Jason Zheng Jiang

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

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.

Passive suspensions incorporating inerters for railway vehicles

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.

Series-Parallel Six-Element Synthesis of Biquadratic Impedances

The object of this paper is to give a complete treatment of the realizability of positive-real biquadratic impedance functions by six-element series-parallel networks comprising resistors, capacitors, and inductors. This question was studied but not fully resolved in the classical electrical circuit literature. Renewed interest in this question arises in the synthesis of passive mechanical impedances. Recent work by the authors has introduced the concept of a regular positive-real functions. It was shown that five-element networks are capable of realizing all regular and some (but not all) nonregular biquadratic positive-real functions. Accordingly, the focus of this paper is on the realizability of nonregular biquadratics. It will be shown that the only six-element series-parallel networks which are capable of realizing nonregular biquadratic impedances are those with three reactive elements or four reactive elements. We identify a set of networks that can realize all the nonregular biquadratic functions for each of the two cases. The realizability conditions for the networks are expressed in terms of a canonical form for biquadratics. The nonregular realizable region for each of the networks is explicitly characterized.

Passive suspensions for ride quality improvement of two-axle railway vehicles

The aim of this paper is to investigate the possibility of improving the ride quality of a two-axle railway vehicle with a single-stage suspension by means of passive suspensions employing an inerter device. The inerter is a mechanical one-port element that is analogous to a capacitor in electrical circuits. The goal is to improve the ride quality in both the vertical and lateral motions in response to track irregularities. Performance benefits for several simple passive suspension layouts are demonstrated and compared with the conventional scheme. The elastic effects of the damper and inerter device are then taken into consideration for practical purposes. The optimum parameter values of the damper, inerter and the parameters representing the elastic effects provide guidance for mechanical design purposes.

Active Adaptive Estimation and Control for Vehicle Suspensions With Prescribed Performance

This paper proposes an adaptive control for vehicle active suspensions with unknown nonlinearities (e.g., 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 (e.g., 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 8.1 and MATLAB Simulink are provided to show the efficacy of the proposed control, and to illustrate the improved performance.

An electromagnetic inerter-based vibration suppression device

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.

Inerter-based configurations for main landing gear shimmy suppression

The work reported in this paper concentrates on the possibility of suppressing shimmy oscillations of landing gear more effectively using a linear passive suppression device incorporating inerter. The inerter is a one-port mechanical device with the property that the applied force is proportional to the relative acceleration between its terminals. A linear model of a Fokker 100 aircraft main landing gear equipped with a shimmy-suppression device is presented. Time-domain optimizations of the shimmy-suppression device are carried out using cost functions of the maximum amplitude and the settling time of torsional-yaw motion. Applying two types of excitations that trigger the shimmy oscillations, the performance advantages of inerter-based configurations for suppressing shimmy of main landing gear, together with corresponding parameter values, are identified.

On the Theorem of Reichert

Abstract This paper reworks and amplifies Reichert’s proof of his theorem (1969) which asserts that any impedance function of a one-port electrical network which can be realised with two reactive elements and an arbitrary number of resistors can be realised with two reactive elements and three resistors.

Experimental testing and modelling of a mechanical steering compensator

This paper describes experimental results for a prototype mechanical steering compensator for motorcycles which was manufactured at Cambridge University Engineering Department (CUED). The compensator realises a mechanical network consisting of inerters, dampers and a spring. The paper extends the previous work of Papageorgiou et al and presents frequency response testing results as well as model fitting and parameter estimation.

Synthesis of positive-real functions with low-complexity series-parallel networks

The purpose of this paper is to continue to develop the recently introduced concept of a regular positivereal function and its application to the classification of low-complexity two-terminal networks. This paper studies five- and six-element series-parallel networks with three reactive elements and presents a complete characterisation and graphical representation of the realisability conditions for these networks. The results are motivated by an approach to passive mechanical control which makes use of the inerter device.