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In response to the severe lag in tracking the response of the Stewart stability platform after adding overload, as well as the impact of nonlinear factors such as load and friction on stability accuracy, a new error attenuation function and a parallel stable platform active disturbance rejection control (ADRC) strategy combining cascade extended state observer (ESO) are proposed.

First, through kinematic modeling of the Stewart platform, the relationship between the desired pose and the control quantities of the six hydraulic cylinders is obtained. Then, a linear nonlinear disturbance observer was established to observe noise and load, to enhance the system’s anti-interference ability. Finally, verification was conducted through simulation.

Finally, stability analysis was conducted on the cascaded observer. Experiments were carried out on a parallel stable platform with six degrees of freedom involving rotation and translation. In comparison to traditional PID and ADRC control methods, the proposed control strategy not only endows the stable platform with strong antiload disturbance capability but also exhibits faster response speed and higher stability accuracy.

A new error attenuation function is designed to address the lack of smoothness at d in the error attenuation function of the ADRC controller, reducing the system ripple caused by it. Finally, a combination of linear and nonlinear ESOs is introduced to enhance the system's response speed and its ability to observe noise and load disturbances. Stability analysis of the cascade observer is carried out, and experiments are conducted on a six-degree-of-freedom parallel stable platform with both rotational and translational motion.

This paper aims to propose numerical-based and experiment-based identification processes, accounting for uncertainties to identify structural parameters, in a wave propagation framework.

A variant of the inhomogeneous wave correlation (IWC) method is proposed. It consists on identifying the propagation parameters, such as the wavenumber and the wave attenuation, from the frequency response functions. The latters can be computed numerically or experimentally. The identification process is thus called numerical-based or experiment-based, respectively. The proposed variant of the IWC method is then combined with the Latin hypercube sampling method for uncertainty propagation. Stochastic processes are consequently proposed allowing more realistic identification.

The proposed variant of the IWC method permits to identify accurately the propagation parameters of isotropic and composite beams, whatever the type of the identification process in which it is included: numerical-based or experiment-based. Its efficiency is proved with respect to an analytical model and the Mc Daniel method, considered as reference. The application of the stochastic identification processes shows good agreement between simulation and experiment-based results and that all identified parameters are affected by uncertainties, except damping.

The proposed variant of the IWC method is an accurate alternative for structural identification on wide frequency ranges. Numerical-based identification process can reduce experiments’ cost without significant loss of accuracy. Statistical investigations of the randomness of identified parameters illustrate the robustness of identification against uncertainties.

Identification in a regression discontinuity (RD) design hinges on the discontinuity in the probability of treatment when a covariate (assignment variable) exceeds a known threshold. If the assignment variable is measured with error, however, the discontinuity in the relationship between the probability of treatment and the observed mismeasured assignment variable may disappear. Therefore, the presence of measurement error in the assignment variable poses a challenge to treatment effect identification. This chapter provides sufficient conditions to identify the RD treatment effect using the mismeasured assignment variable, the treatment status and the outcome variable. We prove identification separately for discrete and continuous assignment variables and study the properties of various estimation procedures. We illustrate the proposed methods in an empirical application, where we estimate Medicaid takeup and its crowdout effect on private health insurance coverage.

This paper aims to present a method for improving the state estimation of a robot in the presence of noise measurement, which can improve the performance of the robot controller.

In this work, a novel nonlinear tracking differentiator (NTD) was formulated to solve the problems of phase lag, low stability and amplitude attenuation faced by traditional tracking differentiators, which can be used for the state estimation of a robot. Based on the user-defined function stu() with linear and nonlinear characteristics, the authors establish a new acceleration function of NTD and confirm its global asymptotic stability by using the Lyapunov method and the system equivalence method. Phase plane analysis shows that the origin is its stable nodal point or focus point and uncovers the basic constraint conditions for parameter regulation. In addition, the convergence property and robustness performance against noises are studied by describing function method.

Comparative simulations, robot state estimation experiments and joint trajectory tracking experiments have indicated that NTD proposed integrates tracking rapidness, accuracy and transitional stability and has high approximation and filtering effects on generalized derivatives of the signal, which contribute to an excellent performance of robot controller in stability and response speed in practice.

The main contribution of this paper lies in the design of a novel NTD, which successfully improves the state estimation of a robot joint in noisy surroundings, the tracking performance of robot controller and the stability of the system.

The purpose of this paper is to derive the Trefftz functions (T-functions) for the Pennes’ equation and for the single-phase-lag (SPL) model (hyperbolic equation) with perfusion and then comparing field of temperature in a flat slab made of skin in the case when perfusion is taken into account, with the situation when a Fourier model is considered. When considering the process of heat conduction in the skin, one needs to take into account the average values of its thermal properties. When in biological bodies relaxation time is of the order of 20 s, the thermal wave propagation appears. The initial-boundary problems for Pennes’ model and SPL with perfusion model are considered to investigate the effect of the finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation. As a reference model, the solution of the classic Fourier heat transfer equation for the considered problems is calculated. A heat flux has direction perpendicular to the surface of skin, considered as a flat slab. Therefore, the equations depend only on time and one spatial variable.

First of all the T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. Then, an approximate solutions of the problems are expressed in the form of a linear combination of the T-functions. The T-functions satisfy the equation modeling the problem under consideration. Therefore, approximating a solution of a problem with a linear combination of n T-functions one obtains a function that satisfies the equation. The unknown coefficients of the linear combination are obtained as a result of minimization of the functional that describes an inaccuracy of satisfying the initial and boundary conditions in a mean-square sense.

The sets of T-functions for the Pennes’ equation and for the SPL model with perfusion are derived. An infinite set of these functions is a complete set of functions and stands for a base functions layout for the space of solutions for the equation used to generate them. Then, an approximate solutions of the initial-boundary problem have been found and compared to find out the effect of finite velocity of heat in the skin, perfusion and thickness of the slab on the rate of the thermal wave attenuation.

The methods used in the literature to find an approximate solution of any bioheat transfer problems are more complicated than the one used in the presented paper. However, it should be pointed out that there is some limitation concerning the T-function method, namely, the greater number of T-function is used, the greater condition number becomes. This limitation usually can be overcome using symbolic calculations or conducting calculations with a large number of significant digits.

The T-functions for the Pennes’ equation and for the SPL equation with perfusion have been reported in this paper for the first time. In the literature, the T-functions are known for other linear partial differential equations (e.g. harmonic functions for Laplace equation), but for the first time they have been derived for the two aforementioned equations. The results are discussed with respect to practical applications.

The aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).

For designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.

The major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.

In practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.

Designing control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

In this paper, improvements in reducing transmitted accelerations in a full vehicle are obtained by optimizing the gain parameters of an active control in a roughness road profile.

For a classically designed linear quadratic regulator (LQR) control, the vibration attenuation performance will depend on weighting matrices Q and R. A methodology is proposed in this work to determine the optimal elements of these matrices by using a genetic algorithm method to get enhanced controller performance. The active control is implemented in an eight degrees of freedom (8-DOF) vehicle suspension model, subjected to a standard ISO road profile. The control performance is compared against a controlled system with few Q and R parameters, an active system without optimized gain matrices, and an optimized passive system.

The control with 12 optimized parameters for Q and R provided the best vibration attenuation, reducing significantly the Root Mean Square (RMS) accelerations at the driver’s seat and car body.

The research has positive implications in a wide class of active control systems, especially those based on a LQR, which was verified by the multibody dynamic systems tested in the paper.

Better active control gains can be devised to improve performance in vibration attenuation.

The main contribution proposed in this work is the improvement of the Q and R parameters simultaneously, in a full 8-DOF vehicle model, which minimizes the driver’s seat acceleration and, at the same time, guarantees vehicle safety.

The purpose of this paper is to address the synthesis and experimental application of a generalized predictive control (GPC) technique on an Orthoglide robot.

The control strategy is composed of two control loops. The inner loop aims at linearizing the nonlinear robot dynamics using feedback linearization. The outer loop tracks the desired trajectory based on GPC strategy, which is robustified against measurement noise and neglected dynamics using Youla parameterization.

The experimental results show the benefits of the robustified predictive control strategy on the dynamical performance of the Orthoglide robot in terms of tracking accuracy, disturbance rejection, attenuation of noise acting on the control signal and parameter variation without increasing the computational complexity.

The paper shows the implementation of the robustified predictive control strategy in real time with low computational complexity on the Orthoglide robot.

The computational accuracy and performance of finite-difference time-domain (FDTD) methods are affected by the implementation of approximating derivative formulae in diverse ways. This study aims to focus on FDTD models featuring material dispersion with negligible losses and investigates two specific aspects that, until today, are usually examined in the context of non-dispersive media only. These aspects pertain to certain abnormal characteristics of coarsely resolved electromagnetic waves and the selection of the proper time-step size, in the case of a high-order discretization scheme.

Considering a Lorentz medium with negligible losses, the propagation characteristics of coarsely resolved waves is examined first, by investigating thoroughly the numerical dispersion relation of a typical discretization scheme. The second part of the study is related to the unbalanced space-time errors in FDTD schemes with dissimilar space-time approximation orders. The authors propose a remedy via the suitable choice of the time-step size, based on the single-frequency minimization of an error expression extracted, again, from the scheme’s numerical dispersion formula.

Unlike wave propagation in free space, there exist two parts of the frequency spectrum where waves in a Lorentz medium experience non-physical attenuation and display non-changing propagation constants, due to coarse discretization. The authors also show that an optimum time-step size can be determined, in the case of the (2,4) FDTD scheme, which minimizes the selected error formula at a specific frequency point, promoting more efficient implementations.

Unique characteristics displayed by discretized waves, which have been known for non-dispersive media, are examined and verified for the first time in the case of dispersive materials, thus completing the comprehension of the space-time discretization impact on simulated quantities. In addition, the closed-form formula of the optimum time-step enables the efficient implementation of the (2,4) FDTD method, minimizing the detrimental influence of the low-order temporal integration.

The purpose of this paper is to enhance consistent partial least squares (PLSc) to yield consistent parameter estimates for population models whose indicator blocks contain a subset of correlated measurement errors.

Correction for attenuation as originally applied by PLSc is modified to include a priori assumptions on the structure of the measurement error correlations within blocks of indicators. To assess the efficacy of the modification, a Monte Carlo simulation is conducted.

In the presence of population measurement error correlation, estimated parameter bias is generally small for original and modified PLSc, with the latter outperforming the former for large sample sizes. In terms of the root mean squared error, the results are virtually identical for both original and modified PLSc. Only for relatively large sample sizes, high population measurement error correlation, and low population composite reliability are the increased standard errors associated with the modification outweighed by a smaller bias. These findings are regarded as initial evidence that original PLSc is comparatively robust with respect to misspecification of the structure of measurement error correlations within blocks of indicators.

Introducing and investigating a new approach to address measurement error correlation within blocks of indicators in PLSc, this paper contributes to the ongoing development and assessment of recent advancements in partial least squares path modeling.