Error Constraints Research Articles

Dual‐Loop Control Design for Dynamic Positioning Ships with Prescribed Performance

AbstractDynamic positioning (DP) system is an advanced positioning system widely used in various special operation ships, and the design of control strategies to cope with different constraint conditions is the core technology of DP system research. In this study, a novel dual‐loop control law is proposed to effectively tackle the control challenges encountered by DP ships, particularly in the presence of input saturation and error constraints. Firstly, a saturation handling model is designed to avoid input saturation in the system. Subsequently, a dual‐loop DP control scheme is developed. The outer‐loop is responsible for the ship's position and heading control, while concurrently providing the command velocity signal essential for the inner‐loop. Specifically, a prescribed performance control strategy is designed in the outer‐loop to ensure precise control over positioning errors within predefined ranges and achieve desirable transient and steady‐state performance. The inner‐loop controls the ship's velocity signal, in which a feedback control law is designed based on Hamilton‐Jacobi‐Issacs (HJI) inequality to estimate generalized faults of the DP system. Finally, the proposed control law is validated through numerical simulations on a 76.2 m supply ship, demonstrating superior transient and steady‐state performance compared to existing methods.

A High-Precision Planar NURBS Interpolation System Based on Segmentation Method for Industrial Robot

NURBS curve parameter interpolation is extensively employed in precision trajectory tasks for industrial robots due to its smoother performance compared to traditional linear or circular interpolation methods. The trajectory planning systems for industrial robots necessitate four essential functional modules: first, the spline curve discretization technique ensuring chord error compliance; second, the contour scanning technique for determining the maximum feasible feed rate for multi-constraint and multi-segment paths; third, the technique for achieving a smooth feed rate profile; and fourth, the continuous curve parameter interpolation technique. Therefore, this paper proposes a high-precision planar NURBS interpolation system for industrial robots. Firstly, a segmentation method for NURBS curves based on a closed-loop chord error constraint is proposed, which segments the original global NURBS curve into a collection of Bezier curves that strictly meet the chord error constraint. Secondly, a bidirectional scanning technique is presented to meet the joint space constraint, establishing an analytical mapping between the tool tip kinematic constraint and the joint kinematic constraint. Then, based on the traditional S-shaped feed rate profile, an adaptive algorithm with a displacement constraint is introduced, considering the real-time speed adjustment requirements of robots. Finally, a compensation interpolation strategy based on arc length parameterization is adopted to solve the accumulated error problem in parameter interpolation. The effectiveness of and potential for enhancing the quality of planar machining of the proposed planar NURBS interpolation system for industrial robots are validated through simulations and experiments. The results demonstrate the system’s applicability and accuracy, and its ability to improve planar machining quality.

Event-triggered dynamic prescribed performance control for oxygen stoichiometry and stack temperature in PEM fuel cell systems with actuators faults

Oxygen stoichiometry (OS) and stack temperature (ST) significantly affect the output performance and durability of proton exchange membrane fuel cells. This paper investigates the prescribed performance tracking control strategy of OS and ST under external disturbances, modeling errors, actuators faults and limited communication resources. The total disturbances are compensated by a variable-bandwidth extended state observer to simplify the control design and enhance the system robustness. To tolerate excessive disturbances and relax the strict requirement on the initial conditions, a new event-triggered adaptive sliding mode controller that integrates modified dynamic performance constraints and nonsingular error transformation is developed to ensure the user-designed transient and steady-state performance constraints, while saving the communication costs and avoiding the chattering and jump in control signals. The numerical validation results under combined working scenarios indicate that the proposed controller always ensures the preset error constraints and possesses superior performance in tracking the optimal OS value 2 and the optimal ST value 353.15K than other three representative controllers, with the integral absolute errors of 0.732 for OS tracking and 12.94 for ST tracking; besides, it achieves satisfactory robustness to uncertain model parameters and relatively large initial tracking errors.

ANALISIS RISIKO DAN PENGENDALIAN INTERNAL DALAM PENGELOLAAN ACCOUNT RECEIVABLE PADA HOTEL HARRIS SURABAYA

This research was conducted to analyze risk and internal control in managing Account Receivable at Harris Hotel, Surabaya. The purpose of this research was to evaluate risk and internal control in the Management of Account receivable at Harris Hotel, Surabaya. The research was conducted using a descriptive qualitative approach including data collection, data reduction, data presentation and finding. The research was conducted using a qualitative approach that involves data collection, reduction, presentation, and finding. Harris Hotel Surabaya has implemented a risk assessment, even though it is not comprehensive, as the result of risk analysis. The risk of paying non-current receivables and monitoring industrial and economic conditions has been assessed. It has not yet assessed the risk of financial feasibility analysis and historical evaluation of customer payments. Hotel Harris has also implemented internal controls in the form of the registration of Account Receivable, as well as a clear division of labour. To identify deficiencies in existing internal controls and make improvements, Companies must implement stricter billing policies and conduct more routine internal audits. Companies must pay attention to human error and system error constraints to minimize the risk of uncollectible accounts

A behavior prediction method for complex system based on belief rule base with structural adaptive

Predicting the behavior of complex systems and taking appropriate measures for system management is of paramount importance for decision-makers. Belief rule base (BRB) is an effective method for modeling complex systems, and its construction relies on expert knowledge. However, in certain complex system prediction problems, deriving the structure and parameters of BRB from limited expert knowledge or existing models is a challenge, and there may even be a lack of available expert knowledge. Data mining plays a crucial role in obtaining the parameters for model construction in the design of decision support systems (DSSs). Therefore, this paper proposes a method for behavior prediction of complex systems called the structural adaptive BRB (SA-BRB). First, to reduce the randomness of K-means+ +, this paper introduces an error constraint and employs this algorithm to mine historical data for constructing a reference value set. Second, a model ensemble construction process is designed to create different model structures. Subsequently, the evidence reasoning (ER) algorithm is applied to derive the models, and the projection covariance matrix adaptive evolution strategy (P-CMA-ES) algorithm is used for model optimization. Finally, a model evaluation method is established, allowing adaptive adjustment of the model structure according to the needs of engineering practice and the preferences of decision-makers. Furthermore, the effectiveness of the proposed method is validated through two case studies: one focusing on predicting the health status of a flywheel system and the other on forecasting full-load power generation in a combined power plant.

Delaunay meshes simplification with multi‐objective optimisation and fine tuning

Abstract3D meshes simplification plays an important role in many industrial domains. The two goals of Delaunay mesh simplification are maintaining high geometric fidelity and reducing mesh complexity. However, they are conflicting and cannot solved by gradient. Such limitation prevents existing Delaunay mesh simplification to obtain a small enough number of vertices and promising fidelity at the same time. To address these issues, this paper proposes an evolutionary multi‐objective approach for Delaunay mesh simplification. Firstly, the authors replace the previous fixed error‐bound threshold by the designed adaptive segment‐specific thresholds. Secondly, a constrained simplification is performed through a series of edge collapses that satisfy both Delaunay and error constraints. Next, the non‐dominated sorting genetic algorithm II (NSGA‐II) is employed to solve the multi‐objective problem to search for the optimal trade‐off threshold sequences. Finally, a fine‐tuning method is designed to further enhance the geometric fidelity of the simplified mesh. Experimental results demonstrate that the authors’ method consistently achieves a satisfactory balance between the approximation error and number of vertices, outperforming existing state‐of‐the‐art methods.

Event-Triggered Tracking Control for a Class of Nonlinear Systems: A Dynamic Gain Approach

This note presents a dynamic gain approach to the event-triggered tracking control for a class of strict-feedback nonlinear systems. A novel shifting function is designed to make the initial tracking error arbitrarily bounded, which significantly relaxes the requirement on the initial tracking error. To achieve the objective that the tracking error does not exceed the constraint after the pre-specified finite time, a barrier Lyapunov function and a new reduced-order observer are constructed by using the shifting function and the desired tracking signal. Based on the proposed dynamic gain approach, an event-triggered output feedback tracking controller is designed. It is proved that the developed control scheme guarantees that all the closed-loop signals are bounded and the tracking error constraint is strictly obeyed after a specified finite time. Compared with the celebrated backstepping method, the dynamic gain approach does not involve any virtual control variables, which avoids the complicated iterative procedure. The effectiveness of the proposed approach is verified by an example.

Adaptive nonlinear second-order sliding mode synchronization control of direct drive H-type platform with zero error constraint

In order to achieve better synchronization performance for H-type platform servo systems during motion, an adaptive nonlinear second-order sliding mode synchronous control method with zero error constraint is proposed in this paper. The reason and mechanism of unsynchronized movement of H-type platform are analyzed. A synchronous thrust allocation algorithm based on dynamics is designed by using the thrust balance equation under zero error constraint to suppress the rotation movement of the crossbeam theoretically. To minimize the impact of external disturbances on the system, the system employs a robust adaptive nonlinear second-order sliding mode control method. In this method, the nonlinear sliding mode function is constructed to enhance the dynamic performance of the system, the second-order sliding mode surface is designed to achieve chatter-free control input. To address the issue of limitations in sliding mode control caused by upper limits of external disturbances, an adaptive control technique is employed to estimate and compensate for uncertainties such as external disturbances. Experimental results demonstrate that the proposed synchronous control strategy can effectively adjust the operating conditions of the two motors, improve the synchronous control performance and enhance the anti-interference ability of the system.

Cubic time-spline fitting and interpolation for five-axis CNC machining

Abstract In CNC machining, G01 codes are widely used to represent the tool path. Directly interpolating these G01 codes is time-consuming and may cause discontinuities. In this paper, we propose a time-spline curve fitting method that combines tool path fitting and feedrate scheduling into a single step for five-axis CNC machining. The input for this method consists of a three-dimensional linear path of the tool tip in the workpiece coordinate system and two-dimensional tool orientations in the machine coordinate system (MCS). The output is a fitted tool path in the MCS represented by a five-dimensional smooth time-parametric B-spline curve, simply referred to as the time-spline curve. The time-spline curve provides not only position information but also kinematic information, including velocity, acceleration, and jerk for each axis, directly derived from the first, second, and third derivatives of the curve. To meet fitting error constraints and axial kinematic constraints, our objective is to find the time-spline curve that is time-optimal. We formulate the optimization problem as a nonlinear optimization model and design a recursive algorithm to solve it. The resulting time-spline curve demonstrates high accuracy and fully utilizes the machine’s kinematic capabilities. Along the tool path defined by the time-spline curve, exact interpolation points can be straightforwardly obtained according to the interpolation period. Simulations and experimental results indicate that the proposed method yields a time-optimal time-spline curve with the desired precision and kinematic constraints.

Enhanced reduced-order extended state observers-based position tracking error constraint control of a pump-controlled hydraulic system via multiparameter singular perturbation theory

In this paper, the position tracking error constraint control is investigated for a pump-controlled hydraulic system (PHS) subject to an unmeasurable velocity signal and disturbances. A barrier Lyapunov function (BLF)-based backstepping controller is designed, and a set of enhanced reduced-order extended state observers (RESOs) is proposed to estimate the velocity and disturbances. Dynamic surface control (DSC) is used to avoid a repeated calculation of the derivatives of virtual control inputs. Multiparameter singular perturbation theory is utilized to clarify the working mechanism of the enhanced RESOs and the closed-loop system stability properties. Theoretical analysis results reveal that the closed-loop system is uniformly ultimately bounded and the position tracking error is always constrained within a prescribed bound by a proper selection of the perturbation parameters. Moreover, the final position tracking error can be arbitrarily small by further tuning these parameters. In addition, the enhanced RESOs are proven capable of improving the convergence performance of the closed-loop system. Experiments are conducted on an actual PHS to validate the superiority of the proposed control strategy.

Research on Tolerance Optimization of High Precision Equipment Assembly Based on Error Transfer Prediction Model

In this paper, the assembly error transfer prediction model was established based on the error transfer attribute and the error transfer path of the assembly process. The assembly accuracy prediction was realized by combining error variation inequality, constraint inequality and mathematical statistics method. Aiming at the lowest processing cost of high-precision equipment assembly, the assembly accuracy required the reliability of index, the value interval of tolerance item and the principle of tolerance selection as constraints, the tolerance optimization model was established. The tolerance optimization of high-precision equipment assembly was carried out by combining the penalty function method and the improved genetic algorithm. Finally, taking gear oil pump assembly as an example, according to the reliability calculation formula of assembly accuracy, the reliability is 97.35%. Compared with the processing cost before and after optimization, the processing cost decreased by 12.13% after optimization, and the assembly accuracy reliability increased by 1.65%. The correctness and effectiveness of assembly accuracy prediction and tolerance optimization are verified.

Research on composite fault diagnosis technology of underwater vehicle actuator with positioning error constraint

When diagnosing the composite fault of the actuator, the characteristics of the motion force of the underwater vehicle are not analyzed, and there are diagnostic errors, resulting in the low accuracy of the diagnosis technology. In order to solve this problem and improve the operation safety of underwater vehicle actuators, this paper proposes a compound fault diagnosis technology for underwater vehicle actuators under positioning error constraints. Analyze the motion force of the underwater robot actuator, control the motion of the underwater robot actuator according to the analysis results, and extract real-time data parameters according to the control results. Under the constraint of positioning error, the composite fault features of the underwater robot actuator are divided, and the diagnosis model is built according to the deep fusion of the features to complete the fault diagnosis. The experimental results show that the technology can diagnose the composite fault data of the actuator, and the positioning error of the horizontal axis and the horizontal axis can be significantly improved, which can improve the diagnosis effect of the composite fault of the actuator and to the improvement of underwater robot running safety of actuators provide certain reference.

Near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints

Compared with general time-optimal robot feedrate planning, trajectory machining tasks require consideration of feedrate command constraints and the complexity of parameter spline curves. The interpolation error generated during the interpolation stage affects the command accuracy and contour accuracy of the trajectory. To ensure that the robot end-effector feedrate maintains consistency with the feedrate command and to improve the contour accuracy of the trajectory, this study proposes a two-stage method: near-time optimal feedrate planning for the NURBS curve considering interpolation error constraints. In the first stage, the end-effector velocity constraint under joint velocity constraint is calculated, and the feedrate command is corrected based on that constraint. Then, the corrected feedrate command is transformed into parameter form, and feedrate planning is carried out utilizing the direct transcription method. In the second stage, interpolation is carried out after feedrate planning, and interpolation error is calculated to detect any over-limit positions. If any over-limit positions are detected, the first over-limit position is recorded, and feedrate planning with reduced feedrate limit is carried out at that position. This process is repeated until the interpolation error constraint is satisfied. A series of simulations and experiments were conducted in this study. The simulation results show that the proposed method can consider feedrate command constraints and limit interpolation errors within specified constraints. The experimental results show that the proposed method can reduce contour errors, particularly at low feedrate command.

Physically consistent deep learning-based day-ahead energy dispatching and thermal comfort control for grid-interactive communities

Grid-interactive communities are an emerging solution for optimal energy dispatching, improving grid stability, and enhancing the usage of on-site renewable energy by leveraging community flexibilities. This work introduces a novel Physically Consistent Deep Learning (PCDL)-based optimization framework for day-ahead energy dispatching and thermal comfort control within grid-interactive communities. Specifically, the PCDL model is developed to capture the thermal dynamics within the community while ensuring strict adherence to physics consistency. This consistency is defined with the aim of generating physically viable solutions in response to modified system inputs. Subsequently, the PCDL model is utilized for load estimation and indoor climate prediction within a proposed scheduling and control strategy: (1) an optimal energy dispatching plan is calculated based on the day-ahead grid market; (2) a real-time model predictive control (MPC) method is applied to minimize the utilization error and indoor comfort constraint violations caused by following the scheduled energy dispatching plan. A simulation case of a residential hall community at Cornell University with on-site renewable energy resources is implemented to demonstrate the effectiveness of the proposed approach. Comparative simulations, which include the Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Gaussian Process (GP) regression models, confirm the performance advantage of capturing community thermal dynamic and control-oriented generalization ability when using the PCDL model. These results leads to notable improvements in indoor thermal comfort control, ranging between 65.4 and 68.7%, 63.6–79.3%, and 60.4–62.2% for each comparative model, respectively. Moreover, by harnessing community demand flexibility, we achieve energy cost savings between 29.5 and 39.7% compared to the baseline controller.

Output Feedback Tracking Control for Vessel with Collision-Avoidance and Performance Constraints

This manuscript investigates an output feedback-tracking control problem of a dynamically positioned vessel with an input constraint. The vessel is exposed to model uncertainty and external disturbances. Compared with the existing results, the primary contribution is to develop a switch-control strategy for achieving collision avoidance and performance constraints by using an extended state observer (ESO), a collision-avoidance controller (CAC), a prescribed performance controller, and an auxiliary dynamic system (ADS). The switch control strategy combined two different controllers, and an extended state observer (ESO) is designed. The ESO is employed to recover velocity information as well as unknown model uncertainty and external disturbances. A collision-risk-analysis module is introduced to evaluate whether there exists a risk of collision avoidance. Based on the analysis, the CASC can choose between a CAC and a PPC. An ADS is constructed to handle the input constraints. The CAC is employed by using an artificial potential function, the ADS, and the ESO. The PPC is designed based on an error constraint function, the ADS, and the ESO. The stability of the closed-loop control system is analyzed based on the Lyapunov direct method. Simulations prove the effectiveness of the presented control strategy.

Prescribed-time control for hypersonic morphing vehicles with state error constraints and uncertainties

This paper focuses on the attitude control problem of hypersonic morphing vehicles (HMVs) with output state constraints and uncertainties in morphing phase. The main contribution of this work is not only realizing arbitrarily predefined settling time based on accelerated tracking rate but also ensuring smooth control performance under morphing effects and uncertainties. Firstly the control-oriented model is established based on the dynamic model of HMVs. Then, a prescribed-time disturbance observer (PTDO) is developed to enhance the robustness of flight control system based on radial basis function neural networks (RBFNN), allowing the lumped disturbances to be estimated within appointed time. Subsequently, based on tangent-type barrier Lyapunov function (TBLF) and prescribed-time convergence technique, the controller is designed via backstepping method, and the tracking errors of output states converge to the near origin within arbitrarily prescribed time without violating the preassigned constraints during tracking process. Finally, the closed-loop stability is ensured via Lyapunov synthesis, and numerical test results are presented to demonstrate the effectiveness of the proposed control scheme. Simulation results show that superior performance is obtained in terms of both transient process and stabilization.

Fixed-time observer-based heading control for underactuated hovercraft with slew rate safety constrain

ABSTRACT This paper presents a safe-guaranteed backstepping sliding mode heading controller for the underactuated hovercraft in the presence of slew safety constraint and system uncertainties. To begin with, based on the four degrees-of-freedom mathematical model of the hovercraft with system uncertainties, a novel slew rate constraint scheme is proposed to constrain the virtual slew rate of the hovercraft by designing auxiliary dynamic function, and redefine the error constraint envelope according to the prescribed performance control idea to realise the slew rate error constraint. In addition, a second-order fixed time disturbance observer is designed to quickly estimate the uncertainties of the system. Finally, all tracking errors of the closed-loop system are verified global asymptotically stable. The simulation results show that the slew rate can be constrained within the set safety range, and the error signals can converge to 0.

Adaptive NN Tracking Control for Uncertain MIMO Nonlinear System With Time-Varying State Constraints and Disturbances.

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

Fixed-Time Controller Design for a Quadrotor UAV with Asymmetric Output Error Constraints

ADAPTIVE NEURAL TRACKING CONTROL FOR SURFACE SHIP WITH COMPENSATED TRACKING ERROR-CONSTRAINS AND DELAY INPUT BASED ON COMMAND-FILTER

The article proposes an algorithm for trajectory tracking control problem of full actuated surface ships in the presence of state constraints, the delay of the input signal, and uncertain model parameters. During the design process, radial basis function neural networks are used to approximate the nonlinear components of uncertainty and a symmetric barrier Lyapunov function is incorporated to cope with the constraints of compensated tracking error. In particular, an auxiliary system is employed to eliminate the delay of the input signals, which often makes the control performance worse, even unstable. The adaptive controller that the article proposes is built based on the backstepping method using a command filter to avoid derivative explosion and reduce the computational burden on the controller. The article shows that tracking errors of surface ship can converge to a small neighborhood of zero, the compensated tracking error constraints of the system are not violated, the system is still stable when the input signal is delayed.