Coprime Factorization Research Articles

Design of inter-stations H∞ decoupling controller in VSC-HVDC system

The purpose of this work is to reduce the mutual interference between converter stations when the AC power or DC voltage fluctuates in VSC-HVDC system. The global small signal mathematical model of VSC-HVDC system is established firstly. Then, according to the principle of mixed sensitivity H∞ robust control, the appropriate weight function is selected and the decoupling controller between stations is deduced. In addition, the high-order controller deduced is reduced to an appropriate order which is beneficial to engineering application by using the balanced truncation method of coprime factors. Finally, the electromagnetic transient simulation is carried out to verify that the H∞ decoupling controller between stations can be effectively weakened the interaction between two converter stations and improves the dynamic performance and robust stability of the system.

Bicoprime factor stability criteria for linear time-varying systems in the nest algebra

ABSTRACT This paper presents a bicoprime factorisation approach to deal with various stability problems for linear discrete time-varying systems within the framework of nest algebra. First, we show that a system has a bicoprime factorisation if and only if it has a right and left coprime factorisation by using the complete finiteness of the nest algebra. Based on the bicoprime factorisations, some stability criteria for internal stability and strong stabilisability are obtained, which generalises similar results for linear time-invariant systems. Finally, we derive a necessary and sufficient condition for simultaneous stabilisability of two systems, Additionally, the condition given in this paper lead to a constructive controller design to stabilise simultaneously two systems.

Modified tracking performance limitation of networked time-delay systems with two-channel constraints

This paper investigates the modified tracking performance limitation of the networked time-delay systems with two-channel constraints. We consider both the white Gaussian noise and packet dropout constraints in the communication channels. In the plant, the non-minimum phase, unstable poles and time-delay are considered. The modified tracking performance limitation expressions will be achieved using the co-prime factorization and the spectral decomposition technique, and the two-parameter controller is adopted. The results show that the modified tracking performance limitation is related to the intrinsic properties of the given plant, including the non-minimum phase zeroes, the unstable poles and the time-delay. Furthermore, the network communication parameters, e.g. the white Gaussian noise, the packet-dropouts probability and the modified factor affect the modified tracking performance limitation of the networked time-delay systems. Finally, some particular examples are provided to illustrate the efficiency of the proposed method.

Development of Operator Theory in the Capacity Adjustment of Job Shop Manufacturing Systems

With the development of industrial manufacture in the context of Industry 4.0, various advanced technologies have been designed, such as reconfigurable machine tools (RMT). However, the potential of the latter still needs to be developed. In this paper, the integration of RMTs was investigated in the capacity adjustment of job shop manufacturing systems, which offer high flexibility to produce a variety of products with small lot sizes. In order to assist manufacturers in dealing with demand fluctuations and ensure the work-in-process (WIP) of each workstation is on a predefined level, an operator-based robust right coprime factorization (RRCF) approach is proposed to improve the capacity adjustment process. Moreover, numerical simulation results of a four-workstation three-product job shop system are presented, where the classical proportional–integral–derivative (PID) control method is considered as a benchmark to evaluate the effectiveness of RRCF in the simulation. The simulation results present the practical stability and robustness of these two control systems for various reconfiguration and transportation delays and disturbances. This indicates that the proposed capacity control approach by integrating RMTs with RRCF is effective in dealing with bottlenecks and volatile customer demands.

On a Class of Constacyclic Codes of Length 4ps over Fpm[u]〈 ua 〉

For any odd prime p such that pm ≡ 3 (mod 4), consider all units Λ of the finite commutative chain ring [Formula: see text] that have the form Λ = Λ0 + uΛ1 + ⋯ + ua−1 Λa−1, where Λ0, Λ1, …, Λa−1 ∊ 𝔽pm, Λ0 ≠ 0, Λ1 ≠ 0. The class of Λ-constacyclic codes of length 4ps over ℛa is investigated. If the unit Λ is a square, each Λ-constacyclic code of length 4ps is expressed as a direct sum of a −λ-constacyclic code and a λ-constacyclic code of length 2ps. In the main case that the unit Λ is not a square, we prove that the polynomial x4 − λ0 can be decomposed as a product of two quadratic irreducible and monic coprime factors, where [Formula: see text]. From this, the ambient ring [Formula: see text] is proven to be a principal ideal ring, whose maximal ideals are ⟨x2 + 2ηx + 2η2⟩ and ⟨x2 − 2ηx + 2η2⟩, where λ0 = −4η4. We also give the unique self-dual Type 1 Λ-constacyclic codes of length 4ps over ℛa. Furthermore, conditions for a Type 1 Λ-constacyclic code to be self-orthogonal and dual-containing are provided.

Robust control for uncertain nonlinear feedback system using operator-based right coprime factorization

The robust control issue for uncertain nonlinear system is discussed by using the method of right coprime factorization. As it is difficult to obtain the inverse of the right factor due to the high nonlinearity, the proving of the Bezout identity becomes troublesome. Therefore, two sufficient conditions are derived to manage this problem with the nonlinear feedback system as well as that with the uncertain nonlinear feedback system under the definition of Lipschitz norm. A simulation of temperature control is given to demonstrate the validity of the proposed method.

A Simple Architecture for Arbitrary Interpolation of State Feedback

Stability of a linear system under fast switching or blending of a set of controllers can be ensured by an appropriate observer-based state-space realization. In this letter, the more specific problem is considered of arbitrary interpolation of a set of state feedback gains based on an initial static state feedback. First, the dynamic augmentation generating this parameterization is derived as well as the associated parameters for local recovery of predefined static controllers. By further simplification, a simple and intuitive structure is obtained with only a single design matrix. We propose to exploit this remaining degree of freedom to maximize robustness in terms of coprime factor uncertainty. The resulting parameterization is comparatively simple to implement in both continuous and discrete time. The robotics problem of active variable impedance control serves to illustrate utility of this parameterization.

Youla–Kučera Parametrization with no Coprime Factorization—Single-Input Single-Output Case

We present a generalization of the Youla—Kučera parametrization to obtain all stabilizing controllers for single-input and single-output plants. This uses three parameters and can be applied to plants that may not admit coprime factorizations. In this generalization, at most two rational expressions of plants are required, while the Youla–Kučera parametrization requires precisely one rational expression.

Iterative Identification and Control Using Non-normalized Coprime Factors With Application in Wafer Stage Motion Control

Robustness against model uncertainty is essential in model-based controller design. It is well known that a relatively small uncertainty in lightly damped poles and zeros can result in a large distance measured in the $\nu $ -gap metric, leading to conservative robust stability and performance guarantees. This paper aims to develop an identification and control procedure that results in less conservative robust stability and performance conditions for linear systems with lightly damped poles and zeros. To achieve this, a connection is established between a distance measure based on a nonnormalized coprime factorization of the system and existing identification criteria in closed-loop system identification. A nominal model of the system is determined by minimizing this distance measure by means of a frequency-domain identification algorithm. Then, a controller synthesis method is proposed that addresses both nominal performance as robust stability. Improved robustness by using the proposed approach compared to existing approaches is confirmed in an experimental example for a system with lightly damped poles and zeros.

Operator-Based Robust Nonlinear Control Analysis and Design for a Bio-Inspired Robot Arm with Measurement Uncertainties

In this paper, a robust nonlinear tracking control design for a bio-inspired robot arm with human-like motion mechanism is investigated, and the bio-inspired operator controller based on human multi-joint viscoelastic properties is designed by using operator-based robust right coprime factorization approach. The motion mechanism of human multi-joint arm is used, and the measurement uncertainties of human multi-joint arm viscoelasticity are considered in designing bio-inspired operator controller. Based on the proposed design scheme, the sufficient conditions for the robust stability are derived in considering the coupling effects and measurement uncertainties, and the output tracking performance is realized. The effectiveness of the proposed design scheme was confirmed by the simulation results based on experimental data, and the time-varying estimated experimental data of human multi-joint arm viscoelasticity is used in simulation.

Tracking Performance Improvement for Operator-based Nonlinear Robust Control of Wireless Power Transfer Systems with Uncertainties

A new operator-based nonlinear robust control design scheme for wireless power transfer systems with uncertainties is proposed in this paper. In the proposed control design system, to deal with the uncertainties in the wireless power transfer system, operator-based robust right coprime factorization approach is adopted to guarantee the robust stability. Moreover, the tracking performance is improved by using the proposed control design scheme. Simulations and experiments are tested to show the effectiveness of this proposed control design scheme.

Evaluation of Control Approaches for Capacity Adjustment in Job Shop Systems

Nowadays, manufacturers increasingly face demand fluctuations while working on a variety of products. To flexibly react to these disturbances, capacity adjustments via flexible working time and staffs are common measures. Within this paper, we focus on a machinery-oriented approach by introducing reconfigurable machine tools into an existing job shop system. As these tools need to be included into the production plan, we tackle the strategic question on how to contemplate hardware with software for a given manufacturing system. To this end, we consider PID as the current standard in capacity control and compare it to two classes of advanced techniques from operator theory and predictive control. While analyzing advantages and disadvantages of these methods, we illustrate differences using operator-based right coprime factorization and model predictive control as representatives of these advanced classes and applying them to a simulated four-workstation job shop system.

IEEE Access Special Section Editorial: Special Section on New Developments on Reliable Control and Filtering of Complex Nonlinear Systems

During the past three decades, the problems of reliable control and filtering have attracted considerable attention due to the growing demands for system safety, reliability, maintainability, and survivability. The main aim of reliable control and filtering is to design a suitable controller and filter with guaranteed stability and performance, respectively; not only when all the system components are in operation, but also when some component failures occur. To guarantee a higher reliability level and better control performance, reliable control systems depending on various control strategies have tried to achieve these critical requirements, i.e., the pole region assignment method, coprime factorization method, the algebraic Riccati equation (ARE)-based method, the Hamilton-Jacobi inequality (HJI)-based method, and linear matrix inequality (LMI)-based method. Although many researchers have investigated the reliable control/filtering problems for linear systems with different scenarios for many years, the topic of reliable control/filtering in complex nonlinear systems is still in the early stages of development and many critical issues remain to be further investigated.

Robust Controller versus Numerical Model Uncertainties for Stabilization of Navier-Stokes Equations

Abstract We consider the stabilization of incompressible fluid flow using linearized and spatially discretized models. In order to potentially work in applications, the designed controller must stabilize the discrete model with a robustness margin that covers linearization, discretization, and modeling errors. We expand on previous results that a linearization error in the infinite-dimensional model amounts to a coprime factor uncertainty and show that H∞-robust controllers can compensate this in the discrete approximation. In numerical experiments, we quantify the robustness margins and show that the H∞-robust controller, unlike the LQG-controller, is capable of stabilizing nonlinear incompressible Navier-Stokes equations with an inexact linearization.

Optimal Control on the Doubly Infinite Time Axis for Well-Posed Linear Systems

We study the problem of existence of weak right or left or strong coprime factorizations in H-infinity over the right half-plane of an analytic function defined and uniformly bounded on some right ...

Operator-Based Control System Analysis and Design for Nonlinear System with Input and Output Constraints

Smart material-based actuators and sensors have been widely used in practice owing to their various advantages. However, in the working process of these actuators and sensors, their output responses always deduce non-smooth nonlinear constraints. The constraint resulting from the actuator is called the input constraint and the constraint caused by the sensor is called the output constraint. These input and output constraints may induce inaccuracies and oscillations, severely degrading system performance. Therefore, the input and output constraints brought about by actuators and sensors should be considered in control system design. In this paper, system analysis for a nonlinear system with input and output constraints will be considered. The effect from the input constraint to the internal signal in the control system will be discussed. Moreover, the influence of the output constraint on the whole system will be studied. Further, the sufficient conditions for maintaining the stability of the system are obtained. Then, by using the robust right coprime factorization approach, an operator-based internal model like control structure is proposed for mitigating the input and output constraints. Finally, the effectiveness of the proposed design scheme will be confirmed through numerical simulation.

Design of switched linear control systems based on Youla parameterization with average dwell time

ABSTRACTA two-steps method of designing switched linear systems is presented with the parameterization of globally uniformly asymptotically stabilising controllers with average dwell time (ADT). First, an observer-based switching controller design is given for a class of switched linear system. Based on the construction of observer-based controller, conceptions of doubly coprime factorization and Youla parameterization of LTI systems are extended to switched linear systems with respect to globally uniformly asymptotical stability (GUAS) using a state-space expression. Second, the parameterization of closed-loop systems, which are affine with any globally uniformly asymptotically stable -parameter, is then described. This description enables the application of the –- parameter approach to a variety of switched linear control-system designs. The control construction provides us a two-steps process design procedure. Above all, based on the Schur complementary lemma and controller variable elimination method, a systematic weighted L2 performance strategy is focused on and a design scheme of to obtain weighted L2-gain performance is clarified. Finally, a numerical example is given to show the validity and potential of the developed results.

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction (EHC) of multivariate polynomials in main variable x and sub-variables u1, u2, · · ·, um over a number field $$\mathbb{K}$$ . This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of xi on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field $$\mathbb{K}$$ (u1, u2, · · ·, um), the computation cost of handling rational functions can be high. Therefore, the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Grobner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.

Performance-based fault detection and fault-tolerant control for automatic control systems

The main focus of this paper is on the analysis and design scheme of performance-based fault detection and fault-tolerant control for automatic control systems with incipient (slowly developing) multiplicative faults. To this end, the realization form of the multiplicative faults is first studied with the aid of the coprime factorization techniques. Then, the fault-tolerant margin is proposed in the closed-loop setup aiming at characterizing the fault-induced performance degradation. By embedding the fault-tolerant margin as a performance indicator, a performance-based fault detection approach is developed. Based on the fault detection and the well-known controller parameterization form, a control performance-based fault-tolerant control strategy is investigated. A case study on three-tank system is given in the end to illustrate the proposed approaches.

Robust decoupling mixed sensitivity controller design of looper control system for hot strip mill process

This article considers a robust decoupling controller design for a multivariate control system with parameter uncertainties for the hot rolling mill process. The left and right coprime factorization theory is used to properly select the free and weighting matrices. The necessary and sufficient conditions for robust decoupling controller are also proposed. Then, by analyzing the changes in the dynamic response resulting from perturbations in the tension and angle system parameters in the hot strip rolling process, a modified multivariate model is developed. Furthermore, the selection method for a practical weighting function is studied, so that the robust and decoupling performance can be simultaneously realized for the controller implementation. Finally, the effectiveness of the proposed control approach is demonstrated using a case study from an industrial hot rolling mill.