This paper presents a new method for correction of dynamic errors occurring when measuring flat surfaces in the presence of mechanical effects. Mechanical effects cause inertial forces and moments that affect the moving components of measuring instruments, thereby causing dynamic errors. The study proposes a mathematical model, on the basis of which algorithms for correction of dynamic errors can be developed. The basic concept of the model is based on determining the optimal estimate in the current coordinate point on the basis of the theoretical model of the measured surface and the information from the measurement that contains errors caused by internal and external factors. Based on this model, an algorithm for real-time data processing has been developed. The algorithm works in “predictor-corrector” mode at each step of which the best estimate is obtained. The estimate is based on minimizing the variance of a random component in which the main values are formed from the accumulated statistical data of the error of the model and the measurement error. This paper presents the results of experimental studies, carried out with simulations of mechanical effects in four modes. The results confirm the high efficiency of the algorithm for high-accuracy measurement of flat surfaces in the presence of mechanical effects.

This article presents an integrated method for measuring the angular orientation of moving objects, combining a simplified mechanical structure to reduce instrumental errors with a hardware–software platform for adaptive compensation of dynamic errors. Unlike existing approaches, the method avoids inertial element stabilization by using an adaptive Kalman structure for real-time correction. Based on this method, a measuring system for determining roll and pitch has been developed and implemented using a two-channel measurement model with two independent signals and MEMS sensors. The accuracy of the system has been experimentally validated in both static and dynamic modes through a highly accurate reference system with traceability to international standards. A metrologically based methodology for quantitative assessment has also been developed, applying both the theory of error and the theory of uncertainty to provide an objective, reproducible, and traceable evaluation under real-world conditions.

In this study, we introduce an advanced framework for state estimation in electro-hydraulic systems, utilizing a structurally adapted Kalman filter. The proposed model was designed to enhance estimation accuracy and robustness under dynamic load variations and evolving measurement conditions. A notable feature of the approach is the algebraic resolution of one system state during each iteration, enabling the seamless inclusion of variables that are otherwise difficult to measure, without disrupting the model’s linear formulation. In addition, the dynamics of the load torque are empirically characterized through a regression-based model derived from experimental observations. The framework integrates adaptive mechanisms for updating the model and measurement error covariance matrices, facilitating the real-time accommodation of system nonlinearities and environmental changes. Experimental results are presented in different operating modes, reflecting characteristic dynamic movements. They show that the method reduced the root mean square error (RMSE) when estimating angular velocity between five and more than six times, depending on the mode. When evaluating the load torque, even in modes with a sharply changing load, the RMSE value remains stable below 0.05 Nm, which indicates the absence of systematic drift and high stability of the estimates. This confirms the stable operation of the algorithm in dynamic conditions and its applicability in real systems.

This article proposes an integrated adaptive algorithm to control the accuracy and reliability of linear motion in electrohydraulic systems operating in dynamic modes and external loads. This algorithm has a multilevel parallel structure in which the physical model, extended measurement information, internal adaptive parameters, and the current of measurement and model uncertainties are combined and synchronized within a single loop. The proposed structure allows the real-time extraction of information about hard-to-determine dynamic characteristics of the electrohydraulic process, which is used to maintain consistency between the mathematical model and the actual behavior of the system, including in the case of rapidly changing modes and load variations. In addition, a functional observation layer for assessing the quality of measurement information is introduced, through which the sensitivity of adaptive mechanisms is managed, and the stability of the algorithm is maintained under degraded measurement conditions. Experimental results demonstrate a significant reduction in dynamic error and a sustainable improvement in the quality of tracking relative to a basic electrohydraulic system without algorithmic correction. This confirms the applicability of the proposed approach to real energy and industrial systems.

This paper presents a mathematical model of the Kalman Extended Filter (EKF) for estimating dynamic states in an electro-hydraulic system. The main goal is to increase the accuracy and stability of estimates in the presence of noise and nonlinearities in the dynamics of the system. EKF combines information from hydraulic motor shaft angular velocity measurements and the pressure difference between its inlet and outlet to provide reliable estimates of basic dynamic system parameters, including the current angular velocity and the moment created by the external load. Simulation studies demonstrate the advantages of the EKF compared to a system without a filter, emphasizing the importance of tuning the covariance matrices Q and R to achieve a balance between response speed and filter stability. The developed model shows high applicability for real electro-hydraulic systems, while offering the possibility of adaptation to other nonlinear dynamic systems.

Electro-hydraulic systems are characterized by high complexity and nonlinearity, caused by the dynamic interactions between the fundamental quantities that determine their operation and control. The present study proposes a method for adaptive parameter estimation using an advanced method of least squares (A-LS) (Advanced Least Squares), applicable to nonlinear dynamical systems. The paper presents a mathematical model describing the dynamics of the electro-hydraulic system, as well as an approach for adaptive parameter estimation using Recursive Least Squares (RLS) in combination with the Stochastic Gradient Method (SGD). The main goal is to minimize errors between measurement results and predicted model values, ensuring high accuracy and stability under variable operating conditions. The results of the simulations show that the use of RLS for angular velocity estimation and SGD for adaptive load torque correction allows for effective noise suppression in measurements and precise tracking of system dynamics. The proposed approach provides a basis for optimizing electro-hydraulic systems through adaptive methods and can be useful for applications requiring high accuracy and reliability.