Left Coprime Factorization Research Articles

A Generalized Anti-windup Approach for Internal Model Control

In this paper, we develop a generalized anti-windup synthesis procedure for saturating internal model control (IMC). Within this framework, the anti-windup design problem reduces to a search over a class of left coprime factorization of the linear internal model controller. An appropriate anti-windup is constructed by solving a set of linear matrix inequalities. As compared to other static anti-windup constructions in the literature, the IMC anti-windup is always feasible with guaranteed closed-loop stability and performance. Using a simulation example, we benchmark the behaviour of the constructed anti-windup with existing state-of-the-art methods.

Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

AbstractThis paper presents novel linear matrix inequalities (LMI)‐based conditions to address the coprime factorization problem for polytopic linear parameter‐varying (LPV) systems in both the continuous‐ and discrete‐time cases. The proposed conditions rely on the use of homogeneous polynomial parameter‐dependent (HPPD) matrix solutions of arbitrary degree g, which are used to obtain coprime factorization descriptions subject to time‐varying parameters defined inside a polytopic structure with known vertices. For a given degree g, synthesis of right and left coprime factorizations in terms of two special state‐feedback and filtering problems under quadratic performance are provided. Existence conditions are given from linear matrix inequalities relaxations based on an extension of Pólya's theorem and the HPPD approach. The effectiveness of the proposed conditions is evaluated by means of numerical examples.

A fault detection scheme for ship propulsion systems using randomized algorithm techniques

This paper studies the fault detection problem in ship propulsion systems based on randomized algorithms. The nominal propulsion system model, model with uncertainties and model with additive and multiplicative faults are first addressed in the form of normalized left coprime factorization (LCF), respectively. The K-gap metric is then introduced to measure how far the system deviates from the nominal operation. To reduce the conservatism in the norm-based threshold, a threshold setting law and the estimation of fault detection rate (FDR) are formulated on the probabilistic assumption of uncertain and faulty parameters. The simulation results on the ship propulsion system show that the randomized technique is an efficient solution to deal with the fault detection issues.

The range of block Hankel operators

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

AbstractIn this paper, nonlinear control design scheme for a class of nonlinear systems is proposed based on operator coprime factorization theory. In detail, two stable controllers are provided to design a Bezout identity by combining left factorization (not coprime) with right factorization. Based on the proposed design method, a realization approach to left coprime factorization for the nonlinear system is obtained, which provides an effective framework for constructing left coprime factorization. Meanwhile, internal‐output stability of the nonlinear system is guaranteed. After that, based on the obtained left coprime factorization, the cases of the nonlinear systems with perturbations are discussed for guaranteeing robust stability for the perturbed systems. For the perturbations, two different cases, known bounded perturbations and unknown bounded perturbations, are investigated from different viewpoints to analyze robust stability issue for the perturbed systems. Finally, a simulation example is given to confirm the effectiveness of the proposed design method.

Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.

Optimal Distributed Control for Platooning via Sparse Coprime Factorizations

We introduce a novel distributed control architecture for heterogeneous platoons of linear time-invariant autonomous vehicles. Our approach is based on a generalization of the concept of leader–follower controllers for which we provide a Youla-like parameterization, while the sparsity constraints are imposed on the controller’s left coprime factors, outlining a new concept of structural constraints in distributed control. The proposed scheme is amenable to optimal controller design via norm based costs, it guarantees string stability and eliminates the accordion effect from the behavior of the platoon. We also introduce a synchronization mechanism for the exact compensation of the time delays induced by the wireless communications.

Robust Regulation Theory for Transfer Functions With a Coprime Factorization

Classical frequency domain results of robust regulation are extended by requiring only a right or a left coprime factorization of a plant, but not both. The famous internal model principle is generalized first, which leads to a necessary and sufficient solvability condition of the robust regulation problem and to a parametrization of all robustly regulating controllers. In addition, a procedure for constructing robustly regulating controllers is proposed.

Data-Driven Approach of KPI Monitoring and Prediction with Application to Wastewater Treatment Process

In this paper, a data-driven scheme of key performance indicator (KPI) monitoring, prediction and KPI related fault detection is applied to the wastewater treatment process (WWTP). By means of a data-driven realization of the so-called left coprime factorization (LCF) of the process, the efficient monitoring and prediction of chemical oxygen demand (COD) concentration in the effluent flow are realized both for the situation that COD is measurable and unmeasurable. The well established Benchmark Simulation Model no. 1 (BSM1) is utilized for the demonstration of the effectiveness of this approach.

Distributed Fault Detection Using Relative Information in Linear Multi-Agent Networks

This paper addresses the problem of fault detection in the context of a collection of agents performing a shared task and exchanging relative information over a communication network. A techniques in the literature is used to construct a meaningful observable system equivalent to the original unobservable system of systems. A solution involving Set-Valued Observers (SVOs) and a left-coprime factorization of the system is proposed to estimate the state in a distributed fashion and a proof of convergence of the estimates is given under mild assumptions. The performance of the detection algorithm against deterministic and stochastic faults; and when the system is subject to unmodeled disturbances is assessed through simulations.

A new robust control method for active front steering considering the intention of the driver

The influence of the active front steering system on the driver’s intention and the trade-off between the robustness and the performance of the active front steering controller have not been adequately addressed by current research studies. A new robust control method based on the normalized left coprime factorization model including uncertainty and perturbations is introduced, and the robustness of this method against high speeds and variations in the cornering stiffness without changing the intention of the driver is guaranteed by the design of the feedforward controller and the feedback controller. A single-step method is adopted to solve the feedforward robust controller and the feedback robust controller. The resulting controllers obtained by the proposed robust control method have a simple structure and do not require online optimization. Furthermore, simulations of the double-lane-change manoeuvre and of braking on a split- μ road are conducted to compare the performance and the stability of the new robust control method with those of the proportional–integral–derivative controller and the standard H∞ controller. Simulation results show that, in comparison with the other two control methods, the established new robust control method can enhance the vehicle stability and handling, and the tracking rapidity is improved by the introduction of feedforward control so that the active steering intervention does not affect the driver’s intention, regardless of the external interferences or emergency evasive manoeuvres.

Introduction to the Discrete LSDP Controller and the Performance by Exploiting the Gap Metric Theory

This paper describes the introduction to the discrete LSDP (Loop Shaping Design Procedure) controller in order to develop a robust controller which guarantees the stability for the family of uncertain systems. To determine the validity domain of the discrete LSDP (DLSDP) we propose to use the gap metric theory for studying robustness properties as a function of the stability margin provided by the DLSDP controller with respect to parameter uncertainties. The latter are modeled by using the left normalized coprime factors (NCFs) representation. The effectiveness of the DLSDP controller is validated on a second-order electrical linear system.

A Novel Scheme for Key Performance Indicator Prediction and Diagnosis With Application to an Industrial Hot Strip Mill

In this paper, a data-driven scheme of key performance indicator (KPI) prediction and diagnosis is developed for complex industrial processes. For static processes, a KPI prediction and diagnosis approach is proposed in order to improve the prediction performance. In comparison with the standard partial least squares (PLS) method, the alternative approach significantly simplifies the computation procedure. By means of a data-driven realization of the so-called left coprime factorization (LCF) of a process, efficient KPI prediction, and diagnosis algorithms are developed for dynamic processes, respectively, with and without measurable KPIs. The proposed KPI prediction and diagnosis scheme is finally applied to an industrial hot strip mill, and the results demonstrate the effectiveness of the proposed scheme.

Right coprime factorizations of MISO fractional time-delay systems

Fractional order models have been more and more used as they offer better characterization of real systems of lumped as well as distributed nature. In this paper, we are interested in multiple-input and single-output (MISO) fractional systems of commensurate order with input or output delays, which have not been well understood so far. With the intent of using Youla parametrization for controller synthesis, we need coprime factorizations and Bézout factors of the systems. In a previous work, we have derived explicit expressions of left coprime factors. The right counterparts are determined in this paper, which allows us to obtain the set of all stabilizing controllers for some classes of delay fractional systems.

Which subnormal Toeplitz operators are either normal or analytic?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmosʼs Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamseʼs theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two bounded analytic functions), whose analytic and co-analytic parts have the “left coprime factorization”, is normal or analytic. We also prove that the left coprime factorization condition is essential. Finally, we examine a well-known conjecture, of whether every subnormal Toeplitz operator with finite rank self-commutator is normal or analytic.

GIMC architecture for linear systems with a single I/O delay

A new feedback controller architecture is presented for linear systems with a single I/O delay in the generalized internal model control (GIMC) framework. According to the doubly coprime factorization of these systems, traditional GIMC strategy is extended to linear systems with a single I/O delay. The distinguished feature of the control system architecture is that high tracking performance and good external disturbance rejection could be done separately by a nominal Smith predictor part and a finite dimensional conditional controller. First, a nominal Smith predictor part could be designed to deal with command tracking performance. Second, according to the left coprime factorization of the nominal controller, a finite dimensional conditional controller could be considered for external disturbance rejection, when the controlled plant should be assumed to be a square one. Finally, a simple design example is illustrated the effectiveness of the presented method.Finally, a simple design example is illustrated the effectiveness of the presented method.

Measurement Fusion Algorithms Based on Left-Coprime Factorization

Using the modern time series analysis method, by the left-coprime factorization, the autoregressive moving average (ARMA) innovation model is constructed, by which two measurement fusion steady-state Kalman filtering algorithms are presented. They have asymptotically global optimality. A numerical simulation example for threesensor tracking system verifies their functional equivalence to the centralized fusion steady-state Kalman filtering algorithms based on the ARMA innovation model and based on the Riccati equation by the classical Kalman filtering method.

Balanced POD for linear PDE robust control computations

A mathematical model of a physical system is never perfect; therefore, robust control laws are necessary for guaranteed stabilization of the nominal model and also "nearby" systems, including hopefully the actual physical system. We consider the computation of a robust control law for large-scale finite dimensional linear systems and a class of linear distributed parameter systems. The controller is robust with respect to left coprime factor perturbations of the nominal system. We present an algorithm based on balanced proper orthogonal decomposition to compute the nonstandard features of this robust control law. Convergence theory is given, and numerical results are presented for two partial differential equation systems.

Constrained multivariable stable predictive control based on Toeplitz equation

A stable constrained multivariable predictive control algorithm based on the Toeplitz predictive equation is presented. An analytical method for transformation between left and right coprime factorization of multivariable system is put forward, and then an unconstrained control law and its stable condition are given. Furthermore, for the constrained multivariable controlled system, a predictive controller and its asymptotically stable condition are presented and proved. Finally, the constrained receding horizon optimization is transformed into a typical linear matrix inequality (LMI) problem and solved. The detailed control algorithm is depicted in a numerical example, and the simulation results reveal the effectiveness and practicability of the presented algorithm. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Parameterization of all stable controllers stabilizing full state information systems and mixed sensitivity

Analytical expressions for the parameterization of all one- and two-degrees-of-freedom stable controllers stabilizing full state information systems are presented. It is assumed that the strictly proper, lumped, and linear time-invariant nominal plant has a stabilizable realization and is strongly stabilizable, and that the number of entries of the plant state is even and is double the number of entries of the plant input. Right and left coprime factorizations of the transfer function of the plant in terms of the matrices of the plant realization are proposed, the Diophantine equation is solved, and stabilizing controllers are obtained using Youla parameterization. Conditions for strong stability are given, and the free parameters of the stabilizing controllers solving the mixed sensitivity problem are established. The results are illustrated through simulation examples of a half-car active suspension system and a two-degrees-of-freedom planar rotational robot.