Coprime Factorization Research Articles

Real-Time Performance Optimization of Electromagnetic Levitation Systems and the Experimental Validation

The electromagnetic levitation (EML) system serves as a key subsystem in maglev trains for the purpose of levitation. It is highly dynamic, open-loop unstable, and safety-critical. The expense of establishing an accurate model out of the Maglev train, in addition to the varying operating conditions, results in an imperfectly known model in engineering practice. Thus high-performance levitation control, w.r.t. an imperfectly known model, is of considerable practical interest. Motivated by such an observation, this article investigates real-time levitation performance optimization of the EML system, with an imperfectly known model. The EML system is first modeled and an equivalent demonstration benchmark is developed. Then, the structure for levitation performance optimization is presented on top of the coprime factorization technique. Furthermore, the real-time levitation performance optimization algorithm is developed, utilizing only the input and output data. In the end, the proposed methods are validated on the benchmark.

Stability analysis for linear time‐varying systems using bicoprime factorization

AbstractThis paper presents a bicoprime factorization (BCF) approach to deal with various stability problems for linear discrete time‐varying (LTV) systems within the framework of nest algebra. Based on the bicoprime factorization, we give necessary and sufficient conditions for (strongly) simultaneous stabilization of three systems, which generalize similar results for systems by coprime factorization (CF). Finally, when the bicoprime factorization for the plant and controller has additive perturbations, we derive sufficient conditions using the norm inequality for robust stability of the system.

Operator-Based Adaptive Tracking Capacity Control in Complex Manufacturing Processes

Nowadays, quickly changing customer demands are a big challenge in the manufacturing industry, especially for job shops, which are typical coupling and nonlinear multi-input–multi-output (MIMO) systems. In order to achieve good shop floor performance in the presence of short-term demand fluctuations, a key performance indicator—work in process (WIP)—is required to be effectively controlled in the vicinity of the desired levels. For this purpose, a machinery-oriented capacity adjustment approach via a reconfigurable machine tool (RMT) is employed to flexibly balance capacity and load in the case of a bottleneck. A mathematical model concerning the RMT and WIP was first established in the presence of uncertainty and delays. The operator-based robust right coprime factorization (RRCF) method was adopted to stabilize the uncertain system, and adaptive integral separated proportional–integral (ISPI) tracking controllers were further designed to improve the transient and robustness performance. The performance of the proposed ISPI-RRCF was analyzed and compared with that of a state-of-the-art method in a simulation. The results showed that both control systems could ensure that the WIP was within an allowed bound, while the former had lower overshoots, shorter setting times, and more concentrated distributions facing stochastic demands. This further indicated the effectiveness of the proposed algorithm in the avoidance of serious bottlenecks and unbalanced capacity distributions.

Passive robust control for uncertain Hamiltonian systems by using operator theory

In this study, the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned. For the system with unknown perturbations, a design scheme is proposed to guarantee the uncertain non-linear systems to be robustly stable while the equivalent non-linear systems is passive, meanwhile the asymptotic tracking property of the plant output is discussed. Moreover, the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.

Regulation performance limitation of networked time‐delay systems with incomplete information

AbstractIn this paper, the regulation performance limitation of networked time‐delay systems is studied. The communication network is mainly affected by parameters such as packet dropouts, encoding‐decoding, interference signal, and channel noises. Non‐minimum phase zeros, unstable poles, and time delay are all considered for a given plant. The corresponding regulation performance expression is derived using coprime factorization and spectral decomposition techniques in the frequency domain. The results indicate that the regulation performance of the system is related to the inherent characteristics of the given plant, including non‐minimum phase zeros, unstable poles, and time delay. Additionally, network communication parameters such as white Gaussian noise, packet dropouts, encoding‐decoding, and external interference signals all affect the regulation performance of networked time‐delay systems. Finally, some simulation examples are provided to demonstrate the effectiveness of the theory.

Stable image representation based stability performance monitoring and recovery for feedback control systems

This paper proposes a scheme to achieve real-time stability performance monitoring (SPM) and designs performance recovery controllers (PRCs) for feedback control systems with multiplicative faults. To be specific, a stability performance indicator is presented with the aid of stable image representation (SIR) for multiplicative faults through coprime factorization techniques. On this basis, a systematically hierarchical SPM and PRC scheme is proposed with three thresholds derived to evaluate the performance degradation degree. Subsequently, an integrated model-based and data-driven SIR-based PRC is presented to recover system stability performance. The embedded PRC parameters are adaptive to system variations by means of identifying the SIR of the faulty plant through a dual parity vector. Besides, some QR-decomposition based data-driven techniques are provided for the implementation of PRC to improve computation efficiency. Finally, the effectiveness of the proposed approach is demonstrated on a boost circuit model.

Fault Detection for Systems With Model Uncertainty and Disturbance via Coprime Factorization and Gap Metric.

The fault detection (FD) problem for systems with both model uncertainty and external disturbance is investigated in this article. First, the mathematical models of systems with model uncertainty and disturbance, systems with additive faults, and systems with multiplicative faults are established with both left and right coprime factorization. Then, an observer-based FD scheme is proposed and the FD thresholds are derived for both open-loop and closed-loop manners. The necessary conditions on multiplicative FD are obtained and the fault detectability analyses are carried out with the aid of the gap metric technique. Finally, the effectiveness of the proposed method is illustrated by a case study on a cart dynamic system.

String stability margin of cyclic vehicle platoons with variable communication range

This paper proposes a new metric in regard to the string stability margin (SSM) of cyclic vehicle platoons and its connection with the platoon’s communication range r and the vehicle dynamics L(s). Unlike the previous works including Stüdli et al. (2018) in which a limited class of L(s) is discussed with no clear concept of SSM, in this paper SSM denoted by α∗ is unambiguously defined via the singular value capturing the platoon’s robustness with respect to gain/phase or coprime factor uncertainties in the network. It is then shown that SSM depends on the network connectivity λ2 which increases with r, as well as the geometric shape of Nyquist plot of L(s). Such dependency is analysed for three different types of L(s), yielding the maximum SSMs at different communication ranges.

A fractional representation approach to the robust regulation problem for multi‐input multi‐output systems

The aim of this paper is in developing unifying frequency domain theory for robust regulation of MIMO systems. The main theoretical results achieved are a new formulation of the internal model principle, solvability conditions for the robust regulation problem, and a parametrization of all robustly regulating controllers. The main results are formulated with minimal assumptions and without using coprime factorizations, thus guaranteeing their applicability with a very general class of systems. In addition to theoretical results, the design of robust controllers is addressed. The results are illustrated by two examples involving a delay and a heat equation.

Evaluating the Normalized Coprime Factor-based Stability Metric for Rigid Systems

Abstract The introduction of flexibility into rigid-body manipulator systems generally complicates the use of simple end-point feedback control. These flexibilities induce an unmodeled oscillation that cannot be necessarily compensated through end-point feedback control. The normalized coprime factor (NCF) based robustness metric ($\varepsilon_{max}$) has been well established in the realm of optimal control and can be applied to a rigid system with flexible modes in order to determine postures that will be robust to the flexibilities. This work illustrates that for rigid (double integrator) systems there is a fixed normalized coprime-factor robustness and, that for the special case of SISO systems, deviation from rigidity yields a similar change in NCF robustness.

Non-linear forced vibration control for a vertical wing-plate with sustainable perturbation by using internal model control mechanism

This article studies the non-linear vibration control problem for a vertical wing-plate with sustainable perturbation by using piezoelectric actuator. For the vertical wing-plate system with hysteresis non-linearity, the operator-based robust right coprime factorisation approach is considered to ensure the stability of the non-linear system. After, for compensating the sustainable perturbation and hysteresis non-linearity to improve the non-linear vibration control performance, the non-linear internal model control scheme that includes the designed internal closed-loop model and the compensator is considered. Finally, simulation and experimental examples are given to show the effectiveness of the proposed control system.

Satellite micro-launcher control: An integrated adaptive-robust and nonlinear approach

In this paper, a composite and multi-technique-based controller for a three-stage micro-launcher is presented. The proposed control law consists in a linear robust component, obtained for the rigid motion using mixed-sensitivity and normalized coprime factor loopshaping, an adaptive command gain, used to compensate the effects of the flexible motion, and a nonlinear component, used for roll control and payload insertion. Moreover, robust stability is ensured in the presence of parametric uncertainty, while also guaranteeing a set of disk margins which accommodate the adaptive gain. Finally, robust performance is validated via structured singular value analysis at successive instants along the trajectory, while the control scheme is tested in simulation upon the micro-launcher’s nonlinear and uncertain dynamics.

Coprime Factorizations of Discrete-time LPV/LFR Systems

Coprime Factorizations of Discrete-time LPV/LFR Systems

DOA Estimation of an Enhanced Generalized Nested Array with Increased Degrees of Freedom and Reduced Mutual Coupling

Aiming at low degrees of freedom (DOF) and high mutual coupling (MC) of the existing sparse arrays, an enhanced generalized nested array (EGNA) is proposed in this paper. Specifically, the proposed array adds a single antenna on the basis of generalized nested array (GNA), and the difference of coprime factors is employed as the spacing between the second subarray and the additional antenna. Then, the values of the coprime factors are analyzed in detail, which indicates that Yang-NA can be explained as a special case. Compared with the majority of the existing sparse arrays, EGNA not only has the closed-form expressions of the physical antenna locations, consecutive lags, and unique lags, but also significantly increases DOF and reduces MC. In view of the above advantages, EGNA can obtain superior performance in direction of arrival (DOA) estimation. Numerical simulation results verify the rationality and superiority of the proposed nested array.

Robust nonlinear control integrated operator theory and sliding mode technology for a system considering the change of thermal conductivity

Based on the mathematical modelling of a cooling and heat system using Peltier elements, thermal conductivity influencing the characteristics of Peltier device is taken into account to increase the temperature control accuracy. Integrating operator theory and sliding mode technology, the control system is designed, where the robust stability of the nonlinear system is ensured with operator-based right coprime factorization and robust stability condition is proposed for system’s robustness analysis. Besides, for the tracking performance of the designed nonlinear system, sliding mode technology is also adopted. New simulations and experiments of the proposed system demonstrate the effectiveness.

Robust passive tracking control for an uncertain soft actuator using robust right coprime factorization

AbstractAs a research of human arm activities, the research of soft actuator is one of the important topics in the field of robotics. This article is concerned with the robust passive tracking control for an uncertain soft actuator by robust right coprime factorization (RRCF). First, applying the recursive least squares identification algorithm, the identification of the actuator modeling is studied by which the parameter of radius is estimated by using the experimental data. Second, the passivity of the soft actuator with inflatable rubber tube is discussed; meanwhile, the robustness of the soft actuator is ensured by the designed robust controllers. Third, by combining the RRCF and integral sliding mode control methods, the tracking performance is improved, for the soft actuator with time‐varying radius. Finally, the proposed methods are confirmed by the simulation with experimental data.

Convergence of coprime factor perturbations for robust stabilization of Oseen systems

<p style='text-indent:20px;'>Linearization based controllers for incompressible flows have been proven to work in theory and in simulations. To realize such a controller numerically, the infinite dimensional system has to be linearized and discretized. The unavoidable consistency errors add a small but critical uncertainty to the controller model which will likely make it fail, especially when an observer is involved. Standard robust controller designs can compensate small uncertainties if they can be qualified as a coprime factor perturbation of the plant. We show that for the linearized Navier-Stokes equations, a linearization error can be expressed as a coprime factor perturbation and that this perturbation smoothly depends on the size of the linearization error. In particular, improving the linearization makes the perturbation smaller so that, eventually, standard robust controller will stabilize the system.</p>

Simulation Study on State Estimation for a Quadrotor Generalized Attitude Model

This paper studies the state estimation of a quadrotor yaw-channel generalized attitude model (GAM) using the subspace identification based state estimation method under the conditions that the measurements for the control quantity and the output attitude angle are corrupted with disturbing noises and that there are no available models. The quadrotor attitude control loop for the yaw-channel is first designed by MATLAB using an observer based state feedback law. A high-order coprime factor (CF) model for the GAM is then identified from simulation data by the subspace identification method. Next, the estimation states for the GAM can be given by the similarity transform and the relations between the GAM and its CF model. Finally, the efficacy of the presented state estimation procedure and the accuracy of the state estimation are verified.

Generalized parallel coprime array for two-dimensional DOA estimation: A perspective from maximizing degree of freedom

Parallel arrays with coprime subarrays have shown its potential advantages for two dimensional direction of arrival (DOA) estimation. In this paper, by introducing two flexible coprime factors to enlarge the inter-element spacing of parallel uniform subarrays, we propose a generalized parallel coprime array (GPCA) geometry. The proposed geometry enjoys flexible array layouts by the coprime factors and enables to extend the array aperture to achieve great improvement of estimation performance. Meanwhile, we verify that GPCA always can obtain M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> degrees of freedom (DOFs) in co-array domain via 2M sensors after optimization, which outperforms sparse parallel array geometries, such as parallel coprime array (PCA) and parallel augmented coprime array (PACA), and is the same as parallel nested array (PNA) with extended aperture. The superiority of GPCA geometry has been proved by numerical simulations with sparse representation methods.

Computing frequency response of non‐parametric uncertainty model of MIMO systems using υ‐gap metric optimization

This paper presents the computation of the non-parametric uncertainty model for multi input multi output (MIMO) systems, which is described by normalized coprime factors (NCF) using the frequency response data of the system. This computation is accomplished by minimizing a υ-gap metric criterion. For this purpose, the problem is formulated to a convex optimization context, such that a semidefinite programming (SDP) can be implemented. Minimization constraints and the normality constraints of coprime factors are converted to linear matrix inequalities (LMI). Thus, by convex optimization algorithms, the semidefinite programming will be optimized. The proposed method can also be used for non-square multi input multi output systems in a conservative assumption. So, through the first process of optimization, the frequency responses of the normalized coprime factors are derived. Finally, to evaluate the performance of the proposed method in the computation of the normalized coprime factors of a system, the simulated results of this method are compared with those obtained by the other methods for two types of systems.