Coprime Factorization Approach Research Articles

Robust Stability and Tracking for Operator-Based Nonlinear Uncertain Systems

In this paper, operator-based robust control for nonlinear uncertain system is considered by using robust right coprime factorization approach. In details, the effects from uncertainties for nonlinear uncertain systems are analyzed through internally stable control design. For the stabilizing system, an internal model control (IMC) like operator-based control design is proposed. Based on the proposed design scheme, the effect from uncertainties is eliminated. By using operator theory-based approach, the system is robustly stable and the desired tracking performance can be realized. Finally, the effectiveness of the proposed design scheme is demonstrated by a simulation example. Note to Practitioners-Robust stability and tracking problems are two well-known topics in the field of control, which play an important role in real application and attract the researchers' attention all the time. Especially, these issues on nonlinear systems still remain challenging owing to complexity and the nonlinear characteristic property. Another challenging issue in nonlinear control is the effects from uncertainties. Motivated by these issues, robust control design by using operator theoretic-based approach has caused for concern owing to its effectiveness in dealing with nonlinearity and uncertainties. This paper provides a survey of the research in the above issues that would help practitioners in controlling nonlinear uncertain systems and in understanding the advantages of operator-based approach.

Nonlinear Perfect Tracking Control for a Robot Arm with Uncertainties Using Operator-Based Robust Right Coprime Factorization Approach

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00270001/06.jpg"" width=""300"" />Plant uncertainties compensation</div> In this paper, a robust nonlinear perfect tracking control for a robot arm with uncertainties is proposed by using operator-based robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the robot arm and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbances on the system performance is considered to be uncertainties of the robot arm dynamics. Considering the uncertainties, a robust nonlinear perfect tracking control using operator-based robust right coprime factorization is investigated. That is, first, considering the unknown uncertain plant generates limitations in obtaining the so-called universal stability and tracking conditions, the effect of uncertain plant is compensated by designed operator-based feedback control scheme. Second, a new perfect tracking condition is proposed for improving the trajectory of the robot arm. Finally, the effectiveness of the designed system is confirmed by simulation results. </span>

Robust tracking control design to nonlinear plants with perturbation using operator-based observers

In this paper, an operator-based robust tracking control design for nonlinear plants with perturbation is proposed by using robust right coprime factorisation approach and operator-based observers. In the real industrial process, most of the controlled systems have nonlinear characteristics, including unknown uncertainties consisting of modelling errors and external disturbances. Considering the nonlinearity and uncertainties, an operator-based robust nonlinear perfect tracking control using robust right coprime factorisation is investigated. That is, first, because the unknown uncertain plant generates difficulties in designing realisable operator controllers to obtain the desired tracking performance, an operator state observer and an operator disturbance observer based on nominal plant properties are designed to compensate the effect of uncertain plant. Second, a realisable operator-perfect tracking controller is designed to improve the control performance and to realise the perfect tracking. Based on ...

Operator-based robust control design for a human arm-like manipulator with time-varying delay measurements

In this paper, an operator-based robust nonlinear control for a human multi-joint arm-like manipulator with time-varying delay measurements is proposed by using robust right coprime factorization approach, a delay compensation operator and a forward predictive operator. That is, first, considering the uncertainties of dynamic model consisting of measurement error and disturbances, an operator-based nonlinear feedback control scheme is designed to eliminate effect of uncertainties. Second, an operator controller based on real measured data from human multi-joint arm viscoelasticity is presented to obtain desired motion mechanism of human multi-joint arm viscoelastic properties, the unknown time-varying delay measurements are described by a delay operator, the delay compensation operator is designed to remove the effect of unknown time-varying delay measurements, and the forward predictive operator is designed to compensate the term related to effect of central nervous system (CNS) during human multi-joint arm movements. The BIBO stability can be guaranteed and the tracking performance can be realized by the designed operator controller, the delay compensation operator and the forward predictive operator. Finally, the effectiveness of the proposed design scheme is confirmed by the simulation results based on experimental data.

Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

This article introduces a new method for model falsification using set-valued observers, which can be applied to a class of discrete linear time-invariant dynamic systems with time-varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set-valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set-valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open-loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd.

Robust nonlinear multivariable tracking control design to a manipulator with unknown uncertainties using operator-based robust right coprime factorization

In this paper, an operator-based robust nonlinear multivariable tracking control for a manipulator with uncertainties is proposed by using a robust right coprime factorization approach. In general, there exist unknown modelling errors in measuring structural parameters of the manipulator and external disturbances in real situations. In the present control system design, the effect of the modelling errors and disturbance on system performance is considered to be uncertainties in the manipulator dynamics. Considering the uncertainties, an operator-based robust nonlinear multivariable tracking control using robust right coprime factorization is studied. That is, firstly a robustly stable control based on robust right coprime factorization is designed. Secondly, a robust nonlinear multivariable tracking system is proposed for improving the trajectory of the manipulator, and the output tracking performance is evaluated based on the exponential iteration theorem. Finally, the effectiveness of the designed system is confirmed by simulation results.

Design of Robust Controller for STATCOM Applied to Large Induction Motor Using Normalized Coprime Factorization Approach

Between the different robust H-infinity methods to design the controller for FACTS, loop shaping is known to be one of the effective and feasible methods. This research presents an investigation on H-infinity loop shaping procedure through normalized coprime factorization (NCF) for STATCOM installed at terminals of a large induction motor. The dynamic behaviors of induction motor are analyzed while the uncertainty of system parameters and STATCOM parameters are considered and will be compared with conventional PI controller. Simulation results prove that NCF method has better dynamic response and is more robust than PI controller against variation of system parameters and STATCOM parameters, so in a specified operating point even the system goes to instability.

Survey of A New Nonlinear Control Technique: An Operator-based Approach

This paper introduces some concepts, theories and applications of operator-based robust right coprime factorization (RRCF) approach, which is a small new method in robust nonlinear control field. In details, the origin and basic concepts of this approach is introduced firstly. Then, the system designs on robust stability, tracking performance and fault detection using the operator-theory-based approach are discussed. Finally, the applications of this method in engineering are shown to validate its effectiveness.

Plasma vertical position, shape, and current control in T-15 tokamak

The paper is devoted to plasma shape, current, vertical position, and vertical speed control systems in T-15 tokamak. Brief definitions of the control problem statement and T-15 tokamak itself as a plant under control are given. A cascade plasma shape and current control system is designed using control channel decoupling matrixes in the inner loop and the H∞ controller in the outer loop obtained by means of H∞ optimization theory based on the normalized coprime factorization approach of a plant model. Proportional and H∞ controllers are used to stabilize the plasma vertical position as well as the plasma vertical speed. The first one was applied to plasma-physics DINA code. During simulations some essential difference between linear DINA-L model and plasma-physics DINA code itself was discovered which led to the conclusion to apply an identification procedure on DINA code to get more accurate linear models for the feedback controller design.

Operator-based robust non-linear control for gantry crane system with soft measurement of swing angle

In this paper, a robust non-linear control scheme is proposed for a gantry crane system with estimation of swing angle by using operator-based robust right coprime factorisation approach. By analysing properties of the crane system, it shows that displacement distance and swing angle are the two main goals. But, there exists only one input force. Also, in real gantry crane system, it is difficult to measure the swing angle. As a result, real-time estimation of the swing angle is presented by using data-based SVM model, where a generalised Gaussian function is adopted as the kernel function. The difference between the estimation and real value leads some uncertainties. Then, operator-based robust right coprime factorisation approach is presented for the non-linear system with uncertainties. Meanwhile, an optimal tracking controller is designed to ensure the tracking performance. Finally, experimental results are given to show the effectiveness of the proposed scheme.

Operator-based robust control for MIMO non-linear systems with uncertain hysteresis

This paper presents a robust control method for multi-input multi-output (MIMO) non-linear systems with uncertain hysteresis using operator-based robust right coprime factorisation approach. In details, a new operator-based robust control system design is proposed for MIMO non-linear plants preceded by hysteresis and some sufficient conditions are proposed. By using the obtained conditions, the controlled system is robustly stable and the desired output tracking performance can be realised. Finally, simulation is done to validate the effectiveness of the proposed control design method.

Operator-based actuator fault detection system design of a thermal process

In this paper, an operator-based fault detection method for actuator fault of an aluminium plate thermal process is proposed by using operator-based robust right coprime factorisation (RCF) approach. In details, operator-based output tracking and fault detection system design for single input single output (SISO) system is proposed, then the theoretical analysis is extended to multi input multi output (MIMO) system. Based on the proposed design schemes, the output tracking performance can be realised and the actuator fault can be detected. After developing a mathematical model of the three-input three-output aluminium plate thermal process, the proposed design schemes are applied and the effectiveness of that is confirmed by the simulation results.

Operator-based robust nonlinear control and its realization for a multi-tank process by using a distributed control system

In this paper, a robust nonlinear control design method using an operator-based robust right coprime factorization approach and its realization based on a distributed control system (DCS) device are considered for a multi-tank process. In detail, for the multi-tank process, consisting of a water-level process and a water-flow process, theoretical models are developed according to the Bernoulli theorem. Based on the obtained models, a robust nonlinear feedback control design is presented by using robust right coprime factorization for the multi-tank process. Further, from a large-scale industrial application viewpoint, the realization of the designed operator-based robust right coprime factorization controllers is considered by using a DCS device. Because there are some nonlinear functions in the designed controllers which cannot be realized straightforwardly in the DCS device such that the designed controllers need to be realized approximately. That is, there exist some parasitic terms for the approximated realization of the controllers in the real system. As a result, the parasitic terms and processes’ unknown uncertainties should be considered simultaneously. In this paper, a robust condition is derived to guarantee robust stability of the nonlinear feedback control system with the parasitic terms and the uncertainties. Moreover, tracking controller design problem for the multi-tank process is discussed. Finally, by using a DCS device (CENTUM CS3000), experimental results are given to confirm the effectiveness of the proposed design scheme.

Operator-based robust nonlinear control and fault detection for a Peltier actuated thermal process

In this paper, operator-based robust nonlinear control design scheme and fault detection technique using robust right coprime factorization approach are considered for a Peltier actuated thermal process. The Peltier actuated thermal process is a typical nonlinear control affine system, where the process temperature depends not only on input current, but also on the square of the input current. In addition, the real system is likely to contain a fault signal owing to various factors. As a result, it is difficult to stabilize the control system and to achieve high accurate control performance, and to detect the fault signal to guarantee the engineering safety when a fault occurs. In this paper, for pursuing robust stability and tracking performance of the nonlinear closed-loop control system, a design scheme of operator-based robust tracking control system is proposed by using robust right coprime factorization approach. Then, for the tracking operator control system, a fault detection design technique based on robust right coprime factorization approach is also investigated. Finally, simulation and experimental results are given to confirm the effectiveness of the proposed method.

Operator-based robust control design for nonlinear plants with perturbation

In this article, operator-based robust control design for nonlinear plants with perturbation is considered by using robust right coprime factorisation approach. In detail, the property of unimodular operator is studied, and a control design structure is proposed. Based on the proposed design scheme, the designed system is robustly stable. Also, output tracking performance can be realised simultaneously. Finally, the effectiveness of the proposed design scheme is demonstrated by a simulation example.

Operator-based output tracking control for non-linear uncertain systems with unknown time-varying delays

In this paper, operator-based output tracking control for non-linear uncertain systems with unknown time-varying delays is considered by using the robust right coprime factorisation approach and delay compensating operator. The property of the time-varying delays is analysed in detail, and a delay compensating operator is designed. Based on the proposed design scheme, the output tracking performance is realised. Also, an example about the temperature control process of an aluminium plate with Peltier element actuator is given to demonstrate the validity of the theoretical analysis, and the effectiveness of the proposed design scheme is also confirmed by the simulation results.

Operator-based non-linear control system design for unstable plants with input saturation

Operator-based robust right coprime factorisation approach is an interesting approach for non-linear control. It provides an effective framework for non-linear unstable system. In practice, the input constraint always exists, which induces that the real control input is different from the controller output, thus the input constraint may destabilise the system. However, control system design for non-linear plants with input saturation has seldom been studied due to the difficulties in dealing with non-linearity. Also in operator-based robust right coprime factorisation method, input saturation is not considered. In this paper, a new control system design for non-linear unstable plants with input saturation is proposed. Based on the robust right coprime factorisation, an operator-based switching controller is designed, which avoids the unstable region. Moreover, based on the proposed design scheme, the output tracking performance is also realised, and the effectiveness of the proposed method is verified by simulation.

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.

Dual-Stage Actuator Control Design Using a Doubly Coprime Factorization Approach

This paper first reveals that the tracking and disturbance rejection problems can be decoupled into two independent optimization problems under the 2-DOF control framework. This result is then used for the design of a 2-DOF controller for a dual-stage actuator (DSA) system to provide desired performance of disturbance rejection and step tracking. The 2-DOF controller is designed based on the doubly coprime factorization approach, with which the closed-loop transfer function is expressed explicitly in terms of design parameters. This greatly simplifies the optimization of design parameters in meeting desired specifications. We further study how to use the design parameters to deal with specific problems in the DSA, i.e., control allocation and trajectory planning. For step tracking beyond the secondary actuator range, a nonlinear controller is also used for the primary actuator to complete the task. Experimental results demonstrate the practical implementation of the DSA control system and verify its effectiveness for step tracking and disturbance rejection and its robust performance under load changes.

Fault Detection System Design for Actuator of a Thermal Process Using Operator Based Approach

Abstract This paper proposes an operator based fault detection method for an actuator fault of an aluminum plate thermal process with input constraints. Operator-based robust right coprime factorization (RCF) approach is utilized in this method. After developing a mathematical model of the thermal process, a robust tracking operator system is designed for the process with input constraints. Following this, design of the fault detection system is given by using operator-based robust RCF approach. Finally, experiment is conducted to support the proposed design method.