State Error Research Articles

Second order sliding mode control with proportional integral observer for wing rock

In this study, a reduced-order fast proportional integral (PI) observer with a fast convergence function based on the equivalent control notion is developed to estimate the side slip angle β. An unknown state can be discovered by forcing the PI term on the state error, which is the difference between the real and estimated states. A second order sliding mode control (SOSMC) based on a proposed nonlinear sliding manifold is designed to achieve improved transient response and control performance by robustness. The proposed sliding manifold ensures the convergence of the roll angle in finite time. To validate the assertion regarding the proposed SOSMC, classical SOSMC and proportional integral derivative (PID) SOSMC are simulated both in the absence and presence of disturbances. The simulation results show that the proposed SOSMC over-performs in terms of achieving the desired response in both cases. Additionally, a numerical analysis is also performed for both scenarios to evaluate the effectiveness of the proposed controller in terms of the power consumption of the control law and burden on the aileron control surface. Finally, Monte Carlo simulations are performed to demonstrate the robustness of the proposed controller against external disturbances.

A new visual-inertial odometry scheme for unmanned systems in unified framework of zeroing neural networks

In recent years, multi-sensor fusion has gained significant attention from researchers and is used extensively in simultaneous localization and mapping (SLAM) applications, such as visual-inertial odometry (VIO). This technology primarily utilizes visual and odometry measurements for unmanned aerial vehicles (UAVs) to estimate their position, orientation, and environment. However, in most previous works, the input error data of sensors in the system were considered independent. To improve system precision and fully utilize sensor data, a new method called Multi-State Constraint Kalman Filter with NearSAC (MSCKF-NearSAC), based on the MSCKF, is proposed. This method eliminates outliers by limiting the range of selected points, which significantly improves the success rate of feature point matching in the front-end. Furthermore, the MSCKF-ZNN method is proposed for the back-end, and combines zeroing neural network (ZNN) (originated from the Hopfield-type neural network) and error state, resulting in an exponentially converging output trajectory error, thus improving the trajectory precision of the SLAM system. The proposed algorithms, MSCKF-NearSAC and MSCKF-ZNN, are used in the excellent work of the stereo multi-state constraint Kalman filter system (S-MSCKF). A plethora of comparison experiments, utilizing precise measurement and calibration techniques, are conducted on open-source datasets and real-world environments. Experimental results demonstrate that the introduced approach exhibits higher stability in contrast to other algorithms.

Reinforcement learning-based trajectory tracking optimal control of unmanned surface vehicles in narrow water areas.

For unmanned surface vehicles (USVs) navigating in narrow water areas in the presence of unknown dynamics and ocean environmental disturbances, this paper develops a reinforcement learning (RL)-based optimal control scheme for the trajectory tracking of USVs under motion state constraints. A nonlinear map is introduced to transform constrained motion state errors into bounded transformed errors, and then the motion state-constrained trajectory tracking problem of USVs is equivalently transformed into a boundedness problem of the transformed errors. Furthermore, an actor-critic framework is developed by utilizing adaptive neural networks (NNs). Within the actor-critic framework, a novel weight update law is designed for the critic NN by combining the gradient descent approach and the concurrent learning technology, thereby relaxing the persistent excitation condition required for adaptive critic NN weight updates. Subsequently, a disturbance compensator is designed and combined with the actor-critic framework to learn the trajectory tracking optimal control law for USVs in the presence of unknown dynamics and disturbances. Finally, theoretical analyses prove that the developed control scheme guarantees the boundedness of all signals in the USV closed-loop trajectory tracking control system, and simulation results show that the developed control scheme can make USVs track the desired trajectory in narrow water areas while reducing the energy consumption by approximately 14.6 % compared with an existing controller.

Voltage profile enhancement of an AVR system using ant lion optimization algorithm

Abstract This paper addresses voltage regulation, which is a critical issue in power systems. The automatic voltage regulator (AVR) plays a crucial role in maintaining voltage regulation within permissible limits The AVR system's dynamic behaviour is improved by applying the Proportional (KP) Integral (KI) Derivative (KD) (PID) controller. The primary challenges of using a PID controller in AVR include difficulties in tuning parameters to handle nonlinearities, load disturbances, and system dynamics, leading to potential instability, overshoot, or slow response. The controller parameters are tuned with Ant Lion Optimisation (ALO) algorithm and Integral Time Absolute Error (ITAE) as an objective function. Also, the proposed system has the ability to improve the transient response of AVR by decreasing the maximum overshoot, settling time, rise time, and peak time magnitudes of the generator terminal voltage with eliminating the steady state error. Once the suggested method had produced the best values for the three gains i.e., KP, KI, and KD of the PID controller, a transient response analysis is examined and compared with some of the existing techniques such as Bat Algorithm (BA), Grey Wolf Optimisation (GWO) and Biogeography Based Optimisation (BBO) algorithm to highlight the novelty of the proposed ALO optimized PID controller. Transient response analysis, root locus analysis, and bode analysis are used to assess the AVR system's stability. Comparisons to three well-known optimization techniques corroborate the findings. The results show that this new suggested method performs exceptionally well even when there are significant variations in power system parameters and load uncertainties.

Comparative Analysis of LQR and Hysteresis Control for Voltage and Power Regulation in a Four-Bus Microgrid

The work incorporates the control strategies in closed loop control of quadratic boost converter based four bus micro grid using –HC (hysteresis controller) and LQR (linear quadratic regulator) controllers. The suggested LQR controls the voltage and current at load buses by using Hybrid Power Flow Controlled system. This work deals with the comparison of closed loop four bus system using HC/LQR controller. Simulation is done for 4 bus system & the outcomes are compared in terms of settling time and steady state error. The outcomes represents that the superior performance of LQR controlled 4 bus system compared to HC controlled 4 bus systems.

Research on Transfer Alignment Algorithms Based on SE(3) in ECEF Frame

The initial attitude error is challenging to satisfy the requirements of the linear model due to the complex nature of the ocean environment. This presents a challenge in the transfer alignment of the ship. In order to enhance the precision and velocity of ship transfer alignment, as well as to streamline the alignment processes, this paper proposes a transfer alignment methodology based on the Earth-Centered Earth-Fixed (ECEF) frame special Euclidean group (SE(3)) matrix Lie group. After introducing the two navigation states, velocity and attitude, from the ECEF frame into SE(3), the nonlinear inertial navigation system error state model and its corresponding measurement equations are derived based on the mapping relationship between the Lie groups and Lie algebra. The method effectively solves the error problem due to linear approximation in the traditional transfer alignment method, and applies to misalignment angles of arbitrary scale. The simulation results verify the effectiveness and rapidity of the proposed alignment method in the case of arbitrary misalignment angles.

Regional consensus of switched positive multi-agent systems with multiple equilibria

This paper investigates regional proportional-integral-derivative consensus of switched positive multi-agent systems with multiple equilibria. A distributed proportional-integral-derivative control protocol is developed by integrating the communication protocol, agent state, and consensus error. A novel switched positive consensus error system is established and analyzed using copositive Lyapunov functions. Subsequently, a Luenberger observer with multiple equilibria is constructed to facilitate the design of an observer-based distributed proportional-integral-derivative control protocol. The regional consensus protocol is designed in the form of linear programming. By employing the proposed protocol, all states of agents are nonnegative and driven into a specific region. The main contributions of the work are summarized as: (i) Construction of a regional proportional-integral-derivative consensus protocol framework for switched positive multi-agent systems with multiple equilibria, (ii) Proposal of an observer-based distributed proportional-integral-derivative control strategy, and (iii) Analysis of the consensus using a matrix decomposition technique, copositive Lyapunov functions, and linear programming. Finally, numerical examples are provided to illustrate the effectiveness of the obtained results.

Research on the Application of PID Control Algorithm and Fuzzy Control Theory in the Field of Temperature Control

In the field of industrial automation control systems, PID control algorithms are widely used in various control fields such as temperature, speed and position. Among them, fuzzy PID control can improve control accuracy and stability, can significantly improve product quality and production efficiency, in food processing, chemical engineering, pharmaceutical and textile industries have a wide range of applications. Therefore, this paper comprehensively discusses the theory of fuzzy PID control algorithm and its application in the field of temperature control. The advantages of fuzzy PID control in complex industrial environments are emphasized through a comparative analysis with other temperature control methods as well as traditional linear PID control. The research indicates that by optimizing the control algorithm and hardware design, the fuzzy PID control algorithm can reduce the system overshoot and steady state error, thus improving the control accuracy and response speed. At the same time, the introduction of multivariable PID controllers or the use of advanced multivariable control strategies can achieve coordinated control of multiple variables, thereby improving the performance of the entire system. In addition, the integration of advanced energy management system and data analysis technology can comprehensively monitor and optimize the management of energy consumption, further improving the energy efficiency of the system

Research on a Hybrid Correction Method for SINS/DVL Kalman Filter Integrated Navigation Based on Convergence Factor Judgment

Abstract The strapdown inertial navigation system (SINS)/doppler velocity log (DVL) integrated navigation is one of the primary methods for underwater navigation, providing autonomous underwater vehicles with precise information on position, velocity, and attitude. The core idea of the SINS/DVL integrated navigation using the Kalman filter is to establish the state and observation equations to estimate the SINS navigation error using DVL velocity. The optimal state estimation and correction strategies are critical to the accuracy of integrated navigation. To address this, this paper proposes a hybrid correction method for SINS/DVL Kalman filter integrated navigation based on a convergence factor judgment (HCKF-CFJ). First, the convergence factor for the Kalman filter is constructed using the diagonal elements of the estimated error covariance matrix corresponding to the velocity error state. Then, the filter's stability is assessed based on this convergence factor. When stability is confirmed, direct feedback correction is applied to the SINS velocity, and indirect feedback correction is applied to the SINS position. SINS velocity and position undergo feedforward correction if the stability condition is not met. Finally, ship experiments validate the effectiveness of the proposed method.

Improved segmental active disturbance rejection control for direct-drive valve controlled hydraulic shaking table

To address the performance degradation of hydraulic shaking table under nonlinear disturbances, an improved segmental active disturbance rejection controller (IS-ADRC) based on a switching control law is designed. A self-coupling PID (SC-PID) control law is designed, and an adaptive speed factor model is proposed to enhance the system’s response speed without compromising disturbance observation ability, thus avoiding oscillations and instability caused by high-gain observer. To overcome the jitter issue in traditional nonlinear state error feedback (NLSEF) control laws, an improved control law (INLSEF) based on a smooth Fal-M function is designed to replace the traditional fal function. Moreover, considering the potential for integral saturation, a switching principle is designed to switch from the SC-PID control law to the INLSEF control law at small errors, ensuring smooth system convergence. The stability of the controller is proved using Lyapunov stability theory. Results demonstrate that the proposed IS-ADRC improves the response speed and anti-disturbance ability of the hydraulic shaking table. Furthermore, the Fal-M function effectively reduces the jitter phenomenon compared to traditional ADRC.

Practical fractional-order terminal sliding-mode control for a class of continuous-time nonlinear systems

Terminal sliding-mode control (TSMC) has been studied and applied extensively in the last few years. This technique gives rise to a robust control with tunable finite-time convergence, providing a fast and accurate response in the presence of parameter uncertainties. In that sense, we present a closed-loop robust controller for a class of nonlinear systems using a terminal sliding-mode controller, with a novel fractional-order sliding surface. The motivation of this work is to consider a time-varying gain for the fractional-order sliding surface that is relatively small at the beginning of the regulation control task to reduce the amplitude of the control input and it increases near the final time to reduce the error in the steady state. Unlike using a constant gain in the conventional terminal sliding surface, the time-varying gain keeps the amplitude of the signal low and enhances the precision simultaneously. An extensive simulation study shows the performance of the proposed design. Finally, the experimental implementation of the fractional-order TSMC in a lightweight (90 g) two-degree-of-freedom manipulator is presented. The implementation used C++ programming language on a Raspberry Pi digital board and a chattering-free modification was presented to address the practical limitation of the actuators.

Design of a Finite-Time Bounded Tracking Controller for Time-Delay Fractional-Order Systems Based on Output Feedback

This paper focuses on a class of fractional-order systems with state delays and studies the design problem of the finite-time bounded tracking controller. The error system method in preview control theory is first used. By taking fractional-order derivatives of the state equations and error signals, a fractional-order error system is constructed. This transforms the tracking problem of the original system into an input–output finite=time stability problem of the error system. Based on the output equation of the original system and the error signal, an output equation for the error system is constructed, and a memory-based output feedback controller is designed by means of this equation. Using the input–output finite-time stability theory and linear matrix inequality (LMI) techniques, the output feedback gain matrix of the error system is derived by constructing a fractional-order Lyapunov–Krasovskii function. Then, a fractional-order integral of the input to the error system is performed to derive a finite-time bounded tracking controller for the original system. Finally, numerical simulations demonstrate the effectiveness of the proposed method.

Derivative-Guided Symbolic Execution

We consider the formulation of a symbolic execution (SE) procedure for functional programs that interact with effectful, opaque libraries. Our procedure allows specifications of libraries and abstract data type (ADT) methods that are expressed in Linear Temporal Logic over Finite Traces (LTL f ), interpreting them as symbolic finite automata (SFAs) to enable intelligent specification-guided path exploration in this setting. We apply our technique to facilitate the falsification of complex data structure safety properties in terms of effectful operations made by ADT methods on underlying opaque representation type(s). Specifications naturally characterize admissible traces of temporally-ordered events that ADT methods (and the library methods they depend upon) are allowed to perform. We show how to use these specifications to construct feasible symbolic input states for the corresponding methods, as well as how to encode safety properties in terms of this formalism. More importantly, we incorporate the notion of symbolic derivatives , a mechanism that allows the SE procedure to intelligently underapproximate the set of precondition states it needs to explore, based on the automata structures latent in the provided specifications and the safety property that is to be falsified. Intuitively, derivatives enable symbolic execution to exploit temporal constraints defined by trace-based specifications to quickly prune unproductive paths and discover feasible error states. Experimental results on a wide-range of challenging ADT implementations demonstrate the effectiveness of our approach.

Prescribed Performance Control for High-Order Odd-Rational-Power Nonlinear Systems with Actuator Faults and Unknown Powers

A global prescribed performance control method is proposed for a class of uncertain high-order odd-rational-power nonlinear systems (a chain of integrators whose power is the ratio of odd integers) with actuator faults, where the high-order odd-rational powers and the parameters of actuator faults are unknown. A new coordinate transformation on the state and tracking errors is introduced based on the tangent function and its inverse function, resulting in a global low-complexity prescribed performance controller. The proposed controller does not require any knowledge of system nonlinearities or powers, and it also does not require the time derivatives of virtual control signals without using any filters, which implies the controller is of low complexity. Finally, two simulation examples, including a practical high-maneuver flight control example, are given to demonstrate the effectiveness of our method.

Evolutionary Bioinformatics with Veiled Biological Database for Health Care Operations

The tremendous growth of biological data processing systems in the realm of health care applications has made real-time information accessible to everyone with no processing lags. Bioinformatics is even integrated into most wireless technology applications to account for all physical characteristics. The planned model focuses on evolutionary bioinformatics for medical sensor applications in health care. The optimization scenario is executed by combining genetic and ant colony optimization methods (GACO). In the proposed technique, the design concerns are implemented with appropriate transmitting and receiving modules, and individual bits are framed for extra bioinformatics data processing components. a design that completely minimizes all errors in the big data processing stage. Such a design completely lowers the overall error in the huge data processing state since all channels can be accessed in accordance with the framed bits. Furthermore, the quality of service is maximized because all channels carrying bioinformatics data are kept at high quality bits, increasing utility rates. The experiments were conducted using five scenarios to evaluate the effectiveness of the proposed design. The findings indicate that the proposed technique can handle bioinformatics data for healthcare in real time with a service quality of 95%.

Mode switching control of independent metering fluid power systems.

An independent metering system (IMS) realizes the decoupling of the meter-in and meter-out orifices. The energy efficiency of the hydraulic system can be effectively improved by switching between different operational modes. However, the tracking accuracy of the IMS mode-switching system is difficult to ensure, which can easily lead to instability in the hydraulic system. In view of this, this paper proposes a mode switching controller based on an IMS. First, the K-filters theory is innovatively applied to the mode switching hydraulic system to estimate unmeasurable state variables of a system accurately. In addition, fuzzy logic systems (FLSs) are applied to handle the unmodeled errors and disturbances in the mechanical system dynamics model and hydraulic system. Further, aiming at the stability and trajectory tracking problems in the mode switching control (MSC) process of an IMS, the average dwell time (ADT) stability analysis method is applied to the mode switching hydraulic system to construct a set of switching rules to make the closed-loop switching system stable. Moreover, based on the prescribed performance control (PPC) theory, all state errors of a hydraulic system are guaranteed to reach the performance function constraint boundary at the specified time. Also, a dynamic surface control (DSC) technique is used to avoid the explosion of computational complexity caused by iterative differentiation inherent in the traditional backstepping method. Finally, the feasibility and effectiveness of the proposed method are verified by simulation, and experiments are carried out on mini-excavators. The results show that the designed controller can not only ensure the tracking accuracy, but also effectively suppress the instability of the hydraulic system caused by MSC.

Fuzzy sliding mode control based on an adaptive sliding surface and extended state observer for automotive electric power steering

Electric power steering control faces several issues related to state errors, sensor noise, and chattering. This article proposes an adaptive robust control method based on a sliding mode control mechanism to address the existing drawbacks. The sliding surface of this controller is adjusted dynamically by a fuzzy technique, which is formed by two inputs and one output. The system disturbances and state variables are estimated by an extended state observer instead of being measured by expensive sensors. Combining the above techniques is a new contribution to the article to improve the system’s control performance. Numerical simulations are performed in three cases with varying driver torque and velocity. The computational results reveal that the output signals of the system controlled by the proposed method closely track the desired values, with errors not exceeding 1.5% (except for the assisted current). The observed error of the system disturbance does not exceed 12.172%, while the observed error of the remaining state variables is less than 3%. Overall, the performance of the proposed algorithm is significantly improved compared with the traditional control methods.

Time/Event‐Triggered Exponential Stabilization for Stochastic Systems: Enhancing Nonlinearity Tolerance

ABSTRACTThis article seeks the enhancement of nonlinearity tolerance in time/event‐triggered stabilization for stochastic systems. In the related results, the controller functions are required to obey global Lipschitz condition for the suppression of sampling/execution error, and the drift and/or diffusion coefficients of the stochastic systems are restricted to polynomial or, even, linear growth. These limitations deserve overcoming for enlarged applications. To this end, a distinct framework of time/event‐triggered controls is established for stochastic systems, targeted at exponential stabilization. Specifically, inclusive Lyapunov‐type feasibility conditions are proposed by capturing the effect of sampling/execution error and distinguishing the role of system nonlinearities. Particularly, different from the related results, the evolution of sampling/execution error is subtly exploited via Lyapunov functions to reveal the dynamic interaction between the sampling/execution errors and system state. Then, time‐triggered exponential stabilization via sampled‐data controller is achieved not only in the moment sense but also in the almost sure sense. Accordingly, Lyapunov function based analysis is performed for the composite dynamics of system state and sampling error, confronted with the coupling of discontinuous and stochastic features. To further reduce execution, periodic event‐triggered control is exploited to achieve exponential stabilization for stochastic nonlinear systems, by virtue of the relation with the dynamic evolution under sampled‐data control. Through typical examples, we demonstrate the potential of our framework in handling the cases with the controller functions violating global Lipschitz condition and with the system nonlinearities beyond polynomial growth.

Ultra-local model based prescribed performance adaptive control of overhead cranes under uncertainties

In this paper, a model-free adaptive control scheme is proposed to address the problem of system performance variations due to inaccurate models of overhead cranes, and external disturbances. First, an adaptive fast integral terminal sliding mode controller with a prespecified performance setting is proposed to accelerate the convergence of the sliding mode surface. In addition, an improved form of performance function is introduced to ensure the high accuracy convergence of state errors, while effectively enhance response performance and state tracking accuracy. Second, a prespecified performance nonlinear disturbance observer is introduced to estimate the lumped dynamics part of the ultra-local model, which can guarantee effective model-free properties. Finally, the stability of the closed-loop control scheme is analyzed by means of Lyapunov stability theory, and the effectiveness and superiority of the proposed method is proved by means of numerical simulation results.

Performance analysis of CKF algorithm for battery SoC estimation with its aging effect

The penetration of electric vehicle (EV) in automobile market is very much dependent on the battery technology. Its size, weight, and cost are issues of concern. To effectively utilize the battery expertise, precise estimate of state of charge (SoC) is vital which greatly depends on the battery model. Current models lack consideration for variations in battery capacity over their lifespan. This paper develops a battery model which depicts the depletion of battery capacity with its life. Subsequently, this model has been utilized for estimation using advanced Kalman filtering (KF) algorithms. For the developed model, the design and effectiveness of the cubature Kalman filter (CKF) is applied as a proposed robust state-estimator for this problem. Moreover, a comparative analysis was undertaken with existing non-linear KFs based on performance metrics. The optimal choice of estimator is identified, through the results obtained from the Octave/MATLAB simulation. The outcomes show CKF algorithm based SoC estimator is superior to others in ensuring high accuracy, strong robustness even under changes in initial conditions (i.e., initial SoC, process and sensor noise levels), system's ability to converge quickly while ensuring that the maximum error in state of charge (SoC) estimation remains within 1% after convergence.