Real Parametric Uncertainty Research Articles

Model Parameter Calibration for Vibration Fatigue Analysis by Means of Bayesian Updating and Artificial Neural Network Based Surrogate Models

Abstract In this paper, a methodology for model parameter calibration for vibration fatigue analysis is proposed. It combines Bayesian updating of uncertain model parameters and artificial neural networks (ANNs). The calibrated parameters are used to increase the accuracy of fatigue lifetime calculations for components submitted to vibrational loads. The Bayesian updating uses eigenfrequencies, mode shapes, total mass, and the frequency response functions (FRFs). These quantities are predicted by ANN-based surrogate models to accelerate the Bayesian updating process. A novel strategy for the prediction of the magnitude and phase of FRFs with ANNs is proposed. The frequency is used as an additional input variable, and a schematic selection of significant points of the FRF curves is presented. A high prediction accuracy of the surrogate models could be achieved. The procedure includes the analysis of the relevant frequency range and a sensitivity analysis based on the Morris method to identify appropriate modes and the most-influential parameters. The proposed framework is applied to a current vehicle component subjected to vibrational loads. An experimental modal analysis is used for the calibration and consideration of real parameter uncertainty. First, the accuracy of the surrogate models and Bayesian updating is verified by a nominal reference simulation and then validated with experimental data. The measurable control parameter thickness and component mass are used to examine the calibration accuracy. Finally, a decrease in the dispersion of the vibration fatigue distribution is obtained with the calibrated parameters.

Artificial neural network-based direct power control to enhance the performance of a PMSG-wind energy conversion system under real wind speed and parameter uncertainties: An experimental validation

With the increasing emphasis on embedding advanced technology into system controls, the Direct Power Control (DPC) approach has garnered considerable attention due to its simple and highly adaptable algorithm. This approach has been increasingly recognized in numerous applications. However, the variable frequency, harmonic distortion of the currents, and power ripples caused by Hysteresis controllers and switching tables decrease its effectiveness and robustness, affecting the system’s performance. For this reason, this paper proposed a new DPC based on Artificial Neural Network (ANN) approaches. In this approach, the hysteresis comparator and the switching table are substituted with ANN controllers and then applied on both sides: machine-side converter (MSC) and grid-side converter (GSC) of a Permanent Magnet Synchronous Generator based Wind Energy Conversion System (PMSG-WECS). Moreover, to make the system more efficient in varying wind conditions, this study expands the utilization of the artificial neural networks (ANN) to encompass the maximum power point tracking (MPPT) control strategy. To demonstrate the effectiveness of the proposed approach on the system behaviors, a simulation test was carried out in the Matlab/Simulink environment, using a real wind profile of a Moroccan city (Essaouira). In comparison to the classical DPC control, the simulation results showed the superior performance of the proposed ANN-DPC control in terms of reference tracking, response time, overshoot, precision, and its capacity to reduce the rate of power ripples and total harmonic distortion (THD) in the injected currents. Furthermore, a robustness test was also included in this work to check the robustness of the proposed control against parameters variation. In conclusion, the feasibility and effectiveness of the ANN-DPC control approach were confirmed through experimental validation using the dSPACE DS1104 board.

Mixed [Formula: see text]-synthesis tracking control and disturbance rejection in a robotic digit of an impaired human hand for anthropomorphic coordination.

In a partially impaired anthropomorphic hand, maintaining the movement coordination of the robotic digits with the central nervous system (CNS) and natural digits is crucial for robust performance. A challenge in the control perspective of movement coordination of a human hand is finding methods robust to the disturbances in a well-posed control problem of a biomechanical model. We use visco-elastic dynamics in the human palm frame of reference to explore the biomechanics of movement coordination to solve this control problem. Our biomechanical model incorporates the time delay due to actuation force, parametric uncertainty, exogenous disturbances, and sensory noise to constitute a 21-degree of freedom model. A mixed [Formula: see text]-synthesis controller, considering the real parametric uncertainty, represents the CNS in the control paradigm. We consider the robotic finger's flexion movement when perturbed from the initial equilibrium. The controller provides feedback force at the joints to regulate the robotic finger movement. The index finger follows a reference trajectory of the joint angular position profile and stabilizes at a flexion angle of 1 rad/s at a time of 1 s. The main control objective is to keep the angular displacement of the finger joint constant when a disturbance force acts. We simulate the modeling scheme in MATLAB/ Simulink. The results demonstrate that our controller scheme is robust against the worst-case disturbance and achieves the desired performance value. Developing a biologically inspired neurophysiological controller with robust performance has many applications, including assistive rehabilitation devices, hand movement disorder diagnosis, and robotic manipulators.

A Novel Robust Strategy for the Concurrent Control of Frequency and Voltage in the Synchronous Generator With Real Structured Uncertainties

In this article, a novel robust strategy is proposed for concurrent control of the synchronous generator's voltage and frequency in a single machine infinite bus plant. The methodology is based on infinity norm and Mu analysis and synthesis to prepare the robust function of the power system stabilizer, automatic voltage regulator, and load frequency control systems. Ten real structured uncertainties have been considered for the K 1, K 2 and K 4 to K 6 coefficients of the Heffron–Phillips generator model, inertia constant, damping coefficient, the governor speed regulation coefficient, and the amplifier and exciter gains. Each uncertain parameter has a nominal value in the generator operating point with 25% tolerance excepts to amplifier and exciter gains where their tolerances are 12.5%. The proposed strategy efficiency lies in the strict converting of all ten real parametric uncertainties into the generalized structure of µ synthesis and the formation of efficient weighting functions. Based on the proposed strategy and H ∞ norm optimization, µ-synthesis D-K iteration procedure and loop-shaping manner, three controllers have been obtained whose robust performances (RPs) are guaranteed. The supremacy of the offered controllers is shown by comparing their functions in four scenarios and three patterns. The simulation results reveal the good RP of the designed controllers. Also, for a benchmark problem as a single machine connected to a 230 kV network, the capabilities of the designed robust controllers have been shown.

Simple adaptive control strategy for a class of systems subjected to real parametric uncertainty with application to unified chaotic system

In this paper, a relatively simplified adaptive control strategy for set of chaotic systems is presented. The results utilise the basic linear state feedback control strategy blended with algebraic...

Simple adaptive control strategy for a class of systems subjected to real parametric uncertainty with application to unified chaotic system

In this paper, a relatively simplified adaptive control strategy for set of chaotic systems is presented. The results utilise the basic linear state feedback control strategy blended with algebraic matrix Riccati equation (AMRE) to derive the control mechanism for chaotic systems operating in uncertain environment. The proposed approach utilises lesser number of control inputs in comparison to methods available in literature. Moreover, the controller structure turns out to be simple linear combination of states of system for the chaotic systems belonging to the proposed class, which are otherwise handled with nonlinear controller design strategies. The Lyapunov stability approach is exploited to analytically derive the control function and the parametric updation laws for uncertain parameters. Extensive simulation results are elaborated for set of chaotic systems to demonstrate effectiveness and validity of the presented approach.

Structured Robust Control Against Mixed Uncertainty

We present new approaches to designing structured controllers, which are robust in the presence of mixed real parametric and complex dynamic uncertainty. As the synthesis of such controllers is inherently NP-hard, we discuss inner and outer relaxation techniques, which make this problem amenable to computations. Our relaxation methods are positively evaluated and compared on the basis of a rich test set and for a challenging missile pilot design problem.

Determination of Most Desirable Nominal Closed-Loop State Space System Via Qualitative Ecological Principles

This paper addresses the issue of determining the most desirable “nominal closed-loop matrix” structure in linear state space systems, from stability robustness point of view, by combining the concepts of “quantitative robustness” and “qualitative robustness.” The qualitative robustness measure is based on the nature of interactions and interconnections of the system. The quantitative robustness is based on the nature of eigenvalue/eigenvector structure of the system. This type of analysis from both viewpoints sheds considerable insight on the desirable nominal system in engineering applications. Using these concepts, it is shown that three classes of quantitative matrices labeled “target sign stable (TSS) matrices,” “target pseudosymmetric (TPS) matrices,” and finally “quantitative ecological stable (QES) matrices” have features which qualify them as the most desirable nominal closed-loop system matrices. In this paper, we elaborate on the special features of these sets of matrices and justify why these classes of matrices are well suited to be the most desirable nominal closed-loop matrices in the linear state space framework. Establishment of this most desirable nominal closed-loop system matrix structure paves the way for designing controllers which qualify as robust controllers for linear systems with real parameter uncertainty. The proposed concepts are illustrated with many useful examples.

Clearance of flight control law based on structural singular value theory

This paper studies the clearance of flight control law for a hypersonic gliding vehicle (HGV) and proposes two linear clearance criteria based on structural singular value (μ) theory. The first criterion is the multiinput-multioutput (MIMO) stability margin, which is defined independently of an exclusive region depicted in Nichols diagrams. Through introducing a measure matrix, the classic phase/magnitude margin can be expanded into an MIMO system, thereby becoming the robust stability criterion of the MIMO system with pure complex uncertainties. The second criterion is setup based on an analysis of the robustness, i.e., the stability under pure real parametric uncertainties. The study establishes a physical linear fractional representation (LFR) model of the HGV and then reduces it to an equivalent model of a lower order. Then a global optimization strategy is proposed to compute μ with real parametric uncertainties. The computational burden can be significantly reduced by model reduction and global optimization. The study evaluates an HGV as an example to demonstrate the validity and efficiency of the proposed methods.

THE LATE K-TYPE BINARY V1104 HER NEAR THE SHORT-PERIOD END OF CONTACT BINARIES

V1104 Her is a newly discovered periodic variable with EW type variability. With an orbital period that is extremely short for a contact binary, it was found to have almost the latest K spectral type. To study its properties and nature, two new sets of multi-color light curves were analyzed with the Wilson-Devinney code. Photometric solutions reveal that the system is a W-type shallow contact binary with a mass ratio of 1/q=M-1/M-2=0.63. +/- 0.01 and a degree of contact of about f=15% +/- 2%. The real parameter uncertainties may be from three to five times larger, depending on the required confidence. Combining the newly determined times of minimum light, some of which were reprocessed from initial data, in conjunction with others published, the period variation is investigated in detail. Different methods of curve fitting were used, based on a weighted least-squares method. Finally, the orbital period of V1104 Her is found to be undergoing a long-term decrease at a rate of dP/dt = -2.9(+/- 0.5) x 10(-8) days . yr(-1), as well as double cyclic oscillations with a period ratio (T-1/T-2) very close to 9:2. The light-travel time effect was found to be the best explanation for the cyclic variations. This indicates that the object is a possible quadruple system, which further implies that multiplicity may be a common phenomenon among close binaries.

Skewed structured singular value‐based approach for the construction of design spaces: theory and applications

This study proposes a computationally efficient algorithm that characterises the set of allowable real parametric uncertainties while ensuring the desired output specifications are satisfied for rational systems. Along with the scaled main loop theorem, the proposed approach reformulates this NP-hard problem by using the skewed structured singular value ν, whose upper and lower bounds can be efficiently computed by existing algorithms and software. A short discussion on the extension to a multi-agent system is also included. Two numerical examples of pharmaceutical crystallisation and nasal spray demonstrate the effectiveness of the proposed algorithm.

On the structure of generalized plant convexifying static [formula omitted] control problems

This paper shows that, under specific structures of generalized plants, the set of static controllers satisfying internal stability and a certain level of H∞ performance becomes convex. More precisely, we characterize such static H∞ controllers by an LMI with controller variables being kept directly as decision variables. The structural conditions on the generalized plant are not too strict, and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions. For the generalized plants of interest, we further prove that full-order dynamical H∞ controllers can be characterized by an LMI with a simple change of variables. In stark contrast to the known LMI-based H∞ controller synthesis, the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems. Related issues such as robust controller synthesis against real parametric uncertainties are also discussed.

Analysis the robustness of control systems based on disturbance observer

Disturbance observer (DOB) estimates the system disturbances by using the inverse of the nominal plant model and a low pass filter (LPF). Although the LPF provides the properness in the inner-loop, it is the main design constraint of the control systems based on DOB. The bandwidth of the LPF is designed as high as possible so that the DOB can estimate the disturbances in a wider frequency range. However, its bandwidth is limited by noise and robustness of the system. The robustness limitation is directly related with the robustness analysis methods, and they significantly affect the performance of the DOB based control systems. In this paper, three different robustness analysis methods are implemented into the DOB based control systems, and the relation between the robustness of the system and bandwidth of DOB is clearly explained. The conservatism, which is the main drawback of the conventional analysis methods, on the bandwidth of DOB is removed by proposing a new real parametric uncertainty based analysis method. The proposed methods are compared in detail, and simulation results are given to show the validation.

An analysis and design framework for robust control of a multi-axis active vibration isolation system with unknown payload

This paper presents a framework for model-based analysis of robust stability and performance for a multi-axis active vibration isolation system with constant but unknown payload and subject to modelling errors associated with structural flexibility. The theoretical treatment involves a linear time-invariant system subject to real parameter uncertainty associated with the unknown payload. A set of performance indices are formulated based on generalized () and measures. A method for stability/performance verification is then developed using a parameter-dependent Lyapunov function that incorporates the kinetic energy of the uncertain payload mass. This allows nonconservative bounds on the performance indices to be established via numerical solution of a corresponding set of matrix inequalities. The approach is especially suitable, and computationally efficient, for multi-degree-of-freedom systems as the overall (symmetric positive-definite) properties of the system mass matrix are accounted for without involving information for each scalar parameter. The associated LMIs can therefore be solved in polynomial time with respect to the number of unknown parameters. Numerical examples for the case of sky-hook damping control and multi-objective control are provided that demonstrate the effectiveness of the method as a tool for model-based controller evaluation and multi-objective optimization.

Bandwidth constraints of disturbance observer in the presence of real parametric uncertainties

Control systems based on disturbance observer (DOB) require a low pass filter (LPF) to avoid the algebraic loop and improperness in the inner-loop. Bandwidth of the LPF of DOB is desired to be as high as possible to improve the performance of a system. Two main constraints, which are noise and robustness of a system, determine the bounds on the DOB's bandwidth. Although the bandwidth constraint due to noise, which causes an upper bound on the bandwidth of DOB, directly depends on the sampling rate and measurement plants and methodology, the constraint due to robustness is affected significantly by robustness analysis methods. Conventional robustness analysis methods limit the bandwidth of DOB unnecessarily due to conservatism. This paper proposes a new robust stability analysis tool for control systems based on DOB in the presence of real parametric uncertainties. The proposed method shows that there is only a lower bound on the bandwidth of DOB to obtain robust stability, and the stability margin of a system increases as the bandwidth of DOB is increased. Consequently, the robustness of a system improves as the bandwidth of DOB is increased in the presence of real parametric uncertainties.

Guardian map approach to robust stability of interval systems

A systematic approach for the robust Hurwitz and Schur stability of the dynamic interval systems is proposed. An interval matrix is expressed as a linear fractional transformation (LFT) of an interconnection matrix with structured real parametric uncertainties. Based on guardian map theory and µ-analysis, a new approach is provided to derive the necessary and sufficient conditions in terms of the structured singular value (μ) ensuring the stability robustness of interval systems. This approach is feasible for both continuous- and discrete-time interval systems by a unified LFT framework, and it is applicable directly to D-stability for performance requirements.

Robust flutter analysis based on genetic algorithm

Robust flutter analysis considering model uncertain parameters is very important in theory and engineering applications. Modern robust flutter solution based on structured singular value subject to real parametric uncertainties may become difficult because the discontinuity and increasing complexity in real mu analysis. It is crucial to solve the worst-case flutter speed accurately and efficiently for real parametric uncertainties. In this paper, robust flutter analysis is formulated as a nonlinear programming problem. With proper nonlinear programming technique and classical flutter analysis method, the worst-case parametric perturbations and the robust flutter solution will be captured by optimization approach. In the derived nonlinear programming problem, the parametric uncertainties are taken as design variables bounded with perturbed intervals, while the flutter speed is selected as the objective function. This model is optimized by the genetic algorithm with promising global optimum performance. The present approach avoids calculating purely real mu and makes robust flutter analysis a plain job. It is illustrated by a special test case that the robust flutter results coincide well with the exhaustive method. It is also demonstrated that the present method can solve the match-point robust flutter solution under constant Mach number accurately and efficiently. This method is implemented in problem with more uncertain parameters and asymmetric perturbation interval.

Local Observer Design For Nonlinear Control Systems Around Equilibria

In this paper, new results have been derived for the local observer design for nonlinear control systems with real parametric uncertainty around equilibia. In this paper, it is first shown that equilibrium-state detectability is a necessary condition for the existence of local asymptotic observers for any nonlinear system and using this result, it is shown that for the classical case, when the state equilibrium does not change with the real parametric uncertainty, and when the plant output is purely a function of the state, there is no local asymptotic observer for the plant. Next, it is shown that in sharp contrast to this case, for the general case of problems where we allow the state equilibrium to change with the real parametric uncertainty, there generically exist local exponential observers even when the plant output is purely a function of the state. In this paper, a characterization and construction procedure for local exponential observers for a general class of nonlinear systems with real parametric uncertainty has also been derived under some stability assumptions. It is also shown that for the general class of nonlinear systems considered, the existence of local exponential observers in the presence of inputs implies, and is implied by the existence of local exponential observers in the absence of inputs.

Robustness via structured H ∞/H ∞ synthesis

Multi-objective H ∞/H ∞-synthesis with structured control laws is discussed and used as a means to enhance robustness of the system in the presence of real parametric uncertainty. NP-hardness of the computation of the structured singular value μ excludes its use within an optimisation procedure and raises the question of how to replace it. We show that the semi-structured distance to instability can be used for that purpose and we indicate how the resulting mixed H ∞ program can be solved efficiently. The method is applied to the regulation of a flexible geostationary satellite.

Stability analysis of negative imaginary systems with real parametric uncertainty – the single-input single-output case

Real parametric uncertainty is common in many applications. In this study, the authors analyse the robust stability of feedback loops of single-input single-output systems with negative imaginary frequency response subject to real parametric uncertainty. A recent result on the stability of such feedback loops is specialised to this case, resulting in a very simple stability condition dependent only on the steady-state parameters of the systems. The structured singular value for this system type is also obtained, and it is shown that it yields related but more constrained, easily computable stability guarantees. In a numerical example, the robust stability of a control loop for a DC machine subject to real parametric uncertainty is analysed.