Identification of normalized coprime factors through constrained curve fitting

This paper deals with identifying finite dimensional normalized right coprime factors (NRCFs) under a stochastic framework from a sequence of their frequency response estimates. A two-step procedure is suggested for the estimation in which two cost functions are sequentially minimized. These cost functions are constructed on the basis of weighted curve fitting and the conditions on NRCFs. A numerical procedure is proposed for computing the estimate. Moreover, it is proved that under some conditions, the estimate converges with probability 1 (w.p.1) to its actual value with increasing the data length, and in general the optimal estimate is asymptotically approximately Gaussian. The efficiency of the proposed method in NRCF identification is illustrated by numerical simulations.     

Guaranteed cost LQG control for uncertain systems with a normalized coprime factor uncertainty structure

The paper extends the robust minimax LQG control design methodology to stochastic uncertain systems with a general uncertainty structure, which includes normalized coprime factor uncertainty, passive uncertainty and sector norm-bounded uncertainty as special cases. The derivation of the result uses a special parameter-dependent Girsanov measure transformation. The efficacy of the proposed methodology is illustrated using the problem of frequency locking of an optical cavity which occurs in the area of experimental quantum optics.     

基于互质因子摄动的系统非脆弱鲁棒解耦控制

研究对象和控制器存在互质因子不确定性时闭环系统鲁棒稳定和非脆弱鲁棒解耦控制问题,得到了闭环系统具有鲁棒稳定性和鲁棒解耦性能的充分条件,给出了鲁棒控制器的优化设计方法.     

Riccati equations and normalized coprime factorizations for strongly stabilizable infinite-dimensional systems

The first part of the paper concerns the existence of strongly stabilizing solutions to the standard algebraic Riccati equation for a class of infinite-dimensional systems of the form Σ(A,B,S^−1/2B^*,D), where A is dissipative and all the other operators are bounded. These systems are not exponentially stabilizable and so the standard theory is not applicable. The second part uses the Riccati equation results to give formulas for normalized coprime factorizations over H_∞ for positive real transfer functions of the form D+S^−1/2B^*(author−A)⁻¹,B.     

Subspace system identification for training-based MIMO channel estimation

The application of state-space-based subspace system identification methods to training-based estimation for quasi-static multi-input-multi-output (MIMO) frequency-selective channels is explored with the motivation for better model approximation performance. A modification of the traditional subspace methods is derived to suit the non-contiguous nature of training data in mobile communication systems. To track the time variation of the channel, a new recursive subspace-based channel estimation is proposed and demonstrated in simulation with practical MIMO channel models. The comparison between the state-space-based channel estimation algorithm and the FIR-based Recursive Least Squares algorithm shows the former is a more robust modeling approach than the latter.     

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.     

Normalized coprime factorizations for linear time-varying systems

In this paper we show that a finite dimensional linear time-varying continuous-time system admits normalized coprime factorizations if and only if it admits a stabilizable and detectable realization. We construct state-space formulas for these factorizations using the stabilizing solutions to standard Riccati differential equations. In the process, we give a simple proof that stabilizability and detectability are sufficient to ensure the existence of such solutions. Based on these results, and on recent advances in the theory of _∞ optimization, we present an algorithm to compute the distance between two systems in the gap metric.     

Robust stability of MIMO nonlinear uncertain systems using operator-based right coprime factorisation

In this paper, a class of multi-input–multi-output (MIMO) nonlinear systems with uncertainties is considered by using operator-based right coprime factorisation. First, based on proposed quotient operators, coupling effect of the MIMO nonlinear systems is discussed. Second, based on the operator-based right coprime factorisation approach, sufficient conditions for guaranteeing robust stability of the MIMO nonlinear systems with uncertainties are proposed by using a new unimodular operator. Finally, a simulation example is shown to illustrate the proposed design scheme for the MIMO nonlinear systems with uncertainties.     

Stable robust feedback control system design for unstable plants with input constraints using robust right coprime factorization

A stable robust control system design problem for unstable plants with input constraints is considered using robust right coprime factorization of nonlinear operator. For obtaining strong stability of the closed‐loop system of unstable plants with input constraints, a design scheme of robust nonhyphen‐linear control system is given based on robust right coprime factorization. Some conditions for the robustness and system output tracking of the unstable plant with input constraints are derived. Numerical examples are given to demonstrate the validity of the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Decentralized voltage control of distributed generation using a distribution system structural MIMO model

The voltage control problem in Low Voltage (LV) distribution systems is becoming increasingly important due to the presence of Distributed Generation (DG). Recently, DG units have been proposed to contribute to voltage control according to a Volt/Var law which does not realize regulation. Moreover, since the existing LV systems are operated in a decentralized way without communication links, the simultaneous response of the controllers of the DG units may result into operational conflicts and instability. To overcome these problems, the present paper illustrates a design methodology for decentralized voltage controllers that act on DG reactive power injections. The controllers are suitable for the LV systems since they ensure voltage regulation and stability by using only local measurements and without information exchanges. The design is based on a proposed structural MIMO model of the distribution system. Robust stability is also analyzed: changes in the operating conditions of the distribution system are modeled as unstructured additive uncertainties affecting the MIMO model. A case study gives evidence of the applicability of the proposed design; the performance of the controllers in terms of both stability and regulation of the nodal voltages of three DG units connected to a LV distribution feeder is tested by numerical simulations; finally, a comparison with a Volt/Var technique is performed.     

Approximation of unstable infinite-dimensional systems using coprime factors

The effectiveness of comprime factor techniques in L₂ and L_∞ model reduction of unstable linear systems is analysed. Asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system, measured in a number of different norms, some involving the associated Hankel operators. The chordal metric is introduced as a measure of approximation and is shown to yield the graph topology. Finally it is deduced that asymptotically optimal L₂ and L_∞ convergence rates can be obtained for a large class of unstable systems.     

Joint direction of arrival estimation and array calibration for coprime MIMO radar

Compared to large-scale MIMO radar, coprime MIMO radar can achieve approximate estimation performance with reduced antenna number. In this paper, joint direction of arrival (DOA) estimation and array calibration for coprime multiple-input multiple-output (MIMO) radar is considered, and an iterative method for the estimations of DOA and array gain-phase errors is proposed. Based on the received data structure of coprime MIMO radar, trilinear decomposition is firstly adopted to obtain the estimations of transmit and receive direction matrices, which are perturbated by the gain-phase errors. Through equation transformation, the un-perturbated direction matrices and gain-phase errors can be iteratively updated based on Least squares (LS). Finally, the unique DOA estimation is determined from the intersection of transmit and receive direction matrices. The proposed algorithm achieves better DOA estimation and array calibration performance than other methods including estimation of signal parameters via rotational invariance techniques (ESPRIT)-like algorithm, multiple signal classification (MUSIC)-like algorithm and joint angle and array gain-phase error estimation (JAAGE) method, and it performs close to the method with ideal arrays. Multiple simulation results verify the algorithmic effectiveness of the proposed method.     

Algebraic Construction of Normalized Coprime Factors for Delay Systems

We introduce an algebraic approach to the problem of constructing normalized coprime factorizations for retarded delay systems. A parametrization is given of all the possible factorizations that can be obtained by solving algebraic equations over the field generated by s and e ^−s. This enables us to provide a means of determining when such factors can be calculated by solving such algebraic equations, and to show that in general they cannot. Some illustrative examples are given. Date received: August 12, 1999. Date revised: October 12, 2001.     

Development of a fractional order based MIMO controller for high dynamic engine testbeds

Testbed are used to tune and assess automotive engines. As more High Dynamic (HD) scenarios need to be simulated, the testbeds require Multi Input Multi Output (MIMO) and robust control systems. A cooperation involving a major testbed manufacturer and two university laboratories was therefore set up. This paper presents the Control-System Design (CSD) methodology developed from system identification to the design and assessment of the MIMO robust controller for a HD testbed coupled with a spark-ignition engine. It is specially highlighted how the entire process has been automated and simplified and how the fractional order based MIMO CRONE CSD has been parameterized to obtain the best performance. Experimental results show that the proposed fractional order based MIMO control system is able to improve robustness and decoupling.     

Explicit characterization of decentralized coprime factors

This paper is concerned with parametrization of all decentralized stabilizing controllers. The auxiliary diagonal system, which is defined by the diagonal elements of Bezout factors, plays an important role in the parametrization of decentralized controllers. This paper gives an explicit characterization of the auxiliary system.     

On the solution of a nonlinear matrix equation for MIMO symmetric realizations

A result concerning a particular solution of a nonlinear solution matrix equation reported in a previous paper [2] and interesting for studying SISO systems, is extended to MIMO symmetric realizations. For such a class of systems other important SISO results can be generalized.     

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii (PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.      

Operator‐Based Robust Right Coprime Factorization and a Nonlinear Control Scheme for Nonlinear Plant with Unknown Perturbations

This paper is concerned with operator‐based robust right coprime factorization for nonlinear plants with unknown perturbations. Firstly, the right factorization for by nonlinear plant with unknown perturbations is realized using isomorphism and some sufficient conditions are proposed to guarantee the robust stability of the obtained nonlinear feedback control system as well as the plant output asymptotically tracking to the reference input. Secondly, a quantitative control scheme is designed to satisfy the sufficient conditions. Finally, the effectiveness of the proposal is demonstrated by the simulation results.     

On the assessment of multivariable controllers using closed loop data. Part I: Identification of system models

Controller performance assessment of SISO and MIMO systems requires effective and systematic identification of the associated system models based on closed-loop data. In this work, a new methodology for the identification of the process, controller and disturbance models is presented for the purpose of enabling the evaluation of the performance of MIMO control systems. The methodology is based on subspace identification algorithms for the identification of the controller, process and disturbance models from closed-loop data. However, identification of the process model is enhanced by the estimation of the associated interactor matrix via the Variable Regression Estimation technique, the existence of which is mathematically proved. The proposed identification methodology is applied to two 2 × 2 systems utilizing both step-response and PRBS closed-loop data.