Estimation of the Hankel Singular Values of Fractional-Order Systems

This paper applies the Rayleigh-Ritz method to approximating the Hankel singular values of fractional-order systems. The algorithm is presented, and estimates of the first ten Hankel singular values of G(s) = 1/(sq+1) for several values of q ∈ (0, 1] are given. The estimates are computed by restricting the operator domain to a finite-dimensional space. The Hankel-norm estimates are found to be within 15% of the actual values for all q ∈ (0, 1].

A New CRONE Suspension: More Compact and More Efficient: Part 2—Synthesis and Achievement

In a vibration isolation context, fractional derivative can be used to design suspensions which allow to obtain similar performances in spite of parameters uncertainties. This paper presents the synthesis and the achievement of a new Hydractive CRONE suspension system. After the study of the different constraint in suspension in the first paper, the ideal transfer function of the hydractive CRONE suspension is created and simulated in different case. Then a method to determine the technological parameters is proposed. A parallel arrangement of dissipative and capacitive components and a gamma arrangement are compared. They lead to the same unusual performances: the stability degree robustness and the rapidity robustness.

Path Tracking Design by Fractional Prefilter Extension to Square MIMO Systems

The aim of this paper concerns motion control and robust path tracking. An approach based on fractional prefilter synthesis was already developed. It allows tracking optimization according to the fractional derivation order, the actuators physical constraints and the control loop frequency bandwidth. The purpose of this paper is the extension of this approach to multivariable systems. A non integer prefilter synthesis methodology for square MIMO systems (Multi-Input, Multi-Output) is presented. It is based on the MIMO-QFT robust synthesis methodology, taking into account of the plant uncertainties. MIMO-QFT robust synthesis methodology is based on multiple SISO (MISO systems) synthesis by considering the loop couplings. The SISO-QFT synthesis methodology can be then used for each SISO synthesis. Then the prefilters are synthesized. The prefilter parameter optimization is founded on the prefilter output error integral minimization, taking into account of the actuators physical constraints and the tracking performance specifications. An application example is given.

Minimum Energy Control of Multibody Systems Utilizing Storage Elements

In this paper, we consider the problem to minimize the energy consumption for controlled multibody systems utilizing passive elastic elements for energy storage useful for robot systems in manufacturing. Firstly, based on the linearized equations of motion, we analyze the relationship between the consumed energy and the operating time, and the optimal trajectory using optimal control theory. Then, we verify the analytical solution by comparing with the numerical one computed considering the full nonlinear dynamics. After that we derive a condition for the operating time to be optimal, and propose the optimal design method for springs. Finally, we show the effectiveness of the design method by applying it to a 2DOF manipulator.

Time Fractional Differential Equation Model With Random Derivative Order

This paper proposes a new type of fractional differential equation model, named time fractional differential equation model, in which noise term is included in the time derivative order. The new model is applied to anomalous relaxation and diffusion processes suffering noisy field. The analysis and numerical simulation results show that our model can well describes the feature of these processes. We also find that the scale parameter and the frequency of the noise play a crucial role in the behaviors of these systems. At the end, we recognize some potential applications of this new model.

On the Stability Properties of a Periodically Forced, Time-Varying Mass System

In this paper the forced vibrations of a linear, single degree of freedom oscillator (sdofo) with a time-varying mass will be studied. The forced vibrations are due to small masses which are periodically hitting and leaving the oscillator with different velocities. Since these small masses stay for some time on the oscillator surface the effective mass of the oscillator will periodically vary in time. Not only solutions of the oscillator equation will be constructed, but also the stability properties, and the existence of periodic solutions will be discussed.

A Stochastic Approach to Integrated Vehicle Reliability Prediction

This paper addresses some aspects of an on-going multiyear research project of GP Technologies in collaboration with University of Wisconsin-Madison for US Army TARDEC. The focus of this research project is to enhance the overall vehicle reliability prediction process. A combination of stochastic models for both the vehicle and operational environment are utilized to determine the range of the system dynamic response. These dynamic results are used as inputs into a finite element analysis of stresses on subsystem components. Finally, resulting stresses are used for damage modeling and life and reliability predictions. This paper describes few selected aspects of the new integrated ground vehicle reliability prediction approach. The integrated approach combines the computational stochastic mechanics predictions with available statistical experimental databases for assessing vehicle system reliability. Such an integrated reliability prediction approach represents an essential part of an intelligent virtual prototyping environment for ground vehicle design and testing.

A New CRONE Suspension: More Compact and More Efficient: Part 1—Problematics and Specifications

This paper presents, in 2 parts, a new CRONE suspension approach. The first part defines the problematics in suspension and gives the different conditions to overcome it. Then in the second paper a new CRONE suspension system is synthesized based on the conclusion of this paper. So, here, is presented how the variations of mass act on the classical suspension and how tools can be set up to simulate the influence of this variation without to choose the technological structure. Then a criterion on the level of wheel holding is established.

Design of a Four Legged Parallel Mechanism to Improve the Dexterity of Walking Robot

This paper designs a four legged parallel mechanism to improve the dexterity of three layered parallel walking robot. Topology design is conducted for a leg mechanism composed of four legs, base and ground, which constitute a redundant parallel mechanism. This mechanism is subdivided into four sub-mechanism composed of three legs. A motor vector is adopted to determine the 6×8 Jacobian of the redundant parallel mechanism and the 6×6 Jacobian of the sub-mechanisms, respectively. The condition number of the Jacobian matrix is used as an index to measure a dexterity. We analyze the condition numbers of the Jacobian over the positional and orientational walking space. The analytical results show that a sub-mechanism has lots of singularities within workspace but they are removed by a redundant parallel mechanism improving the dexterity. This paper presents a parallel typed walking robot to enlarge walking space and stability region. Seven types of three layered walking robots are designed by inserting an intermediate mechanism between the upper and the lower legged parallel mechanisms. They provide various types of gaits to walk rough terrain and climb over a wall with small degrees of freedom.

The Modeling of Great Salt Lake Elevation Time Series Based on ARFIMA With Stable Innovations

Great Salt Lake (GSL) is the largest salt lake in the western hemisphere, the fourth-largest terminal lake in the world. The elevation of Great Salt Lake has critical effect on the people who live nearby and their properties. It is crucial to build an exact model of GSL elevation time series in order to predict the GSL elevation precisely. Although some models, such as FARIMA or ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity), have been built to characterize the variation of Great Salt Lake elevation, these models can not characterize it perfectly. Therefore, it became a key point to build a more appropriate model of GSL elevation time series. In this paper a new model based on fractional autoregressive integrated moving average (ARFIMA) with Stable innovations is applied to analyze the data and predict the future levels. From the analysis we can see that the new model can characterize GSL elevation time series more accurately. The new model will be beneficial to predict GSL elevation more precisely.