedback signal of PFC output is only added to the conventional SAC control input. Therefore, the proposed method can be applied to various field in which the SAC method has been implemented, e.g., process control, mechanical systems, power systems, robotics, and others. In the present study, the effectiveness of the proposed method is also demonstrated through experiments for a motor control.

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.

Adaptive Output Feedback Control System Design with Adaptive PFC for Combustion Control of Diesel Engine

This paper deals with a combustion control system design problem of diesel engines. We propose an adaptive output feedback control system design scheme with an adaptive parallel feedforward compensator (PFC) for diesel engines with triple fuel injections. In order to guarantee the stability of the designed adaptive control system, a PFC is introduced and adaptively adjusted for maintaining the almost strictly positive real (ASPR) property of the resulting augmented system. The SISO control system is designed by considering main injection timing as the control input and peak pressure timing as the output. The effectiveness of the proposed method is confirmed through numerical simulations.

Adaptive Output Feedback based Output Tracking Control with Adaptive Parallel Feedforward Compensator

This paper deals with an almost strictly positive real (ASPR) based adaptive output tracking control system design problem. A design scheme of adaptive output feedback based output tracking control system with an adaptively adjusting parallel feedforward compensator is proposed. For non-ASPR system, in order to guarantee the stability of the designed adaptive control system, a parallel feedforward compensator (PFC) is introduced and is adaptively adjusted for remaining the ASPR-ness of the resulting augmented system. Furthermore, an adaptive NN feedforward control is added to attain the output tracking. The stability of the resulting control system is analyzed theoretically and the effectiveness of the proposed method will be confirmed through numerical simulations.

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>

Adaptive output predictor based adaptive predictive control with ASPR constraint

The predictive controls are one of the major control strategies in the process control. However, in general, an exact model of the controlled system is required in order to predict the system’s outputs accurately. In this paper, we propose an adaptive predictive control using an adaptive output predictor with a simple structure for uncertain controlled systems. In the proposed method, the stability of the obtained adaptive predictive control system will be confirmed by setting a novel input constraint, “almost strictly positive real (ASPR) constraint”.

Stable Adaptive Predictive Control System Design via Adaptive Output Predictor for Multi-rate Sampled Systems

This paper deals with a design problem of an adaptive predictive control for uncertain multi-rate sampled systems. In the proposed method, an adaptive predictive control using a simple adaptive output estimator, which has been previously proposed for single-rate sampled system, will be expanded to a multi-rate sampled system. A robust and model-free design method of feedforward compensators for designing the adaptive output estimator for predictive control and for setting an input constraint, “almost strictly positive real (ASPR) constraint” for stable control system will also be provided for the considered multi-rate systems. The effectiveness of the proposed method will be confirmed through an experiments of two-tank process control.

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.

Adaptive Output Feedback based Output Tracking Control for a Time‐Delay System with a PFC

AbstractThis output tracking control system for time‐delay systems with a parallel feedforward compensator (PFC). It has been clarified that one can design an adaptive output tracking control system for systems with almost strictly positive real (ASPR) properties. However, the robust stability for non‐ASPR time‐delay systems with a PFC introduced for making the resulting augmented system ASPR has not been analyzed. In this paper, it will be clarified that one can design a stable adaptive output tracking control system for time‐delay systems with a PFC, even if the resulting augmented system is not exactly ASPR.

Almost Passivity and Simple Adaptive Control in Discrete‐Time Systems

AbstractSuccessful implementations of simple direct adaptive control techniques in various domains of application have been presented over the last two decades in the technical literature. The theoretical background concerning basic conditions needed for stability of the controller and the open questions relating the convergence of the adaptive gains have been clarified recently, yet only for the continuous‐time algorithms. Apparently, asymptotic tracking in discrete time systems has been possible only with step input commands and the scope of the so called “almost strictly positive real (ASPR)” condition has also remained not clear. This paper expands the feasibility of discrete simple adaptive control methodology to include any desired input commands and almost all real‐world systems. The proofs of stability are also rigorously revised to solve the ultimate adaptive gain values question that has remained open until now. Finally, a complex algebraic loop that seemed to be inherent in discrete ASPR systems and might prevent the use of passivity properties in discrete systems has also been eliminated.

The Combined Effect of Missile IMU Shift, Model Following and Add-on SAC on the Autopilot Response

Proper location of the missile's inertial measurement unit renders the transfer function from the control surfaces to the acceleration measurement minimum-phase. Usually the poles and zeros of the missile actuators and rate gyros lie in the open left half plane. In this case the minimum-phase transfer function implies minimum-phase autopilot. Missile autopilots are designed to guarantee stability and performance throughout the flight envelope. The stability and performance are conflicting objectives. The final design is a compromise between stability margins and autopilot agility. In this paper the presented control architecture has the potential to resolve the conflict between robust stability and robust performance. The performance of the missile autopilot resulted from the combined effect of IMU location and reference model following can be further improved by using a simple Add-On adaptive control algorithm. The paper demonstrates the improved performance via example. The simple adaptive control (SAC) algorithm used in the paper involves the synthesis of parallel feedforward which guarantees that the controlled plant is almost strictly positive real (ASPR).

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.

Improving the Performance of Existing Missile Autopilot Using Simple Adaptive Control

AbstractA simple add-on adaptive control algorithm is presented. It is demonstrated via example that the performance of existing missile autopilot can be improved. The algorithm involves the synthesis of parallel feedforward which guarantees that the controlled plant is almost strictly positive real (ASPR). It is proved in the paper that such a parallel feedforward always exists. The proof is based on the parameterization of a set of stabilizing controllers. This parameterization enables straight-forward design and implementation of the add-on simple adaptive control (SAC) algorithm.

Design of discrete time adaptive PID control systems with parallel feedforward compensator

This paper deals with the design of an adaptive PID control system with a parallel feedforward compensator (PFC) for discrete-time SISO systems and its application to water level control of a 3-tank system. The proposed method utilizes the characteristics of almost strict positive realness (ASPR) of the controlled plant. A conventional design scheme of a PFC which realizes an ASPR augmented controlled plant is also proposed. Further it is shown that the introduction of an internal model improves the control performance of the control system with the PFC. The effectiveness of the proposed method is confirmed through water level control experiments on a three-tank SISO system.

An Improved Simple Adaptive Control Applied to Power System Stabilizer

A conventional power system stabilizer (PSS) can improve the steady-state stability margin and increase the system positive damping, but it has some drawbacks, such as the time-consuming tuning and nonoptimal damping in the entire operating process. A proportional--integral (PI) adaptive control law in simple adaptive control (SAC) can overcome these drawbacks. However, it can only be applied to the plants with almost strict positive realness (ASPR), and the computation of adaptive control law is really complex. A new improved SAC (ISAC) based on quadratic performance index was proposed. A new PSS can be designed using the ISAC. The simulation and experimental results show that this stabilizer possesses good dynamic characteristics and regulation precision. They also show that the new PSS can improve the dynamic stability of the power system and suppress the low-frequency oscillation effectively.