Parameters Of Dynamic Model Research Articles

Adaptive backstepping fast terminal sliding mode control of dynamic positioning ships with uncertainty and unknown disturbances

Considering the complexity of the operating environment of marine ships, higher demands are placed on the positioning accuracy and positioning performance of Dynamic Positioning (DP) systems. This paper designs an Adaptive Backstepping Fast Terminal Sliding Mode Control (ABFTSMC) to solve the problems of low positioning accuracy, slow convergence, and poor anti-interference performance in ship positioning due to uncertainty of dynamic model parameters and unknown time-varying environmental disturbances. A Fast Terminal Sliding Mode Control (FTSMC) is combined with backstepping techniques to ensure the robustness of the system to uncertainties and disturbances. Meanwhile, an adaptive law is used to estimate the unknown uncertainty terms. Moreover, the Lyapunov stability criterion is used to prove the convergence and stability of the designed controller. Multiple simulation results show that ABFTSMC has better control performance compared with Adaptive Backstepping Control (ABC) and Adaptive Backstepping Sliding Mode Control (ABSMC). All the comparisons could fully verify the effectiveness and superiority of the proposed control method.

Dynamic Modeling and Analysis of an RV Reducer Considering Tooth Profile Modifications and Errors

Due to their advantages of compact size, high reduction ratio, large stiffness and high load capacity, RV reducers have been widely used in industrial robots. The dynamic characteristics of RV reducers in terms of vibratory response and dynamic transmission error have a significant influence on positioning accuracy and service life. However, the current dynamic studies on RV reducers are not extensive and require deeper study. To bridge this gap, a more effective and realistic lumped parameter dynamic model for RV reducers is developed, considering the tooth profile modification of cycloid gears and system errors. Firstly, for an efficient solution, the equivalent pressure angle and equivalent mesh stiffness of the cycloid–pin gear pair are introduced in the dynamic model based on the loaded tooth contact analysis. Secondly, the differential equations of the system are derived by analyzing the relative displacement relationships between each component, which are solved using the Runge–Kutta method. With this, the effects of errors such as machining errors, assembly errors and bearing clearances on the dynamic behaviors and transmission precision are investigated by comparison to quantify or qualify their influence. This research is helpful in characterizing the multi-tooth mesh and dynamic behavior, and revealing the underlying physics of the RV reducer.

Disentangling the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union

In this work, we manage to disentangle the role of virus infectiousness and awareness-based human behavior in the COVID-19 pandemic. Using Bayesian inference, we quantify the uncertainty of a state-space model whose propagator is based on an unusual SEIR-type model since it incorporates the effective population fraction as a parameter. Within the Markov Chain Monte Carlo (MCMC) algorithm, Unscented Kalman Filter (UKF) may be used to evaluate the likelihood approximately. UKF is a suitable strategy in many cases, but it is not well-suited to deal with non-negativity restrictions on the state variables. To overcome this difficulty, we modify the UKF, conveniently truncating Gaussian distributions, which allows us to deal with such restrictions. We use official infection notification records to analyze the first 22 weeks of infection spread in each of the 27 countries of the European Union (EU). It is known that such records are the primary source of information to assess the early evolution of the pandemic and, at the same time, usually suffer underreporting and backlogs. Our model explicitly accounts for uncertainty in the dynamic model parameters, the dynamic model adequacy, and the infection observation process. We argue that this modeling paradigm allows us to disentangle the role of the contact rate, the effective population fraction, and the infection observation probability across time and space with an imperfect first principles model. Our findings agree with phylogenetic evidence showing little variability in the contact rate, or virus infectiousness, across EU countries during the early phase of the pandemic, highlighting the advantage of incorporating the effective population fraction into pandemic modeling for heterogeneity in both human behavior and reporting. Finally, to evaluate the consistency of our data assimilation method, we performed a forecast that adequately fits the actual data. Statement of significanceData-driven and model-based epidemiological studies aimed at learning the number of people infected early during a pandemic should explicitly consider the behavior-induced effective population effect. Indeed, the non-isolated, or effective, fraction of the population during the early phase of the pandemic is time-varying, and first-principles modeling with quantified uncertainty is imperative for an adequate analysis across time and space. We argue that, although good inference results may be obtained using the classical SEIR type model, the model posed in this work has allowed us to disentangle the role of virus infectiousness and awareness-based human behavior during the early phase of the COVID-19 pandemic in the European Union from official infection notification records.

Cylinder position control driven by pneumatic digital bridge circuit using a fuzzy algorithm under large stroke and varying load conditions

A digital bridge circuit based on the concept of independent metering control can enable the precise position control of a pneumatic cylinder, but large strokes and variable loads still cause challenges. To solve this problem, a piecewise on/off valve flow compensator and a composite friction observer were innovatively designed in this study, and they were combined with a multiple fuzzy intelligent algorithm to ensure the accuracy and robustness of pneumatic position control. Considering the starting and stopping delays and the response processes of on/off valves, a six-stage flow–duty ratio linearization relationship was proposed. Employing a parameter identification method, a static and dynamic composite friction model was presented. Then, a fuzzy PID controller was proposed, and a genetic algorithm was used to optimize the control parameters. Experiment results showed that, when focusing on a large stroke (250 mm) and varying loads (8.5–18.5 kg), for sinusoidal signal with amplitude of 150 mm and frequency of 0.125 Hz and the air supply pressure is 0.5 Mpa, the algorithm in this study could ensure that the steady-state step response error was less than 1% and the root mean squared error of the sinusoidal trajectory tracking was less than 3%.

Noise-immune state of charge estimation for lithium-ion batteries based on optimized dynamic model and improved adaptive unscented Kalman filter under wide temperature range

Due to diverse vehicle driving conditions, it is difficult to ensure that lithium-ion batteries operate at a fixed ambient temperature. Meanwhile, the environmental noise accompanying vehicle driving can also affect the data sampling accuracy of batteries. To achieve a high-robustness state of charge (SOC) estimation for lithium-ion batteries at different ambient temperatures with noise effects, a noise-immune SOC estimation method under a wide ambient temperature range is proposed. First, based on the moving window principle, a high-precision fitting model of the open-circuit voltage is established. Second, based on the Multi-Verse Optimizer, a new dynamic model parameter identification method is proposed, while the complete optimized dynamic battery model is established relying on the data of Dynamic Stress Test at different temperatures. Third, to enhance the SOC estimation accuracy and stability, based on adaptive theory and matrix diagonalization theory, the unscented Kalman filter is improved. Finally, the effectiveness and robustness of the proposed method are validated under two other working conditions with random noise added at various temperatures. Under every set of working conditions at all temperatures, the SOC estimation results can maintain stability after converging to the reference SOC, while root mean square errors and mean absolute errors under all cases do not exceed 1.5 %.

Dynamics Modeling and Load-Sharing Performance Optimization of Concentric Face Gear Split-Torque Transmission Systems

The concentric face gear split-torque transmission system (CFGSTTS) has the advantages of a large reduction ratio and high power density. The CFGSTTS has considerable potential to be applied in helicopter main reducers. As such, in this study, we analyzed the load distribution characteristics of a dual input–dual output concentric face gear split-torque transmission system. A load-dependent time-varying meshing stiffness surrogate model was designed based on a feedforward neural network. The difference in the meshing stiffness between the pinion driving and face gear driving was analyzed. The coupled lumped parameter dynamic model of the bending–torsion–axis–pendulum was developed through Newton’s second law, and the influences of the time-varying meshing stiffness, backlash, comprehensive transmission error, support stiffness, and damping were considered. Finally, the impact of the support stiffness on the load-sharing coefficient was analyzed. An optimization model was constructed with the objective function of minimizing the sum of the load-sharing coefficients and was solved by the marine predator algorithm. In addition, the validity of the optimization results was verified with a finite element model. The results indicate that (1) smaller support stiffnesses of input gears benefit the corresponding load balance; (2) the support stiffnesses of the face gears have different laws of influence on the load-sharing coefficient at the input gear and idler, and the support stiffnesses of the other gears need to be comprehensively considered; (3) the larger supporting stiffnesses of the idler gears and tail gear are beneficial for decreasing the load-sharing coefficient at the input gear; and (4) the optimized load-sharing coefficients at Input Gears 1 and 2 and the idler gear decrease by 23.7%, 24.2%, and 4.6%, respectively.

An explicit finite element approach for simulations of transient meshing contact of gear pairs and the resulting wear

A 3D time-domain modelling approach is developed with the explicit finite element method to simulate transient meshing contact of gear pairs and the resulting wear. Taking a helical gear pair used in a locomotive as an example, the dynamic contact states of gear teeth are predicted for different speeds in consideration of actual geometries (including those of damaged teeth), time dependent torques, and structural and continuum vibrations of the gear system. The friction between mating teeth is taken into account by a non-Newtonian EHL friction model. A tiny time step of 4.5 × 10−8 s determined by conditional stability of the explicit time integration ensures the capture of transient effects. Based on detailed contact solutions during meshing, the dynamic wear on teeth is further calculated using an Archard wear model to predict tooth profile evolvement. Taking initial involute profiles and a speed of 120 km/h, the model is first validated for dynamic contact solutions. More results show that structural vibrations and worn profiles influence the dynamic meshing contact significantly, tooth wear increases as lubrication fails, and tooth pitting's influence is localized. This approach provides key load boundaries for detailed studies on mating gears, and may be employed for studies on tooth damages and as a reference for lumped parameter dynamic models of gear pairs.

Deep learning and differential equationsfor modeling changes in individual-level latent dynamics between observation periods.

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction and differential equationsfor dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equationparameters are allowed for observation subperiods. Still, estimation for intra-individual subperiods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as outcomes for predicting resilience from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allow to stably select predictors, that is, resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observationsubperiods.

Predicting and controlling ecological communities via trait and environment mediated parameterizations of dynamical models

Predicting or controlling the state of an ecological community is a core global change challenge. Dynamical models provide one toolkit, but parameterizing these models can be challenging, and interpretation can be difficult. We here propose rewriting dynamical model parameters in terms of more interpretable and measurable functional traits and environmental variables (trait and environment mediated parameterizations; TEMPs). For prediction, this approach could help make interpretable forecasts of equilibrium community dynamics (species coexistence), invasibility surfaces (dynamics due to biotic context), and responses to environmental change (dynamics due to abiotic context). For control, this approach could help identify policies that yield desired species and trait compositions through perturbations of the abundance of species with certain traits, or of the environment.

The Neptunian gravity estimated from the motion of Triton based on astrometric observations

Context. Accurate gravity and ephemerides estimations for Neptune and its satellites are necessary for the forthcoming deep space exploration missions targeting its system. In addition, these estimations are also meaningful for the modeling of Neptune's interior and for solar system dynamics studies. The body of astrometric data concerning Triton has been accumulating for about two hundred years, but more accurate updates to the ephemerides of this moon and revisions to the relevant gravity parameters would be possible with more precise astrometric data. The new Gaia catalog of star positions plus observations from Voyager 2 and the Hubble Space Telescope provide such a basis for high-precision astrometry and to complement and extend the existing body of data. Aims. We aim to report integrated orbital fits for Triton based on all the available astrometric data from 1847 to 2020, including observations from Earth-based telescopes, Voyager 2, and the Hubble Space Telescope. We also estimate the Neptunian gravity using the motion of Triton. Methods. Triton’s orbital solution was determined by a weighted least-squares method to fit the model to the most complete astrometric data set to date. The DOP853 algorithm was adopted in the numerical integration calculations. For the dynamical model parameters, our orbital model for Triton is similar to the NEP081 but with an update. The perturbations from the inner satellites (Naiad, Thalassa, Despina, Galatea, Larissa, Proteus, and Hippocamp) were considered by adding corrections to J2 and J4 for Neptune. As the gravitational oblateness coefficient of Neptune is correlated with its orientation, the pole parameters were thus kept fixed in the integration when estimating Neptunian gravity. A Monte Carlo analysis was performed, however, to obtain reliable accuracy estimations and to assess the uncertainty of pole parameters on the results’ formal error. Results. We provide a new orbit and dynamical model values for Triton. The estimated accuracy of the model we built and updated fit all the astrometric data. The RMS of the residuals was 0.074 arcsec in the right ascension and 0.071 arcsec in declination. The RMS was 0.102 arcsec for X and 0.139 arcsec for Y in differential coordinates. The RMS for the position angle was 0.834 degrees, and the angular separation distance was 0.257 arcsec for the data collected before 1960. The orbit of Triton was well determined with the orbit differences from NEP081 and NEP097 (so far the latest Triton ephemerides from Jet Propulsion Laboratory) as being less than 300 km (about 15 mas) during the observation coverage period of this study. The large body of astrometric data for Triton over a time interval from 1847 to 2020 was used to constrain its position at the initial epoch, allowing us to reduce formal uncertainty to about 3 km. Based on the most complete weighting astrometric observations of Triton, the estimated mass of the Neptune system is GMs = 6 836 525.210 ±19.526 km3 s−2. Our revised gravity model yields J2 = 3401.655 ±1.850 × 10−6 and J4 = −33.294 ±10.000 × 10−6. The astrometric observations showed little sensitivity to GMs and J4, but acted well on J2. A Monte Carlo method was used to analyze the error caused by a variation in the pole parameters and showed that J2 = 3401.655 ± 3.994 × 10−6 was a more realistic error.

Machine tool multibody dynamic model updating using vision-based modal analysis

Machine tool dynamic behaviour is influenced by the structural properties of its subsystems assembled at interfaces as well as by the interface characteristics. Interfaces are commonly modelled as spring-damper connections, parameters of which are usually updated by minimizing the difference between model-predicted and measured dynamics characterized by frequency response functions. This model updating approach requires global mode shapes to be measured by roving the hammer and/or the sensor such as to localize the joint parameters to be updated. Such measurements are time consuming and fraught with errors. As a new, alternative, and simpler way to update joint parameters of a machine tool multibody dynamic model, this paper reports on the use of full-field vision-based modal analysis methods. Mode shapes thus identified agree with those estimated with the traditional experimental modal analysis procedures. The updated machine tool multibody dynamic model is a step towards realizing an accurate digital twin.

Online fusion of multi-resolution multispectral images with weakly supervised temporal dynamics

Real-time satellite imaging has a central role in monitoring, detecting and estimating the intensity of key natural phenomena such as floods, earthquakes, etc. One important constraint of satellite imaging is the trade-off between spatial/spectral resolution and their revisiting time, a consequence of design and physical constraints imposed by satellite orbit among other technical limitations. In this paper, we focus on fusing multi-temporal, multi-spectral images where data acquired from different instruments with different spatial resolutions is used. We leverage the spatial relationship between images at multiple modalities to generate high-resolution image sequences at higher revisiting rates. To achieve this goal, we formulate the fusion method as a recursive state estimation problem and study its performance in filtering and smoothing contexts. Furthermore, a calibration strategy is proposed to estimate the time-varying temporal dynamics of the image sequence using only a small amount of historical image data. Differently from the training process in traditional machine learning algorithms, which usually require large datasets and computation times, the parameters of the temporal dynamical model are calibrated based on an analytical expression that uses only two of the images in the historical dataset. A distributed version of the Bayesian filtering and smoothing strategies is also proposed to reduce its computational complexity. To evaluate the proposed methodology we consider a water mapping task where real data acquired by the Landsat and MODIS instruments are fused generating high spatial–temporal resolution image estimates. Our experiments show that the proposed methodology outperforms the competing methods in both estimation accuracy and water mapping tasks.

Is there a national housing market bubble brewing in the United States?

AbstractWe use a time-varying parameter dynamic factor model with stochastic volatility estimated using Bayesian methods to disentangle the relative importance of the common component in Federal Housing Finance Agency house price movements from state-specific shocks, over the quarterly period of 1975Q2 to 2017Q4. We find that the contribution of the national factor in explaining fluctuations in house prices is critical. We then use a Bayesian change-point vector autoregressive model that allows for different regimes throughout the sample period, to study the impact of aggregate supply, aggregate demand, (conventional) monetary policy, and term-spread shocks, identified based on sign restrictions on the national component of house price movements. While monetary policy and other shocks are found to be quite dominant early on, we find evidence that the national factor has been detached from the identified macroeconomic shocks since 2014, thus suggesting that a “national bubble” might be brewing again in the US housing market.

Identification of Differential Drive Robot Dynamic Model Parameters.

The paper presents the identification process of the mathematical model parameters of a differential-drive two-wheeled mobile robot. The values of the unknown parameters of the dynamics model were determined by carrying out their identification offline with the Levenberg-Marguardt method and identification online with the Recursive least-squares method. The authors compared the parameters identified by offline and online methods and proposed to support the recursive least squares method with the results obtained by offline identification. The correctness of the identification process of the robot dynamics model parameters, and the operation of the control system was verified by comparing the desired trajectories and those obtained through simulation studies and laboratory tests. Then an analysis of errors defined as the difference between the values of reference position, orientation and velocity, and those obtained from simulations and laboratory tests was carried out. On itd basis, the quality of regulation in the proposed algorithm was determined.

Parametric estimation of long memory in factor models

A dynamic factor model is proposed in that factor dynamics are driven by stochastic time trends describing arbitrary persistence levels. The proposed model is essentially a long memory factor model, which nests standard I(0) and I(1) behavior smoothly in common factors. In the estimation, principal components analysis (PCA) and conditional sum of squares (CSS) estimations are employed. For the dynamic model parameters, centered normal asymptotics are established at the usual parametric rates, and their small-sample properties are explored via Monte-Carlo experiments. The method is then applied to a panel of U.S. industry realized volatilities.

БАЗА ЗНАНЬ ІНТЕЛЕКТУАЛЬНОЇ ІНФОРМАЦІЙНОЇ СИСТЕМИ ПРОГНОЗУВАННЯ ФАЗОВОЇ СТАБІЛЬНОСТІ ТВЕРДИХ РОЗЧИНІВ

This research work is devoted to the development of a knowledge base for solving the current problem of forecasting the phase stability of solid solutions. Knowledge bases mean a set of facts and inference rules that allow logical conclusion and purposeful processing of information. The most important property of information stored in knowledge bases is the reliability of specific and generalized information in the database and the relevance of the original information obtained using the rules of inference embedded in the knowledge base. The best knowledge bases include the most relevant, reliable and fresh information, have perfect information search systems, a carefully thought-out structure and format of knowledge. The expert system embodies the methodology of adapting the algorithm of successful solutions from one sphere of scientific and practical activity to another. With the spread of computer technologies, it is an identical intelligent computer program that contains the knowledge and analytical abilities of one or more experts in some field of application and is able to draw logical conclusions based on this knowledge, thereby providing a solution to specific tasks. An intelligent information system (IIS) is one of the types of automated information systems, which is a complex of software, linguistic and logical-mathematical tools for the implementation of the main task, which usually consists of data interpretation and forecasting. Data interpretation is one of the traditional tasks for expert systems. Interpretation means the process of determining the content of data, the results of which must be agreed and correct. A multivariate analysis of the data is usually assumed, and the findings from this model form the basis for probabilistic estimates. Forecasting allows you to predict the consequences of some events or phenomena based on the analysis of available data. A parametric dynamic model is usually used in the forecasting system, in which parameter values are set for a given situation. As a result of the development, a knowledge base model was built for predicting the phase stability of solid solutions using a set of production rules, predicates, functions and operators.

ІНТЕГРАЛЬНА ІНФОРМАЦІЙНО-ОБЧИСЛЮВАЛЬНА СИСТЕМА, ЩО ЗАБЕЗПЕЧУЄ ТЕХНІЧНЕ ОБСЛУГОВУВАННЯ ЗА СТАНОМ СИЛОВИХ ГАЗОТУРБІННИХ УСТАНОВОК

The effectiveness of the chosen maintenance strategy is determined by the completeness of information about the current technical condition of the facility. The real current state of a dynamic object should specify the list and scope of preventive and remedial work for each specific maintenance object. Existing strategies and programs according to the technical condition of dynamic objects are conditionally divided into three groups: with control over the level of reliability of the operating object; with control of the parameters of the object of operation; hybrid. Power gas turbine plants are objects of operation with high functional significance. They have an insufficient degree of redundancy, as well as a low level of operational manufacturability. Therefore, it is advisable for them to apply a maintenance strategy as per the parameter control. The article proposes general principles on the basis of which an integral information-computing system for processing parameters can be built. This system is the main element of the automated control system for the technical condition of the gas turbine power plant. Synthesized adaptive system for dynamic control of parameters characterizing the current technical state of a gas turbine power plant. Closing the control loop of the technical condition of the object with negative feedback allows you to switch from the strategy of its maintenance according to the operating time to the maintenance strategy according to the state with the control of parameters. The integrated information-computing system should solve two main tasks: a reliable assessment of the current technical state of a dynamic object and prediction of a pre-failure state in the medium and long term. The main condition for organizing the maintenance of dynamic objects according to the state with the control of parameters is the possibility of continuous monitoring of the parameters characterizing the current technical state. The choice of such parameters is ambiguous, which is due to both the specific features of dynamic object and diverse nature of relationship between faults and controlled parameters. The requirements for the determining parameters are of a general nature: the parameters must have acceptable accuracy and stability of readings over time; have the greatest diagnostic value among other parameters; not depend on changes in external operating conditions and modes of operation; based on standard measurements. The system of continuous monitoring of parameters characterizing technical state of a dynamic object must be adaptive. It should change in accordance with the change in technical condition of the gas turbine power plant. The use of a set of parameters of its dynamic linear model as characteristic of the current technical state of an object is justified for a wide class of objects. The control system of such objects operates in the stabilization mode, therefore, the adaptive system of continuous monitoring synthesized on the basis of this model provides the possibility of assessing the current technical state of the gas turbine power plant and makes it possible to predict its technical state. At the same time, the adaptation of the parameters of the linear dynamic model of the object to the new technical condition of the gas turbine plant should be carried out with the least interference in the normal operation of the plant.

Photovoltaic Arrays’ Dynamic Model Parameter Estimation

This paper deals with the problem of on-line identification of the parameters of a realistic dynamical model of a photovoltaic array connected to a power system through a power converter. It has been shown in the literature that, when interacting with switching devices, this model is able to better account for the PV array operation, as compared to the classical five parameter static model of the array. While there are many results of identification of the parameters of the latter model, to the best of our knowledge, no one has provided a solution for the aforementioned more complex dynamic model since it concerns the parameter estimation of a nonlinear, underexcited system with unmeasurable state variables. Achieving such objective is the main contribution of the paper. We propose a new parameterisation of the dynamic model, which, combined with the powerful identification technique of dynamic regressor extension and mixing, ensures a fast and accurate online estimation of the unknown parameters. Realistic numerical examples via computer simulations are presented to assess the performance of the proposed approach—even being able to track the parameter variations when the system changes operating point.

Model Parameter Identification via a Hyperparameter Optimization Scheme for Autonomous Racing Systems

In this letter, we propose a model parameter identification method via a hyperparameter optimization scheme (MI-HPO). Our method adopts an efficient exploreexploit strategy to identify the parameters of dynamic models in a data-driven optimization manner. We utilize our method for model parameter identification of the AV-21, a full-scaled autonomous race vehicle. We then incorporate the optimized parameters for the design of modelbased planning and control systems of our platform. In experiments, MI-HPO exhibits more than 13 times faster convergence than traditional parameter identification methods. Furthermore, the parametric models learned via MIHPO demonstrate good fitness to the given datasets and show generalization ability in unseen dynamic scenarios. We further conduct extensive field tests to validate our model-based system, demonstrating stable obstacle avoidance and high-speed driving up to 217km/h at the Indianapolis Motor Speedway and Las Vegas Motor Speedway. The source code for our work and videos of the tests are available at https://github.com/hynkis/MI-HPO.

Adaptive Energy Reference Time Domain Passivity Control of Haptic Interfaces.

Haptic devices are designed to assist humans in operating tasks in a remote or virtual environment. The passivity-based controllers feed back the forces from the environment while maintaining stability. This article presents the adaptive energy reference time domain passivity approach to overcome the sudden force change inherent in the conventional time domain passivity approach (TDPA). The main advantage of the proposed method is that it can be applied to the haptic interfaces interacting with delayed unknown environments without increasing conservatism compared to the conventional TDPA with or without energy reference. The adaptive energy reference is learned at each interaction by a passive estimation of the haptic interface energy. The energy reference is found using force and velocity data, which does not need the foreknowledge of the environment dynamic model parameters and time delay. Therefore, the designed controller can adapt to different environments and time delays. The proposed method is evaluated in both simulation and experimental setups where the parameters of the environments are unknown to the controller. It is shown that the sudden change in force is decreased compared to the conventional TDPA for haptic interface with or without time delay in the system.