State Feedback Control Research Articles

Influences of Feedback Gains on Vehicle–Bridge Coupled Vibration for a Mid-Mounted Maglev Train

Levitation control systems play a vital role in ensuring the operational performance of medium and low speed maglev trains. Improper gain values may induce excessive vibrations in vehicles and bridges, potentially leading to collisions. This research investigates the influence of feedback gains on the levitation subsystem and the vehicle-bridge coupled system, leveraging a newly designed maglev vehicle equipped with mid-mounted suspension and a state feedback control strategy. A dynamic model of the vehicle-bridge coupled system was developed, incorporating control strategies, track irregularities, and bridge flexibility, and was validated through experimental data. The dynamic responses of the bogie and bridge under varying gain values were analyzed in-depth. By examining pole locations and frequency responses, the mechanisms through which each gain impacts the coupled system were clarified. The study identifies that gains associated with acceleration, velocity, and displacement each have unique stability domains that interact with one another. To maintain system stability, the gains must adhere to the Routh-Hurwitz stability criterion while fulfilling specific bandwidth and damping requirements. Gains set too low or too high may result in levitation failures. Recommended ranges for these gains are as follows: acceleration (0.2–0.6), velocity (30–100), and displacement (5,000–10,000). These findings could provide valuable guidance for designing control systems that enhance the stability and safety of maglev train operations.

New order-dependent conditions to control a class of nonlinear real-order systems

In many application points of interest, controlling the responses of real-world applications that vary with time seems quite challenging and puzzling. A linear time-varying state feedback controller is widely known and can be useful to estimate bounds to the state control matrix in the design of many control systems. The issue of initialization of real-order control system enhancement remains a challenging issue in the systems analysis subject to random initial-time placed on a real number line. We address a new design of a class of real-order control systems that consists of separated linear and nonlinear terms affected by input functions to be controlled with an implemented time-varying linear state feedback controller. We utilize the fractional comparison method and under Lipschitz nonlinearity with a constant bounding matrix of time-varying coefficients of control systems to address new order-dependent conditions that provide local and global stabilization to controlled systems. Applications of results that include practical real-order single-machine-infinite-bus power systems have been illustrated to control the responses by the utility of theoretical conditions examined along with validation of numerical simulations. It is shown that the proposed controller is practically convenient and demonstrates the efficiency of measuring the performances of control systems.

Sliding Mode Fault-Tolerant Control for Nonlinear High-Order Fully Actuated Systems.

The high-order fully actuated systems (HOFASs) approach can only completely eliminate known nonlinearities. However, the practical systems often encounter unknown nonlinearities, including disturbances and faults. Therefore, this article studies a class of nonlinear HOFAS with component faults and disturbances. By applying the HOFAS theory, a novel integrated sliding mode fault-tolerant control strategy is proposed to ensure the stability of the closed-loop system. The state feedback and output feedback controllers are designed, respectively. For output feedback control, an extended state observer is designed to estimate system states. Once the HOFAS model is established, the designed controller and extended state observer can be directly implemented, facilitating the analysis and design of the control system. And the stability analysis does not depend on the complexity of the nonlinear functions. Finally, a numerical simulation example shows the effectiveness of the proposed method.

Edges’ Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs

In this note we investigate the problem of global exponential synchronization of multi-agent systems described by non-linear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without leader. We present a set of sufficient conditions based on a Riemannian metric approach in order to design a state-feedback distributed control law. Then, we study the convergence properties of the overall network. By exploiting the properties of the edge Laplacian we construct a Lyapunov function that allows to conclude global exponential synchronization of the overall network.

Data-driven stabilization of switched and constrained linear systems

We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov–Metzler inequalities and on a matrix S-lemma, we derive data-dependent bilinear programs, whose solution directly returns a provably stabilizing controller and ensures H2 or H∞ performance. We further present relaxations that considerably reduce the computational cost, still without requiring stabilizability of any of the switching modes. Finally, we showcase the flexibility of our approach on the constrained stabilization problem for an unknown perturbed linear system. We validate our theoretical findings numerically, demonstrating the favorable trade-off between conservatism and tractability achieved by the proposed relaxations.

Fixed-time adaptive fault-tolerant output consensus control for heterogeneous multi-agent systems

Aiming at the fault-tolerant output consensus problem of heterogeneous multi-agent systems with external finite energy interference in the case of simultaneous additive and multiplicative faults of the actuators, this paper proposes a fault-tolerant output control strategy combining fixed-time feedforward control and adaptive state feedback control. First, a fully distributed adaptive fixed-time observer is designed for the follower, so that each follower can estimate the leader state and the state matrix within a fixed time. Then, combined with the output adjustment equation with fault matrix, a distributed adaptive fault-tolerant output consensus control scheme is proposed to compensate for the impact of fault on the system, and the sufficient conditions for consensus system output are deduced by using Lyapunov stability theory. Finally, the effectiveness and feasibility of the proposed method are verified by a heterogeneous multi-agent faulty system composed of a leader and four followers.

Comparative Analysis of the Performance of Linear Quadratic Regulator and State Feedback Control on DC-DC Shunt Boost Converter

In recent years, DC-DC converters, particularly shunt boost types, have become essential components in power systems, especially for applications requiring efficient voltage and current regulation. Proper control of these converters is crucial for ensuring optimal performance. This study analyzes two commonly used control methods: Linear Quadratic Regulator (LQR) and State Feedback Control for shunt boost DC-DC converters. LQR is known for its ability to minimize a cost function and optimize system performance, while State Feedback Control offers a simpler yet effective approach to system state control. Through MATLAB/Simulink-based simulations, this study evaluates the performance of both methods in terms of transient response, stability, and energy efficiency. The results show that LQR offers faster and more stable responses compared to State Feedback Control. However, the complexity of LQR in implementation makes it less practical than State Feedback Control, which is easier to apply in real-time applications

Study of a Dual‐Loop Digital Control System for High‐Power Input‐Parallel Output‐Series Phase‐Shifted Full‐Bridge Converters Based on Pole Configuration

ABSTRACTDigital control is characterized by mature analysis technology and easy implementation and is widely used in high‐power input‐parallel‐output series (IPOS) phase‐shifted full‐bridge (PSFB) converters. However, in modern industrial applications, most digital controllers are still designed with traditional technologies, such as PID control. Some characteristics of this control technology, such as control time delay and approximate design process, make the results fail to achieve the expected performance. At the same time, this digital control needs to be tested in the process of use, and the process is cumbersome and difficult to achieve. Based on the existing problems, this paper deduces a discrete state space model from the application of the IPOS‐PSFB converter, focusing on the characteristics of control delay. At the same time, this paper puts forward a double‐loop control strategy to ensure the accuracy of controller design. Among them, the current and voltage loop designs are independent. The current loop and voltage loop adopts two controllers, namely, the proportional controller and PI plus state feedback controller, and the parameters of the voltage loop controller are accurately calculated according to overshoot and bandwidth index. Finally, the IPOS‐PSFB converter is simulated and analyzed by MATLAB/Simulink software, and the controller's steady‐state performance and anti‐interference are analyzed.

Fault-Tolerant Time-Varying Formation Trajectory Tracking Control for Multi-Agent Systems with Time Delays and Semi-Markov Switching Topologies

The fault-tolerant time-varying formation (TVF) trajectory tracking control problem is investigated in this paper for uncertain multi-agent systems (MASs) with external disturbances subject to time delays under semi-Markov switching topologies. Firstly, based on the characteristics of actuator faults, a failure distribution model is established, which can better describe the occurrence of the failures in practice. Secondly, switching the network topologies is assumed to follow a semi-Markov stochastic process that depends on the sojourn time. Subsequently, a novel distributed state-feedback control protocol with time-varying delays is proposed to ensure that the MASs can maintain a desired formation configuration. To reduce the impact of disturbances imposed on the system, the H∞ performance index is introduced to enhance the robustness of the controller. Furthermore, by constructing an advanced Lyapunov–Krasovskii (LK) functional and utilizing the reciprocally convex combination theory, the TVF control problem can be transformed into an asymptotic stability issue, achieving the purpose of decoupling and reducing conservatism. Furthermore, sufficient conditions for system stability are obtained through linear matrix inequalities (LMIs). Eventually, the availability and superiority of the theoretical results are validated by three simulation examples.

Uniform stabilization in Besov spaces with arbitrary decay rates of the magnetohydrodynamic system by finite-dimensional interior localized static feedback controllers

We consider the d-dimensional MagnetoHydroDynamics (MHD) system defined on a sufficiently smooth bounded domain, d=2,3 with homogeneous boundary conditions, and subject to external sources assumed to cause instability. The initial conditions for both fluid and magnetic equations are taken of low regularity. We then seek to uniformly stabilize such MHD system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of explicitly constructed, static, feedback controls, which are localized on an arbitrarily small interior subdomain. In additional, they will be minimal in number. The resulting space of well-posedness and stabilization is a suitable product space B~q,p2-2/p(Ω)×B~q,p2-2/p(Ω),1<p<2q2q-1,q>d, d,$$\\end{document}]]> of tight Besov spaces for the fluid velocity component and the magnetic field component (each “close” to L3(Ω) for d=3). Showing maximal Lp-regularity up to T=∞ for the feedback stabilized linear system is critical for the analysis of well-posedness and stabilization of the feedback nonlinear problem.

Stabilization of control systems associated with a strongly continuous group

This paper is devoted to the stabilization of a linear control system $y' = A y + B u$ and its suitable non-linear variants where $(A, \cD(A))$ is an infinitesimal generator of a strongly continuous {\it group} in a Hilbert space $\mH$, and $B$ defined in a Hilbert space $\mU$ is an admissible control operator with respect to the semigroup generated by $A$. Let $\lambda \in \mR$ and assume that, for some {\it positive} symmetric, invertible $Q = Q(\lambda) \in \cL(\mH)$, for some {\it non-negative}, symmetric $R = R(\lambda) \in \cL(\mH)$, and for some {\it non-negative}, symmetric $W = W(\lambda) \in \cL(\mU)$, it holds [[EQUATION]] We then present a new approach to study the stabilization of such a system and its suitable nonlinear variants. Both the stabilization using dynamic feedback controls and the stabilization using static feedback controls in a weak sense are investigated. To our knowledge, the nonlinear case is out of reach previously when $B$ is unbounded for both types of stabilization.

Perancangan Kendali Integral State Feedback (KISF) Pada Sistem Pengaturan Kecepatan Motor DC

This research aims to design and simulate a DC motor speed control system using integral state feedback (KISF) control. This control is designed to maintain DC motor speed stability with high accuracy despite disturbances or load changes. The research stages include mathematical modeling of the DC motor, PID control design, integral state feedback control design, simulation implementation and simulation results analysis. The show that althought integral state feedback control has a rise time 273.501 ms, slightly slower than PID 197.604 ms, integral state feedback compensates with higher slew rate of change 6.540 V/ms compared to PID 4.344 V/ms. Integral state feedback offers greater flexibility through pole placement values with Ackerman’s formula J3 = [-12 -100 -600], indicating that this system has good capability in responding to input changes, thus maintaining motor speed stably and efficiently. This indicates that integral state feedback control is superior in system adaptation and handling complex dynamics.

Neighboring Mode‐Dependent Dynamic Event‐Triggered Control for Markov Jump Interconnected Systems With Unknown Interconnections

ABSTRACTThis work is absorbed in the neighboring mode‐dependent event‐triggered control scheme for Markov jump systems with unknown interconnections. To save communication resources and reduce cost, a dynamic event‐triggered scheme relies on neighboring modes information is proposed. Then, the state feedback controllers are designed based on neighboring mode–dependent dynamic event‐triggered approach to assure the stability of the system. Distinguished from existing results, the proposed method does not need to access the operation modes of all sub‐systems. The cyclic‐small‐gain criterion is used to tackle the unknown interconnections, thereby a novel stability criteria are obtained for the closed‐loop systems with performance. Finally, two simulation results are given to reveal the validity of the obtained results.

A multivariable adaptive formation control for multiple UAVs with external uncertain disturbances

PurposeA multivariable model reference adaptive control method is proposed to solve a distributed leader–follower formation control problem of unmanned aerial vehicles (UAVs) with uncertain parameters and unknown external disturbances for both leader and followers.Design/methodology/approachA case of uncertain stochastic external disturbances for UAVs is considered, and based on the distributed communication network of UAVs, a state-feedback adaptive controller is proposed to maintain the formation of UAVs consistently. Then, the stability and asymptotic tracking performance of the UAV formation control system are analyzed by the Lyapunov function.FindingsThe simulation results demonstrate that this formation control scheme can effectively solve the stochastic external disturbance problem of UAVs and ensure the stability of their formation.Originality/valueThe proposed multivariable model reference adaptive control method reduces the error of formation control system and improves the stability and control performance of UAV compared with fixed control.

Robust preview tracking control for LPV/LFR continuous-time systems

This study proposes a novel preview control method for linear parameter-varying (LPV) continuous-time systems (CTS) utilizing linear fractional representation (LFR). First, a formal system equivalent to the LFR of the LPV continuous system, which includes the preview compensation and tracking error, was developed to use the available reference signal values. In order to give innovative preview controller designs, the suggested conditions then depend on the utilization of decision matrices and slack variables related to the LFR technique. To provide minimal conservative synthesis criteria to the LPV/LFR continuous-time system, parameter-dependent Lyapunov functions and full-block multipliers were also taken into consideration. To create reliable state-feedback and output-feedback tracking controllers with preview actions, the design conditions were modeled as linear matrix inequalities (LMIs). Two scenarios were simulated to show how effective the suggested control strategy is.

Robust low-complexity vibration suppression control of rolling mill with time-varying state constraints

In this paper, a novel robust low-complexity vibration suppression control scheme is proposed for the vertical-torsional-horizontal coupling vibration of the rolling mill. To facilitate the control design, the overall coupling vibration system is decoupled into vertical-horizontal coupling vibration subsystem and torsional vibration subsystem. For the vertical-horizontal coupling vibration subsystem, a novel robust low-complexity controller is designed via constructed error transformations to provide strong robustness against uncertainties and disturbances. For the torsional vibration subsystem, a new robust state feedback controller is constructed via a backstepping technique to ensure the vibration angle of the motor rotor within given constraints via a proper asymmetric barrier function. The overall coupling vibration system is proved to be stable in the sense of uniform ultimate boundedness, and the vibration amplitude of the rolling mill can be reached arbitrarily small by selecting appropriate controller parameters. The numerical simulation is performed to verify the effectiveness and the superiority of the proposed control strategy.

Observer‐Based Switching‐Like Adaptive‐Triggered Resilient Coordination Control of Discrete Singular Systems Under DI Attacks with Uncertain Occurrence Probabilities

ABSTRACTIn this paper, we investigate observer‐based switching‐like adaptive‐triggered resilient state feedback control for discrete singular systems under deception‐injection (DI) attacks. Considering state variables are not completely measurable, a delayed state observer is engineered to reconstruct system states and the occurrence of DI attacks is described by Bernoulli random variables. The upper bound method is used to deal with the DI attacks with jumping patterns and imprecise occurrence probabilities. Taking into account the sporadic nature of DI attacks, switching‐like adaptive‐triggered resilient control method is presented, and the collaboratively designed triggered mechanism and resilient control strategy can not only automatically adjust data transmission based on the system states, but also save communication resources and network bandwidth, and enhance the tolerance to hostile attacks so as to improve safety and reliability of networked singular systems. By utilizing singular value decomposition technique, the noncausal behavior of the singular system is avoided and by applying linear matrix inequality (LMI) technology, the desired gains of controller and observer are achieved concurrently, then neoteric conditions about stochastic admissibility of closed‐loop discrete singular systems are provided. Ultimately, the validity of the proposed resilient coordination control approach is verified via a direct current (DC) motor model.

Prescribed-time observer-based output feedback stabilisation of switched uncertain planar systems with asymmetric output constraints

This paper presents an observer-based output feedback control strategy to solve the prescribed-time stabilisation of uncertain planar switched nonlinear systems with asymmetric output constraints. Based on adding a power integrator technique, prescribed-time switched state feedback controllers and a common fractional-type barrier Lyapunov function are developed. Then, deliberately constructed prescribed-time switched reduced-order observers are presented to estimate the unmeasurable state. Combing the switched state feedback controllers and reduced-order observers proposed in this note, the closed-loop switched planar systems achieve prescribed-time stability. Meanwhile, the violation of asymmetric output constraints is prevented implicitly by the developed barrier Lyapunov function. The novelty of this approach lies in the ingenious construction of prescribed-time switched observers and the unified design characteristics of the method, which enable the accomplishment of prescribed-time output feedback stabilisation for switched systems with/without output constraints without necessitating any structure modifications to the switched controllers and observers.

Control of Three-Phase Two-Level Inverters: A Stochastic LPV Model Approach

This paper proposes a stochastic linear parameter-varying (LPV) model approach to design a state feedback controller for three-phase, two-level inverters. To deal with the parameter changes, stochastic noise, and delays faced by the inverter, it is modeled as a stochastic LPV system with time delay. Stability analysis and control synthesis are conducted for the LPV system. With parameter-dependent Lyapunov functionals, a condition of sufficient stability for asymptotical mean-square stability is obtained. In addition, the slack matrix technique is employed to improve the feasibility and reduce the conservatism of the conditions. The obtained theoretical results are applied to the three-phase, two-level inverter, whose currents are treated as state variables and are controlled to reach the equilibrium point. The simulation results validate the effectiveness of the proposed theories and demonstrate the advantages of using the slack matrix.

Robust finite-time H2/H∞ control for stochastic Markovian jump systems via state feedback

The robust finite-time [Formula: see text] control problems for linear discrete-time stochastic Markovian jump systems (MJSs) with external disturbance are investigated. Firstly, the definitions of robust finite-time boundedness, and robust finite-time [Formula: see text] boundedness are presented. Subsequently, by using the stochastic Lyapunov–Krasovskii functional method and linear matrix inequality technique, sufficient conditions for the existence of a robust finite-time [Formula: see text] controller are provided for stochastic MJSs. A state feedback controller is designed. Furthermore, the finite-time guaranteed cost bounds are given. More specifically, the designed controller not only ensures the finite-time [Formula: see text] bounded but also makes the [Formula: see text] cost function less than the bound given by the performance index of the systems. Finally, two examples are given to illustrate the validity of the proposed approach.