Stability Analysis Of Systems Research Articles

A decentralized optimal PID controller with disk margin-based robust stability analysis for higher-order industrial systems

ABSTRACT Decentralized control systems are frequently employed to tackle control challenges in multi-input multi-output (MIMO) systems. Hence, this paper proposes a decentralized PID controller that relies on frequency domain specifications. This controller is designed to minimize the loop interactions and fulfill the design criteria of the MIMO system. The PID parameters are calculated based on gain and phase margin specifications. Additionally, a first-order plus dead time model is derived for each of the decoupled subsystems. Furthermore, robust stability is analysed using disc margin analysis, which overcomes the constraints of traditional margins. Moreover, the paper determines a secure range of uncertainty for various levels of gain and phase uncertainties. The findings suggest that the proposed controller achieves robust stability over a broader range of margins when compared to alternative control methods.

Stability analysis for neutral stochastic time-varying systems with delayed impulses

This article investigates the stability of stochastic neutral delayed systems (SNDS) with delayed impulses, which includes the stability in input-to-state exponentially stable in pth moment (p-ISES), integral ISES in pth moment (p-iISES) and eλt-weighted ISES in pth moment (eλt-p-ISES). Compared with the existing works, we allow the neutral term, delayed impulses, time-varying coefficients in the diffusion condition, bounded time-varying delay (BTVD) to be in a stochastic system, which arise the difficulty. By utilizing the techniques of Lyapunov-Krasovskii (L-K) function, generalized delay integral inequality and average impulsive interval (AII), some desired results are obtained by surmounting the underlying difficulty. Finally, an example is given to show the validity of our work.

Fixed-time stability analysis of general impulsive systems and application to synchronization of complex networks with hybrid impulses

In this paper, the fixed-time stability of general impulsive systems and the fixed-time synchronization issue of impulsive complex networks are investigated. First, the fixed-time stability of a class of nonlinear systems with general impulsive effects is analyzed by means of inequality method and using some special functions. Then, the developed fixed-time stability results are used to study the fixed-time synchronization of impulsive complex networks under the saturation controller. Compared with some early published works, in this paper, the estimation accuracy of settling time is improved by calculating the value of improper integral more precisely, and the saturation controller effectively suppresses chattering phenomenon caused by discontinuous signum function. Lastly, some numerical examples are given to verify the feasibility of our theoretical results.

Ensuring grid resilience: Voltage stability analysis and contingency ranking in electric power systems

Modern-day power systems are highly stressed and operate close to the stability limit. The bus voltage variation in power systems generally infringes on the researcher's mind about voltage stability. The main focus of this manuscript is the voltage stability problem and voltage security assessment rather than the angle stability problem. Voltage security can be determined by running a full-load AC load flow with contingency analysis. In real-time analysis, running thousands of contingencies in online mode is quite a cumbersome task, so here in this manuscript, we have proposed a functional link-based ANN for voltage security assessment and then predicted the weakest voltage control area by the entropy concept along with the placement of FACTS devices according to the voltage control area weakness factor and contingencies ranking. The novel technique is then tested with IEEE-14 Bus and IEEE-30 Bus systems with voltage stability performance indicators.

Stability analysis of homogeneous cooperative positive differential systems with time-varying delays and its generalization

This article is devoted to studying the asymptotic behavior of differential systems with bounded delays. We first focus on the analysis of homogeneous cooperative positive systems. Under the assumption that the vector field is homogeneous of a degree greater than 1, we show that the non-trivial solutions of the system converge to the origin at a polynomial rate. In the case when the degree of homogeneity equals 1, we prove that the solutions will decay at an exponential rate. As a generalization of these results, we consider nonlinear non-autonomous differential systems with time-varying delays that are bounded above by stable homogeneous positive systems. By some additional imposed conditions, in light of the comparison principle, we obtain the locally exponential stability and polynomial stability of the equilibrium point to these systems. Finally, specific examples and discussions are provided to illustrate the validity of the proposed theoretical results.

Wirtinger-based fractional summation inequality for stability analysis of nabla discrete fractional-order time-delay systems

Wirtinger-based fractional summation inequality for stability analysis of nabla discrete fractional-order time-delay systems

Lyapunov’s stability analysis for first degree polynomial systems, subject to risk-sensitive control

This work presents a novel methodology to verify the stability of first-degree stochastic polynomial systems under a Risk-Sensitive (RS) optimal control using Lyapunov’s stability analysis theory. The so-called Lyapunov’s indirect method is applied to prove its stability when it is combined with the dynamics of Riccati’s gain equation. The proposed methodology guarantees both the exponential stability of deterministic systems and the robustness of stochastic systems. Simulation results demonstrate the robustness, the effectiveness and the feasibility of this proposal.

Lifelong reinforcement learning tracking control of nonlinear strict-feedback systems using multilayer neural networks with constraints

This paper presents a novel safe integral reinforcement learning (IRL)-based optimal trajectory tracking scheme for nonlinear systems with uncertain dynamics that is subject to constraints. We leverage multilayer neural networks (MNNs) for actor-critic MNNs along with an NN identifier in the backstepping process for minimizing a discounted value function. A time-varying barrier Lyapunov function (TVBLF) is utilized for handling constraints and to provide safety assurances. Online weight update laws for the actor and critic MNNs are derived that are driven by Bellman error and control input error. We introduce an online lifelong learning (LL) method in the critic NN, utilizing the Bellman error in MNNs to address catastrophic forgetting. The method’s effectiveness is demonstrated through simulations on mobile robot multitask tracking. The paper concludes with a stability analysis of the closed-loop system.

Analysis and optimization of smart home control system stability analysis and optimization

Analysis and optimization of smart home control system stability analysis and optimization

Stability analysis of LTV systems via gain and phase

Abstract This paper considers the feedback stability analysis of infinite-dimensional discrete-time linear time-varying systems with combined gain and phase information. The framework considers a system to be a causal linear operator described by a lower triangular infinite-dimensional complex matrix. For $r$-sectorial operators, we first derive a sufficient condition for the invertibility of $I+AB$ using the gain and phase information. Finally, we use this invertibility criterion to give a sufficient condition for feedback stability of $r$-sectorial systems.

On the optimal multi-objective design of fractional order PID controller with antlion optimization

This study introduces an optimal multi-objective design approach for a robust multimachine Fractional Order PID Controller (FOPID) using the Antlion algorithm. The research focuses on the need for effective stabilizers in multimachine power systems by employing traditional speed-based lead-lag FOPID controllers. The study formulates a multi-objective problem, optimizing the damping factor and damping ratio of lightly damped electromechanical modes to maximize a composite set of objective functions, tackled through the Antlion algorithm. Stability analysis of Single-Machine Infinite-Bus (SMIB) and multimachine power systems is conducted based on rotor speed and power deviation minimization in the time domain response, along with damping ratio and eigenvalue analysis. The proposed approach is implemented and tested on three IEEE test cases, showcasing significant improvements in stability through the reduction of maximum overshoot (Mp) and settling time (ts) of speed deviation. Comparative analysis with other optimization-based FOPID controllers underscores the superiority of the proposed approach in enhancing stability in multimachine power systems. The main impact of this research lies in its contribution to the advancement of stability enhancement techniques in multimachine power systems, offering a systematic framework for optimal FOPID controller design and empowering decision-making processes in power engineering.

Stability Analysis for Large-Scale Multi-Agent Molecular Communication Systems.

Molecular communication (MC) is recently featured as a novel communication tool to connect individual biological nanorobots. It is expected that a large number of nanorobots can form large multi-agent MC systems through MC to accomplish complex and large-scale tasks that cannot be achieved by a single nanorobot. However, most previous models for MC systems assume a unidirectional diffusion communication channel and cannot capture the feedback between each nanorobot, which is important for multi-agent MC systems. In this paper, we introduce a system theoretic model for large-scale multi-agent MC systems using transfer functions, and then propose a method to analyze the stability for multi-agent MC systems. The proposed method decomposes the multi-agent MC system into multiple single-input and single-output (SISO) systems, which facilitates the application of simple analysis technique for SISO systems to the large-scale multi-agent MC system. Finally, we demonstrate the proposed method by analyzing the stability of a specific large-scale multi-agent MC system and clarify a parameter region to synchronize the states of nanorobots, which is important to make cooperative behaviors at a population level.

Stability analysis of discrete dynamical system using khan-iteration technique

Stability analysis of discrete dynamical system using khan-iteration technique

Stability Analysis of Multi-Bus Power Electronics Defined Power Systems Using Phase Information of Nodal Admittance Matrix

Stability Analysis of Multi-Bus Power Electronics Defined Power Systems Using Phase Information of Nodal Admittance Matrix

A Simple Testbed for Stability Analysis of Quantum Dissipative Systems

A Simple Testbed for Stability Analysis of Quantum Dissipative Systems

Analysis of System Stability in Dual-Area Network Incorporating Renewable Energy Sources with Learning Method

Analysis of System Stability in Dual-Area Network Incorporating Renewable Energy Sources with Learning Method

WITHDRAWN: Robust voltage regulation of DC-DC buck converter with ZIP load via an energy shaping control approach

ZIP loads (the parallel combination of constant impedance loads, constant current loads and constant power loads) exist widely in power system. In order to stabilize buck converter based DC distributed system with ZIP load, an adaptive energy shaping controller (AESC) is devised in this paper. Firstly, based on the assumption that the lumped disturbances are known, a full information controller is designed in the framework of the port Hamiltonian system via energy shaping technique. An obvious merit is that it is PI-type controller, which is easy to implement in practical application. Besides, using mathematical deductive method, an estimation of the domain of attraction is given to ensure the strict stability. Furthermore, to eliminate the influence of parameter perturbations on the system, a disturbance observer is proposed to reconstruct the lumped disturbances and then the estimated terms are introduced to above controller to form an adaptive control scheme. In addition, the strict stability analysis of the closed-loop system is given. Lastly, the simulation and experiment results are presented for assessing the designed controller.

Numerical threshold stability of a nonlinear age-structured reaction diffusion heroin transmission model

This paper deals with the numerical threshold stability of a nonlinear age-space structured heroin transmission model. A semi-discrete system is established by spatially domain discretization of the original nonlinear age-space structured model. A threshold value is proposed in stability analysis of the semi-discrete system and named as a numerical basic reproduction number. Besides the role it plays in numerical threshold stability analysis, the numerical basic reproduction number can preserve qualitative properties of the exact basic reproduction number and converge to the latter while stepsizes vanish. A fully discrete system is established via a time discretization of the semi-discrete system, in which an implicit-explicit technique is implemented to ensure the preservation of the biological meanings (such as positivity) without CFL restriction. Some numerical experiments are exhibited in the end to confirm the conclusions and explore the final state.

Analysis of corrugation development on a Tianjin metro straight line focusing on wheel-rail contact mechanics

The development features of corrugation on the straight track metro line are studied to find the root cause of corrugation. Firstly, the measured corrugation characteristics on the line are investigated and a three-dimensional wheel-rail (WR) rolling contact finite element (FE) model is constructed. Then, the WR stick-slip (SS) characteristics, WR contact and rail wear are analyzed to understand the evolution process of corrugation from the micro transient point of view. Finally, combined with a system stability analysis, the development trend of corrugation is characterized from the macro perspective. The results show that the WR contact has a significant SS variation under the corrugation condition, which promotes the initial corrugation to develop further. For the fixed node in the contact area on the rail surface, the maximum stress and strain of the section where it is located will gradually transfer from the subsurface to the surface with the wheel running, so the damage prone position will also form first on the subsurface and gradually transfer to the surface. This shows from the micro viewpoint that the formation of wave crest/trough in the corrugation section is a bottom-up process of damage accumulation. The corresponding frequency of 648 Hz of the unstable vibration mode in the WR system is close to the passing frequency of 656 Hz of measured corrugation, demonstrating that the initial corrugation will tend to intensify with the wheel running.

Bifurcation analysis and control of an improved continuous traffic model considering weather effect

PurposeHighway traffic systems are complex and variable, and studying the bifurcation characteristics of traffic flow systems and designing control schemes for unstable bifurcation points can alleviate traffic congestion from a new perspective. Bifurcation analysis is used to explain the changes in system stability, identify the unstable bifurcation points of the system, and design feedback controllers to realize the control of the unstable bifurcation points of the traffic system. It helps to control the sudden changes in the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.Design/methodology/approachIn this paper, we improve the macroscopic traffic flow model by integrating severe weather factors such as rainfall, snowfall, and dust. We use traveling wave transform to convert it into a traffic flow stability model suitable for branching analysis, thus converting the traffic flow problem into a system stability analysis problem. First, this paper derives the existence conditions of the model Hopf bifurcation and saddle-node bifurcation for the improved macroscopic model, and finds the stability mutation point of the system. Secondly, the connection between the stability mutation points and bifurcation points of the traffic system is analyzed. Finally, for the unstable bifurcation point, a nonlinear system feedback controller is designed using Chebyshev polynomial approximation and stochastic feedback control method.FindingsThe Hopf bifurcation is delayed and completely eliminated without changing the equilibrium point of the system, thus controlling the abrupt behavior of the traffic system.Originality/valueCurrently there are fewer studies to explain the changes in the stability of the transportation system through bifurcation analysis, in this paper; we design a feedback controller for the unstable bifurcation point of the system to realize the control of the transportation system. It is a new research method that helps to control the sudden change of the stable behavior of the traffic system and helps to alleviate traffic congestion, which is of great practical significance.