Structured Singular Value Research Articles

Robust active vibration control of flexible smart beam by μ-synthesis

This paper presents a comprehensive method for designing a robust active vibration control system to suppress low-frequency vibrations in smart structures. A novel finite element method based on the first-order shear deformation theory is used to calculate the dynamic response of a smart beam. Through a comprehensive system identification process, the uncertain model of the smart beam is extracted considering both the magnitude and phase. The model fits the experimental data successfully. In addition, a generalized low-frequency vibration control performance function is designed for the piezoelectric smart beam. Using a linear fractional transformation, the system is converted into a standard μ-synthesis control framework, and the controller K is synthesized using structural singular values μ. The effectiveness of the proposed method is experimentally validated using a setup with a piezoelectric smart beam. The experimental results suggest that the proposed control method exhibits robust stability and robust performance, effectively enhancing the performance of smart structure control in various scenarios. The proposed control framework utilizes structured singular value analysis to provide optimal robust stability margins and superior robust control performance, effectively addressing system uncertainties and non-linearities.

Structured singular value of a repeated complex full‐block uncertainty

AbstractThe structured singular value (SSV), or , is used to assess the robust stability and performance of an uncertain linear time‐invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full‐blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full‐blocks. This specific class of uncertainty is relevant for the input‐output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full‐blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full‐blocks. The upper bound can be formulated as a semi‐definite program (SDP), which we solve using a standard interior‐point method to compute optimal scaling matrices associated with the repeated full‐blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full‐block structure.

Failure Risk Assessment of Grid-Connected Inverter With Parametric Uncertainty in LCL Filter

Grid-connected inverter failure may be caused by outliers of a population of units in field operation, due to the LCL filter parameter uncertainty. This paper proposes a probabilistic framework to analyze the impact of multiple filter parameter variances due to component tolerances, operating points, and aging effects. Both robust stability and filter performance are selected as the risk of failure. The robust stability of the grid-connected inverter is quantified by the structured singular value (SSV). The total harmonic distortion (THD) of the grid current is estimated to evaluate the filter performance. A case study on a three-phase inverter is performed to verify the proposed method through Hardware-in-the-Loop (HIL) simulation and physical prototype testing.

Nearest rank deficient matrix polynomials

The distance from a given n×n regular matrix polynomial to a nearest matrix polynomial of normal rank at most r for a specified positive integer r⩽n−1, is considered in two different norm settings. Particular emphasis is given on the distance to nearest singular matrix polynomials. The problem is shown to be equivalent to computing smallest structure preserving perturbations such that certain convolution matrices associated with the matrix polynomial become suitably rank deficient. In particular, the distance to singularity is seen to be equivalent to the rank deficiency of two different types of block Toeplitz matrices. This leads to new characterizations of the distance. Upper and lower bounds as well as information about the minimal indices of nearest singular matrix polynomials follow from these characterizations. The distances are also established to be reciprocals of certain generalized structured singular values, thus showing that computing the distance to singularity may be an NP hard problem. Based on the results, a strategy to compute the distance to singularity is devised and implemented via numerical algorithm based on BFGS and Matlab's globalsearch.m. Numerical experiments show that the computed distances compare favourably with values obtained in the literature and the bounds are tight.

Droop-based active voltage regulation control and robust stability analysis for VSCs in the large-scale RES-integrated power system

New features like high penetration level, low inertia, and weak damping are decreasing voltage support capacity in the power system as it sees large-scale renewable energy source (RES) integration continuously. The reasonable solution to this challenge is developing an additional active voltage regulation function for voltage source converters (VSCs). This study proposes a droop-based active voltage control strategy for VSCs in large-scale RES-integrated power systems to make VSCs continue to operate and regulate the voltage at the point of common coupling (PCC) during a fault without causing overcurrent. In order to meet the requirements of RESs and grid code, all control boundary conditions are designed based on practical engineering data. Meanwhile, plant uncertainty and parameter disturbance are introduced into a robust stability margin analysis model based on the component connection method (CCM) and structured singular value (SSV) to improve the engineering application prospect. The effectiveness and feasibility of this control strategy are proved by logical deduction and practical simulation based on a generalized small-signal model.

Robust Stability Assessment of Single-Phase Inverter With Multiparameter Distributions

Grid-connected inverters inevitably operate under uncertain system parameters. These uncertain parameters such as inductance and capacitance are caused by device aging or uncertain grid conditions. And they will affect the stability margin of the inverter and bring an unstable operation risk even with a well initial design. The existing research articles mainly focus on robust stability analysis and control strategies while ignoring the influence of parameter distributions on operational risk. How to evaluate the instability risk of the inverter under multiparameter distribution is still an open question. In this article, the structured singular value (SSV) method is proposed to evaluate the robust stability of the inverter with multiparameter distributions. The distribution characteristics of uncertain parameters are briefly reviewed. The system model of a single-phase grid-connected inverter is established with the parameter distributions of the system key components. The probability of stable system operation can be quantified by the SSV method. Experiment and case study results verify the correctness and effectiveness of the proposed method.

Robust Vibration Control for Active Suspension System of In-Wheel-Motor-Driven Electric Vehicle Via μ-Synthesis Methodology

Abstract This paper proposes a robust vibration controller design for active suspension system of in-wheel-motor-driven electric vehicles (IWMD-EVs) based on unified μ-synthesis framework. First, multiple parameter uncertainties and unmodeled high-order dynamics of the suspension are analyzed and discussed. By applying the mixed uncertainties and linear fraction transformation, model perturbations are separated from the suspension system and their perturbation bounds can also be limited. Then, the uncertain quarter-vehicle active suspension model with dynamic damping in-wheel-motor-driven system is established, in which in-wheel motor is suspended as a dynamic vibration absorber. The resulting robust μ-synthesis feedback controller of generalized closed-loop active suspension system is designed with the concept of structured singular value (SSV) μ and μ-synthesis theoretics, and solved via comprehensive solution of the D–G–K iteration. The μ analysis results show that the μ-controller possesses less conservative stability and performance margins as compared to the H∞ method against system uncertainties. Furthermore, simulations of nominal and perturbed suspension systems are implemented and the corresponding frequency and time-domain responses are compared, and then simulation results confirm that the developed μ-controller is capable of attenuating the negative vibration of the active suspension system compared with H∞ controller and passive suspension.

Predictive Analysis for Cancer and Diabetes Using Simplex Method Based Social Spider Optimization Algorithm

Early stage of prediction and diagnosis is the only way to solve the challenges due to medical data. Machine learning tools and techniques help in prediction and diagnosis of different types of medical data. In this paper, Simplex Method based Social Spider Optimization (SMSSO) method is used which modifies the Social Spider Optimization (SSO) method. Different types of datasets were used to validate the SMSSO-NN technique. SMSSO-NN shows 99.36%, 94%, 95.78%, and 98% accuracy in Wisconsin Breast Cancer (WBC), Lung cancer, Diabetic, and Cervical cancer datasets, respectively that is better than other methods. The accuracy of the SMSSO-NN algorithm is associated with different classification techniques like Structured Singular Value (SSV), Local Linear Wavelet Neural Network-Firefly Algorithm (LLWNN-FA), and Rough Set Theory.

가변속 냉동시스템의 견실 온도 제어를 위한 구조화 불확실성 기반의 μ-Synthesis 제어기 설계

This paper investigates μ-synthesis robust control for a variable speed refrigeration system to enhance robustness against model uncertainty and external disturbance. As the practical transfer function model obtained by experiments to design a controller inevitably contains model uncertainties such as unmodeled dynamics and modeling errors, a robust controller is necessary to track references in the system. Target temperature and superheat were simultaneously controlled in the system by adjusting rotating speed of compressor and opening angle of an electronic expansion valve respectively. Moreover, the μ-synthesis controller treats model uncertainty as structured perturbation; it is designed using structured singular value. It is shown that the μ-synthesis approach which takes structured uncertainties into account provides robust control performance against both dynamic perturbations including modeling errors and external disturbances. The validity of the proposed method was demonstrated by simulations and experiments.

Computing $\mu$-values for LTI Systems

In this article we consider certain linear time-varying control systems and investigate their stability using structured singular values ($\mu$-values). We use the low rank ordinary differential equations based methodology to compute the lower bounds for $\mu$-values. The inner-outer algorithm computes the local extremizer of an admissible perturbation and adjusts the desired perturbation level. Further, we present a comparison of our results via the well-known MATLAB routine mussv which is available in MATLAB control toolbox.

Multivariable Iterative Learning Control Design Procedures: From Decentralized to Centralized, Illustrated on an Industrial Printer

Iterative Learning Control (ILC) enables high control performance through learning from measured data, using only limited model knowledge in the form of a nominal parametric model. Robust stability requires robustness to modeling errors, often due to deliberate undermodeling. The aim of this paper is to develop a range of approaches for multivariable ILC, where specific attention is given to addressing interaction. The proposed methods either address the interaction in the nominal model, or as uncertainty, i.e., through robust stability. The result is a range of techniques, including the use of the structured singular value (SSV) and Gershgorin bounds, that provide a different trade-off between modeling requirements, i.e., modeling effort and cost, and achievable performance. This allows control engineers to select the approach that fits the modeling budget and control requirements. This trade-off is demonstrated in a case study on an industrial flatbed printer.

Legacy recovery and robust augmentation structured design for the VEGA launcher

SummaryThis paper presents a systematic robust control framework based on the structured approach to address the synthesis of the atmospheric ascent‐flight control system of a launch vehicle. To introduce this synthesis framework, the control problem is first formulated to recover the classically designed baseline rigid‐body controller of the actual VEGA launcher VV05 mission. This legacy recovery builds the necessary background for a good understanding of the problem and increases confidence for its transfer to the Space industry. Subsequently, it is shown how to systematically augment the robustness of the design from the synthesis stage against wind turbulence perturbations and parametric uncertainty. The resulting controller is verified via classical stability margins and robust structured singular value analyses and finally validated using nonlinear, time‐domain simulations in a Monte Carlo campaign. It is highlighted that this robust synthesis framework allows to obtain a controller with improved robust stability and global performance, and more importantly, it provides a more systematic methodology for design.

Event-triggered Control With Self-triggered Sampling for Discrete-time Uncertain Systems

This paper proposes a resource-aware control approach for discrete-time linear uncertain systems. The approach uses a self-trigger condition to determine the sampling time to guarantee that the system is uniformly ultimately bounded and an event-trigger condition to determine control updates. The self-trigger condition is constructed using the skewed structured singular value to treat uncertainties in the prediction, and the event-trigger condition is constructed by considering the costs of sampling and control updates. A numerical example is provided to illustrate the approach.

$\mathcal{H}_{\infty}$ and $\mu$ -Synthesis for Nanosatellites Rendezvous and Docking

In this brief, the nanosatellite rendezvous and docking problem is tackled. It was never attempted for small spacecraft, as critical technologies, such as six-degree-of-freedom (DoF) micropropulsion systems, have only recently become available due to advances in MEMS. The typical level of noise in nanosatellites’ sensors and actuators combined with the dynamics uncertainties, low actuation capabilities, and reliability requirements makes the use of robust control appropriate. The system is described by a linearized rotation/translation, six DoFs, and coupled dynamics, including fuel sloshing. An ${\mathcal {H}_\infty }$ controller is first designed, in which robust stability and performance are assessed using structured singular values. The controller robustness is then improved using ${{\mu }}$ -synthesis. Nonlinear Monte Carlo simulations for both controllers, including realistic sensors and actuators models, are provided allowing a thorough assessment of the complete guidance, navigation and control (GNC). The sought GNC schemes are shown to be robust to the modeled uncertainties and to satisfy the docking requirements.

Application of the Robust Control Toolbox for Time Delay Systems with Parametric and Periodic Uncertainties Using SSV to Uncertain Time Delay System with Astatism

Abstract Application of the Robust Control Toolbox for Time Delay Systems with Parametric and Periodic Uncertainties Using SSV (Structured Singular Value) for the Matlab system to Uncertain Time Delay System with Astatism is performed. The D-K iteration and the algebraic approach implemented in the toolbox are applied to 2nd order system with astatism and uncertain time delay and two other parameters in the numerator and denominator of the plant transfer function. Multiplicative uncertainty is used for treating uncertain time delay, the parametric uncertainty is modelled using general interconnection for the systems with parametric uncertainty in numerator and denominator.

Computing Structured Singular Values for Sturm-Liouville Problems

In this article we present numerical computation of pseudo-spectra and the bounds of Structured Singular Values (SSV) for a family of matrices obtained while considering matrix representation of SturmLiouville (S-L) problems with eigenparameter-dependent boundary conditions. The low rank ODE's based technique is used for the approximation of the bounds of SSV. The lower bounds of SSV discuss the instability analysis of linear system in system theory. The numerical experimentation show the comparison of bounds of SSV computed by low rank ODE'S technique with the well-known MATLAB routine mussv available in MATLAB Control Toolbox.

Design and Experimental Validation of a Robust Output Feedback Control for the Coupled Dynamics of a Micro Air Vehicle

This paper addresses the design and experimental validation of a linear robust static output feedback controller for a 150 mm span fixed wing micro air vehicle (MAV). Severe coupling between longitudinal and lateral dynamics of the MAV lead to the design of a multivariable controller for the combined dynamics. The control design problem is posed in the framework of static output feedback (SOF) due to the inexpensive computational requirements for implementation. The multiobjective control design problem including stability requirements, closed loop damping ratio requirements and H∞ norm minimization is solved using the hybrid technique of linear matrix inequalities (LMI) and genetic algorithm (GA). The design is carried out in the discrete time domain, facilitating in direct implementation of the multivariable controller in the onboard autopilot hardware. The robustness of the resulting closed loop system under parametric uncertainties is evaluated using structured singular value analysis. The effectiveness of the proposed controller is demonstrated through outdoor flight trial of the micro air vehicle with a customized lightweight autopilot hardware.

Robust Control for Inductively Coupled Power Transfer Systems With Coil Misalignment

Coil misalignment in inductively coupled power transfer (ICPT) systems will lead to fluctuation of transferred power, and even instability of the ICPT systems. To obtain robust control for ICPT system with coil misalignment, a μ-controller based on structured singular value (SSV) is used to set up a closed-loop system in this paper. A generalized state-space averaging (GSSA) model is established using GSSA method first. Then a standard M-Δ configuration is obtained by a linear fractional transformation of the nominal and uncertainty parts of the GSSA model. Finally, a μ-controller is designed by D-K iteration. Besides, the theoretical results are validated by computer simulations and practical experiments.

Structure singular value theory based robust motion control of live maintenance robot with reconfigurable terminal function for high voltage transmission line

In a complex rigid–flexible coupling environment of overhead high-voltage transmission line, the manipulator robust trajectory tracking motion control of live maintenance robot is the premise of fulfilling the entire maintenance operations. In the process of manipulator’s different function reconfigurable (drainage board bolt tightening and insulator strings replacement), in response to the shortage of excessive pursuit of robust stability for robot manipulator when using H∞ control, as it ignores the influence of structure changes caused by terminal reconfigurable on the system stability to a certain extent, the structured singular value theory–based robot robust μ synthesis control method was proposed in this article. The intrinsic relationship between structured singular value control (μ method) and H∞ control was elaborated, a general control model of the multi-arms and multi-actions robot system was established, the multifunction terminal reconfigurable live maintenance robot with its two kinds of operations was set as a research object, and the corresponding robot μ controller was designed. In the MATLAB development environment, simulation results have shown that on the premise of maintaining the robust stability, compared to the H∞ control method, μ control can obtain better performance robustness for the perturbation of its own structural changes in the process of different operation functions switch. Finally, the validity and engineering practicability of this method is verified by actual 220 kV live operation experiments.

$\mu$ Approach to Robust Stability Domains in the Space of Parametric Uncertainties for a Power System With Ideal CPL

Power electronic systems are prone to instability. The problem, generally attributed to the constant power load (CPL) behavior of their power electronic controlled loads, can become more acute when the systems are subject to parametric uncertainties. The structured singular value (SSV) based $\mu$ method has proven to be a reliable approach for assessing the stability robustness of such uncertain systems. Despite its numerous benefits, the $\mu$ method is not often applied to electrical power systems (EPS) with multiple uncertainties. This may be due to the mathematical complexity underlying the $\mu$ theory. This paper aims to make the $\mu$ approach more application-friendly by providing clearer insights into the meaning and usefulness of the robust stability measure $\mu$ for EPS with multiple parametric uncertainties. This is achieved by presenting a methodology for translating $\mu$ analysis results from the frequency domain to the more perceivable uncertain parameters domain. The method directly demonstrates dependences of system stability on uncertain system parameters. Further, it clearly identifies robust stability domains as subsets of the much wider stability domains. The work is based on a representative EPS connected to an ideal CPL. $\mu$ analysis predictions are evaluated and validated against analytical results, for example, CPL system.