Estimation Of Stability Region Research Articles

Estimation and Expansion of Vehicle Stability Region With Sums of Squares Programming

The vehicle stability region can be used to evaluate vehicle stability performance and lay the foundation for vehicle safety improvement. It can be obtained via the region of attraction (RoA) based on sums of squares (SOS) programming. However, it is usually conservative, and the computational burden is large. This article focuses on the above issues and proposes a well-developed method for RoA estimation, with application to the estimation and expansion of the vehicle stability region. For RoA estimation, an improved SOS program is formulated, and its optimization objective combined with the customized algorithm significantly reduces conservatism. In addition, the feasibility prejudgment strategy and the dynamic search range are proposed in the algorithm. As a result, the computational burden is greatly reduced, which also indirectly helps reduce conservatism. Then, a more accurate vehicle stability region is obtained with less time consumption, and a map-based controller is proposed to improve vehicle stability. Better stability performance and larger stability regions are guaranteed under different scenarios due to the adaptive adjustment of controller gains. Finally, simulations and hardware-in-the-loop experiments with an embedded vehicle controller are performed to verify the effectiveness of our method.

Toward multiscale simulations for solidification microstructure and microsegregation for selective laser melting of nickel-based superalloys

In this study, we carried out multiscale simulations that integrate a macro-scale finite element method simulation for mass and heat transfer of the transient molten pool and a micro-scale quantitative phase-field model for dendritic growth and solute distribution based on selective laser melting (SLM) experiments. Macroscopic simulations reveal an approximately inverse coupling of solidification velocity Vs and thermal gradient G near the solid–liquid interface at the tail end of the molten pool. It was found that the maximum flow velocity of the Inconel 718 alloy melt in the molten pool exceeds 2×10−2 m/s and the maximum negative pressure reaches −5.28×10−4 Pa. Through quantitative phase-field simulations, the map about G/Vs for each solidification morphology was obtained, and it was found that solidification velocity dependent solute partition coefficients k(Vs) can strongly influence the estimated stability regions. The power law relationship of the primary dendritic arm spacing (PDAS) λ1 versus solidification velocity λ1∝Vsα agrees with the previous experimental results for lower G, and the exponent α decreases with increasing G. The PDAS λ1 versus cooling rate R following λ1∝R−0.512 is consistent with previous investigations. We found that λ1 is a nonlinear function with G−0.5Vs−0.25, i.e., λ1∝(G−0.5Vs−0.25)α, with α ranging from 0.887 to 2.466 for various G. Comparison of the predicted λ1 with Trivedi's model reveals that λ1 is still nonlinear with G−0.25Vs−0.25.

The CORALIE survey for southern extrasolar planets

Context. A historical search for exoplanets among a sample of 1647 nearby southern main sequence stars with the CORALIE spectrograph at La Silla Observatory has been underway since 1998, with a backup subprogram dedicated to the monitoring of binary stars. Aims. We reviewed 25 years of CORALIE measurements and search for Doppler signals consistent with stellar or brown dwarf companions to produce an updated catalog of both known and previously unpublished binary stars in the planet-search sample. We assessed the binarity fraction of the stellar population and survey the prospects for more precise searches for planets in the binary sample. Methods. We performed a new analysis on the CORALIE planet-search sample’s radial velocity measurements, searching for stellar companions and obtaining orbital solutions for both known and new binary systems. We performed simultaneous radial velocity and proper motion anomaly fits on the subset of these systems for which HIPPARCOS and Gaia astrometry measurements are available, obtaining accurate estimates of true mass for the companions. Results. We found 218 stars in the CORALIE sample to have at least one stellar companion, 130 of which are not yet published in the literature and for which we present orbital solutions. The use of the proper motion anomaly allowed us to derive true masses for the stellar companions in 132 systems, which we additionally used to estimate stability regions for possible planetary companions on circumprimary or circumbinary orbits. Finally, we produced detection-limit maps for each star in the sample and obtained occurrence rates of 0.43−0.11+0.23% and 12.69−0.77+0.87% for brown dwarf and stellar companions, respectively, in the CORALIE sample.

Phase portrait‐based stability region estimation for grid‐connected VSC with PLL

Here, the stability region of grid-connected VSC with phase locked loop (PLL) is estimated. First, the conservative stability region is derived via the classical Lyapunov method. Then an energy function is constructed as the general stable condition for the VSC system. Based on the constructed energy function, two estimation methods of the system stability region by approximation of phase trajectory are proposed. The stability regions by the proposed methods are less conservative than that by the classical Lyapunov method. A stability evaluation function for the initial states of the VSC system is further proposed based on the estimated stability region. Time-domain simulations verify the correctness of the proposed methods and the effectiveness of the stability evaluation function.

Inequality Constraints Based Method for Fast Estimation of Droop Slope Stability Regions for MMC-Based MTDC Systems

This paper proposes an inequality constraints based method to efficiently and quickly estimate stability regions of droop control slopes for modular multilevel converter (MMC)-based multi-terminal dc (MTDC) systems. At first, a general small-signal model of the MMC-MTDC system is developed, which consists of the dc network and the MMCs with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$dq$</tex-math></inline-formula> controllers and multiple droop controllers. When deriving corresponding nonlinear state-space models, the edge-node matrix is introduced for the dc network modeling with arbitrary grid topology and transmission line model. Then, based on the eigenvalues sensitivity and the Taylor Series of eigenvalues, a set of inequality constraints are proposed to expeditiously estimate the suprema of the droop slopes and identify the droop slope stability regions for the MMC-MTDC system. To verify the state-space model, a comparison of dynamic responses between the math model calculation in MATLAB and the EMT simulation in PSCAD/EMTDC is conducted, which demonstrates the accuracy and the correctness of the developed small-signal model. The effectiveness of the proposed parameter stability region estimation method is demonstrated by several examinations including the supremum tests of droop slopes, the stability region sketches on accuracy, and the predicted unstable operations in PSCAD/EMTDC.

On the random aspect of intermittent stick/slip motion

A stochastic interpretation of the stick/slip mechanism is proposed to model and mitigate the complicated friction interaction that occurs between surfaces, with direct implications on the stability of dynamic mechanical systems involved. Most investigations dealt with the estimation of such stability regions in a deterministic framework. A realistic approach is to consider random aspects in the analysis of complex dynamic behaviors. In the present article, a stick–slip nonlinear model possessing multiple periodic solutions is considered under fluctuating random excitations. The time evolution of the probability density function is studied by employing an adaptive path integration method and then compared through Monte-Carlo simulations. A parametric study is performed on characteristics such as noise intensity and initial distribution. The physical example employed will permit to assume the entrance of noise through a first-order linear filter. Results reveal that the randomness factor extremely affects the probability of occurrence of each solution, justifying the application of such analyses in reliability-related studies and situations where sensitivity to randomness is acute.

Stability Regions of Vehicle Lateral Dynamics: Estimation and Analysis

Abstract A new method is proposed to estimate and analyze the vehicle lateral stability region, which provides a direct and intuitive demonstration for the safety and stability control of ground vehicles. Based on a four-wheel vehicle model and a nonlinear two-dimensional (2D) analytical LuGre tire model, a local linearization method is applied to estimate the vehicle lateral stability regions by analyzing the vehicle stability at each operation point on a phase plane, which includes but not limited to the equilibrium points. As the collections of all the locally stable operation points, the estimated stability regions are conservative because both vehicle and tire stability are simultaneously considered, which are especially important for characterizing the stability features of highly/fully automated ground vehicles (AGV). The obtained lateral stability regions can be well explained by the vehicle characteristics of oversteering and understeering in the context of vehicle handling stability. The impacts of vehicle lateral load transfer, longitudinal velocity, tire-road friction coefficient, and steering angle on the estimated stability regions are presented and discussed. To validate the correctness of the estimated stability regions, a case study by matlab/simulink and CarSim® co-simulation is presented and discussed.

Generalized Energy Functions for a Class of Third-Order Nonlinear Dynamical Systems

Nonlinear dynamical systems exhibiting complex structure in their limit sets, such as chaotic and closed orbits, do not admit energy functions. The theory of generalized energy functions, which may assume positive derivative in some bounded sets, appears as an alternative to study the asymptotic behavior of solutions of these systems. In this article, a generalized energy function and a complete characterization of the stability boundary and stability region are developed for a class of third-order dynamical systems. This class of systems appears in electrical power system models and has a class of quasi-gradient systems and second-order systems as particular cases. These systems may admit complex structure in their limit sets and do not admit an energy function that is general for the class. Numerical examples illustrate how generalized energy functions provide estimates of stability regions.

Entire stability region estimation using the invariant manifolds and singularities at infinity

This study provides a new perspective to study the formation and wholeness of the stability region of power systems. The main idea of the approach proposed in this study is to project the system into a closed area and then investigate the behaviours of the field in a neighbourhood of infinity on a sphere that is topologically equivalent to the original system. The invariant manifolds and singularities at infinity are described in detail to indicate the boundary of the entire stability region, based on the concept of the basin of attraction. The proposed method is applied to the single-machine model, two-machine model and multi-machine system to illustrate the complex geometry structure of the transient stability region. A singularity variation index is presented to estimate the size of the entire region and indicate the transient stability degree of the power system. Simulation results verify the correctness and effectiveness of the theoretical analysis.

Estimation of stability region for an interconnected AC/multi-terminal DC grid

Estimation of stability region for an interconnected AC/multi-terminal DC grid

On stability for learning human control strategy by demonstrations using SVM

PurposeThis paper aims to deal with the trade-off of the stability and the accuracy in learning human control strategy from demonstrations. With the stability conditions and the estimated stability region, this paper aims to conveniently get rid of the unstable controller or controller with relatively small stability region. With this evaluation, the learning human strategy controller becomes much more robust to perturbations.Design/methodology/approachIn this paper, the criterion to verify the stability and a method to estimate the domain of attraction are provided for the learning controllers trained with support vector machines (SVMs). Conditions are formulated based on the discrete-time system Lyapunov theory to ensure that a closed-form of the learning control system is strongly stable under perturbations (SSUP). Then a Chebychev point based approach is proposed to estimate its domain of attraction.FindingsSome of such learning controllers have been implemented in the vertical balance control of a dynamically stable, statically unstable wheel mobile robot.

Estimation of stability region for discrete‐time linear positive switched systems with multiple equilibrium points

AbstractThis paper investigates the regional stability for discrete‐time linear positive switched systems with multiple equilibrium points (PSS‐MEP). Every subsystem possesses a unique stable equilibrium point. Firstly, by establishing a special Lyapunov function, a sufficient condition for region stability of considered systems is presented. Although, estimating the stability region for n‐dimensional PSS‐MEP with l ≥ 3 subsystems is still a challenging work, we study the one and two dimensional PSS‐MEP, and the corresponding accurate stability regions are given in our main job. Finally, a simulation example is presented to demonstrate the correctness of the theoretical results.

Robust $${H_\infty }$$ H ∞ control for singular time-delay systems with saturating actuators via static output feedback

The problem of \({H_\infty }\) robust exponential stability and static output feedback stabilization of uncertain singular time-delay systems with saturating actuators are investigated. First, the delay-dependent condition is given to guarantee that the singular time-delay systems are not only exponential admissible, but also satisfies \(H_{\infty }\) performance \(\gamma \). Moreover, the estimation of stability region and the design method of \(H_{\infty }\) static output feedback controller are given by solving a convex optimization problem. Some simulation examples are provided to demonstrate the merit of the proposed design methods.

Differential Quadrature Method for Stability and Sensitivity Analysis of Neutral Delay Differential Systems

This work develops a computationally efficient stability analysis method for the neutral delay differential systems. This method can be also conveniently applied for the optimal parameter tuning of related control systems. To facilitate this development, at each sampling grid point, the time derivative of the concerned differential system is first estimated by the differential quadrature method (DQM). The neutral delay differential system is then discretized as numbers of algebraic equations in the concerned duration. By combining the obtained discretized algebraic equations, the transition matrix of the two adjacent delay time durations can be explicitly established. Subsequently, the stability boundary is estimated, and the optimal parameters for the controller design are evaluated by searching the global minimum of the spectral radius of the transition matrix. In order to solve such optimization problems with the gradient descent algorithms, this work also analytically formulates the gradient of spectral radius of transition matrix with respect to the concerned parameters. In addition, a strong stability criterion is introduced to ensure better robustness. Finally, the proposed method is extensively verified by numeric examples, and the proposed differential quadrature method demonstrates good accuracy in both parameter tuning and stability region estimation for the neutral delay differential systems.

Generalization of a stability domain estimation method for nonlinear discrete systems

In this paper, we present a generalization approach of an algebraic existing method to estimate stability regions for discrete nonlinear polynomial systems of degree 3. The existing method is based on the enlargement of a guaranteed stability region by applying various steps of a proposed algorithm. Its main limitation is that the initial result has only been subsequently developed in a particular case of a single iteration. The stability domain obtained is consequently not the widest one. Our main contribution in this paper is to develop generalized functions that allow the enlargement of the guaranteed stability region after k iterations, for any value of k. A required fundamental tool is developed and consists in a general formula allowing to give the result of the Kronecker power calculation of two matrices sum. The advantages of this generalization are to reach a larger region of asymptotic stability and to improve the existing methods results. Two application examples illustrate the proposed method.

Numerical Estimation of Stability Region of Self-Clocked Bipedal Robots with Inertial Disk

Bipedal robot control techniques implementing self clocking properties, as presented in Westervelt et al. (Feedback control of dynamic bipedal robot locomotion, Taylor & Francis LLC, Milton Park, 2007) and Novaes et al. (IFAC 19th world congress, 4843–4848, 2014), have desirable properties, like the ability to drive the robot step with respect to its own geometry. In this control technique, one of the possible angular coordinates of the robot is made monotonic during the step execution. The other angular coordinates will track reference functions of the former. One difficulty with this approach is to determine the region around the nominal step for which the stability is assured. In this paper, we propose an algorithm to estimate this stability region by computing numerically an interval matrix related to a Poincare return map. In conjunction with the algorithm proposed in Ahn and Chen (IEEE Trans Autom Control 52(3):510–514, 2007), we are able to determine the maximum singular value of this interval matrix and so determine a guaranteed stability region.

Observer-based H ∞ guaranteed cost control for uncertain singular time-delay systems with input saturation

In this paper, the problem of observer-based H∞ guaranteed cost control for uncertain singular timedelay systems with actuator saturation is concerned. A delay-dependent sufficient condition is proposed, which guarantees that the closed-loop system is admissible via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region, the upper bound of cost function and the design method of observer-based H∞ guaranteed cost controller are given by solving linear matrix inequalities and convex optimization problems. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Observer-based $$H_{\infty }$$ H ∞ control for nonlinear Markovian jump systems with time-delay and input saturation

This paper focus on the problem of observer-based \(H_{\infty }\) control for uncertain nonlinear Markovian jump systems with time-delay and actuator saturation. A delay-dependent sufficient condition is proposed which guarantees that the uncertain nonlinear Markovian jump system with time-delay and input saturation is stochastically stable via Lyapunov theory and linear matrix inequality (LMI) approach. Then, with this condition, the estimation of stability region and the design method of observer-based \(H_{\infty }\) controller are given by solving LMIs and convex optimization problems. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed method.

Robust exponential stability and memory state feedback control for uncertain singular time‐delay systems with saturating actuators

This study is concerned with delay-dependent H ∞ robust exponential stability and memory state feedback stabilisation of singular time-delay systems with saturating actuators. First, a delay-dependent linear matrix inequality condition is obtained, which guarantees that the uncertain singular time-delay systems subject to actuator saturation are not only robustly exponential admissible, but also satisfy H ∞ performance γ via a tighter integral inequality and the method of free-weighting matrices. Then, using the conditions, the estimation of stability region and the controller with memory state feedback are given by solving a convex optimisation problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results.

Observer-basedH∞control for uncertain singular time-delay systems with actuator saturation

Summary In this paper, the observer-based H∞ control problem for uncertain singular time-delay systems with actuator saturation is concerned. First, a delay-dependent linear matrix inequality (LMI) condition is obtained which, guarantees that the uncertain singular time-delay systems with actuator saturation are regular, impulse free, and asymptotically stable with H∞ performance condition. Then, with this condition, the estimation of stability region and the design method of observer-based H∞ controller are given by solving LMIs and convex optimization problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results. Copyright © 2015 John Wiley & Sons, Ltd.