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Table Of Integrals Series And Products

Nonlinear Oscillations: Exact Solutions and their Approximations

https://hal.archives-ouvertes.fr/hal-00555464/document

Interval observers for linear time-invariant systems with disturbances

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

Neural Networks-Based Adaptive Finite-Time Fault-Tolerant Control for a Class of Strict-Feedback Switched Nonlinear Systems

Control: A perspective

This paper proposes an adaptive control for vehicle active suspensions with unknown nonlinearities (eg, nonlinear springs and piecewise dampers) A prescribed performance function that characterizes the convergence rate, maximum overshoot, and steady-state error is incorporated into the control design to stabilize the vertical and pitch motions, such that both the transient and steady-state suspension response are guaranteed Moreover, a novel adaptive law is used to achieve precise estimation of essential parameters (eg, mass of vehicle body and moment of inertia for pitch motion), where the parameter estimation error is obtained explicitly and then used as a new leakage term Theoretical studies prove the convergence of the estimated parameters, and compare the suggested controller with generic adaptive controllers using the gradient descent and e-modification schemes In addition to motion displacements, dynamic tire loads and suspension travel constraints are also considered Extensive comparative simulations on a dynamic simulator consisting of commercial vehicle simulation software Carsim 81 and MATLAB Simulink are provided to show the efficacy of the proposed control, and to illustrate the improved performance

/pdf/active-adaptive-estimation-and-control-for-vehicle-2gzl6epfz7.pdf

Active Adaptive Estimation and Control for Vehicle Suspensions With Prescribed Performance

This paper investigates the possibility of improving the performance of railway vehicle suspensions by incorporating a newly developed mechanical device known as the inerter A comparative study of several low-complexity passive suspension layouts is made Improved performance for the lateral and vertical ride comfort, as well as lateral body movement when curving are demonstrated in comparison with the conventional suspension layout The constraints imposed are to maintain the same level of other performance metrics The calculations and optimisations are based on linearised plan-view and side-view high-speed train mathematical models

Passive suspensions incorporating inerters for railway vehicles

This paper describes how an inerter-based device for structural vibration suppression can be realized using an electromagnetic transducer such as a linear motor. When the motor shaft moves, a difference of voltage is generated across the transducer coil. The voltage difference is proportional to the relative velocity between its two terminals. The electromagnetic transducer will exert a force proportional to current following the Lorentz principle if the circuit is closed around the transducer coil. If an electronic circuit consisting of a capacitor, an inductance and a resistance with the appropriate configuration is connected, the resulting force reflected back into the mechanical domain is equivalent to that achieved by a mechanical inerter-based device. The proposed configuration is easy to implement and very versatile, provided a high quality conversion system with negligible losses. With the use of electromagnetic devices, a new generation of vibration absorbers can be realized, for example in the electrical domain it would be relatively uncomplicated to synthesize multi-frequency or real time tunable vibration absorbers by adding electrical components in parallel. In addition by using resistance emulators in the electrical circuits, part of the absorbed vibration energy can be converted into usable power. Here an electromagnetic tuned inerter damper (E-TID) is tested experimentally using real time dynamic substructuring. A voltage compensation unit was developed in order to compensate for coil losses. This voltage compensation unit requires power, which is acquired through harvesting from the vibration energy using a resistance emulator. A power balance analysis was developed in order to ensure the device can be self sufficient. Promising experimental results, using this approach, have been obtained and are presented in this paper. The ultimate goal of this research is the development of autonomous electromagnetic vibration absorbers, able to harvest energy, convert it into usable power, and use it for vibration control and health monitoring.

https://iopscience.iop.org/article/10.1088/0964-1726/24/5/055015/pdf

An electromagnetic inerter-based vibration suppression device

Summary

In this paper, the use of a tuned inerter damper (TID) as a vibration absorber is studied numerically and experimentally, with civil engineering applications in mind. Inerters complete the analogy between mechanical and electrical networks, as the mechanical element equivalent to a capacitor and were developed in the 2000s. Initially, inerters were used for applications in automotive engineering, where they are known as J-dampers. Recently, research has suggested that inerter-based networks could be used for civil engineering applications, offering interesting advantages over traditional tuned mass dampers. In the civil engineering context, research has been mainly theoretical, considering ideal inerters. Because the dynamics of an inerter device include nonlinearities, especially at the low frequencies associated with civil engineering applications, the performance of the TID device using an off-the-shelf inerter has been experimentally tested in the work presented here. The chosen system, comprising a host structure with a TID attached to it, was tested using real-time dynamic substructuring (RTDS) or hybrid testing. The inerter was tested physically, while the remaining components of the TID device, the spring and damper, together with the host structure, were simulated numerically. Displacements and forces at the interface between numerical and physical components are updated in real time. This numerical–physical split allows the optimisation of the TID parameters, because the values of the spring and the damper can be changed without altering the experimental setup. In addition, this configuration takes into account the inerter's potentially complex dynamics by testing it experimentally, together with the characteristics of the host structure. Developing RTDS tests for physical inertial substructures, where part of the fed back interface forces are proportional to acceleration, is a challenging task because of delays arising at the interface between the experimental and the numerical substructures. Problems associated with stability issues caused by delay and causality arise, because we are dealing with neutral and advanced delayed differential equations. A new approach for the substructuring algorithm is proposed, consisting of feeding back the measured force deviation from the ideal inerter instead of the actual force at the interface. The experimental results show that with appropriate retuning of the components in the TID device, the performance in the TID incorporating the real inerter device is close to the ideal inerter device. © 2016 The Authors. Structural Control and Health Monitoring published by John Wiley & Sons, Ltd.

/pdf/assessing-the-effect-of-nonlinearities-on-the-performance-of-48nhod3vpi.pdf

Assessing the effect of nonlinearities on the performance of a tuned inerter damper

This paper classifies the positive-real biquadratic functions which can be realized by five-element networks. The concept of regular positive-real functions is introduced to facilitate this classification. Networks are grouped into quartets which may sometimes reduce to two or one network(s). It is shown that a biquadratic can be realized by a series-parallel network with two reactive elements if and only if it is regular. Moreover, there are two such network quartets which can realize all regular biquadratics. It is shown that the only five-element networks which can realize nonregular biquadratics can be arranged into three network quartets. The quartets comprise: 1) two bridge networks with two reactive elements; 2) four series-parallel networks with three reactive elements; and 3) two bridge networks with three reactive elements. The necessary and sufficient realizability conditions are derived for each of these networks. The results are motivated by an approach to passive mechanical control which makes use of the inerter device.

Jason Zheng Jiang

Papers

Active Adaptive Estimation and Control for Vehicle Suspensions With Prescribed Performance

Passive suspensions incorporating inerters for railway vehicles

An electromagnetic inerter-based vibration suppression device

Assessing the effect of nonlinearities on the performance of a tuned inerter damper

Regular Positive-Real Functions and Five-Element Network Synthesis for Electrical and Mechanical Networks