Practical stability and controllability for nonlinear discrete time-delay systems

In this paper we study the practical asymptotic stability for a class of discrete-time time-delay systems via Razumikhin-type Theorems. Further estimations of the solution boundary and arrival time of the solution are also investigated based on practical stability. In addition, the proposed theorems are used to analyze the practical controllability of a general class of nonlinear discrete systems with input time delay. Some easy testing criteria for the uniform practical asymptotical stability are derived via Lyapunov function and Razumikhin technique. Finally a numerical example is given to illustrate the effectiveness of the proposed results

On the assessment of passive devices for structural control via real-time dynamic substructuring

In this work, the applicability of a dynamic testing technique known as real-time dynamic substructuring (RTDS) for the assessment of passive vibration suppression systems in seismic protection of buildings is analysed. RTDS is an efficient method for the assessment of dynamic and rate-dependent behaviour of systems subjected to dynamic excitation at real scale and in real scenarios. The actuators used in RTDS test introduce additional undesirable dynamics into the system, which are often not fully compensated for in the actuator controller—these dynamics are commonly approximated as a feedback delay. To guarantee the validity and accuracy of an RTDS simulation, a stability analysis of the substructured system that includes the feedback delay should be carried out. In this paper, we present explicit analyses that provide a dynamic characterization of the delay-induced phenomena in RTDS simulations when considering passive vibration suppression systems with strong nonlinearities. We present a complete set of closed-form expressions to describe the main phenomena because of delay in terms of dynamic stability in an RTDS simulation. Through an experimental study, we confirm the existence of self-sustained oscillations caused by very small delay in the feedback loop. This lead the system to instability in the form of high-frequency oscillations. Copyright © 2011 John Wiley & Sons, Ltd

Passivity control with adaptive feed-forward filtering for real-time hybrid tests

Real-time hybrid testing combines the reliability of experimental testing with the convenience of numerical simulation. The system to be tested is split into a physical substructure and a real-time numerical simulation which are coupled using actuators and sensors to transfer data at the interface in real-time. In order to achieve stable and accurate hybrid testing representative of the true system, high fidelity control is required at the substructure interface. However, actuators have a response lag which results in tracking errors and potential instability in hybrid tests. This paper investigates the effectiveness of a combined compensation strategy based on passivity control and adaptive feedforward filtering to improve stability, robustness and tracking performance in real-time hybrid testing. The combined strategy is adaptive and requires no prior information of the actuator dynamics unlike conventional transfer dynamics compensators in real-time hybrid testing. Moreover, the scheme requires no extra hardware making it inexpensive and applicable to a wide range of systems. Experimental results on a single degree of freedom nonlinear real-time hybrid test show the potency of the scheme in synchronising substructure displacements while improving stability. The scheme was also found to restore stability of hybrid tests inherently unstable due to actuator delay whilst phase lags of up to 58 degrees have been successfully mitigated in a lumped parameter mechanical oscillator system

A test of general relativity from the three-dimensional orbital geometry of a binary pulsar

Binary pulsars provide an excellent system for testing general relativity because of their intrinsic rotational stability and the precision with which radio observations can be used to determine their orbital dynamics. Measurements of the rate of orbital decay of two pulsars have been shown to be consistent with the emission of gravitational waves as predicted by general relativity, providing the most convincing evidence for the self-consistency of the theory to date. However, independent verification of the orbital geometry in these systems was not possible. Such verification may be obtained by determining the orientation of a binary pulsar system using only classical geometric constraints, permitting an independent prediction of general relativistic effects. Here we report high-precision timing of the nearby binary millisecond pulsar PSR J0437-4715, which establish the three-dimensional structure of its orbit. We see the expected retardation of the pulse signal arising from the curvature of space-time in the vicinity of the companion object (the `Shapiro delay'), and we determine the mass of the pulsar and its white dwarf companion. Such mass determinations contribute to our understanding of the origin and evolution of neutron stars.Comment: 5 pages, 2 figure

Long-Time Stability of Ni-Ti-Shape Memory Alloys for Automotive Safety Systems

In automotive a lot of electromagnetically, pyrotechnically or mechanically driven actuators are integrated to run comfort systems and to control safety systems in modern passenger cars. Using shape memory alloys (SMA) the existing systems could be simplified, performing the same function through new mechanisms with reduced size, weight, and costs. A drawback for the use of SMA in safety systems is the lack of materials knowledge concerning the durability of the switching function (long-time stability of the shape memory effect). Pedestrian safety systems play a significant role to reduce injuries and fatal casualties caused by accidents. One automotive safety system for pedestrian protection is the bonnet lifting system. Based on such an application, this article gives an introduction to existing bonnet lifting systems for pedestrian protection, describes the use of quick changing shape memory actuators and the results of the study concerning the long-time stability of the tested NiTi-wires. These wires were trained, exposed up to 4years at elevated temperatures (up to 140°C) and tested regarding their phase change temperatures, times, and strokes. For example, it was found that A P-temperature is shifted toward higher temperatures with longer exposing periods and higher temperatures. However, in the functional testing plant a delay in the switching time could not be detected. This article gives some answers concerning the long-time stability of NiTi-wires that were missing till now. With this knowledge, the number of future automotive applications using SMA can be increased. It can be concluded, that the use of quick changing shape memory actuators in safety systems could simplify the mechanism, reduce maintenance and manufacturing costs and should be insertable also for other automotive application

Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper derives new formulations for designing dominant pole placement based proportionalintegral-derivative (PID) controllers to handle second order processes with time delays (SOPTD). Previously, similar attempts have been made for pole placement in delay-free systems. The presence of the time delay term manifests itself as a higher order system with variable number of interlaced poles and zeros upon Pade approximation, which makes it difficult to achieve precise pole placement control. We here report the analytical expressions to constrain the closed loop dominant and nondominant poles at the desired locations in the complex s-plane, using a third order Pade approximation for the delay term. However, invariance of the closed loop performance with different time delay approximation has also been verified using increasing order of Pade, representing a closed to reality higher order delay dynamics. The choice of the nature of non-dominant poles e.g. all being complex, real or a combination of them modifies the characteristic equation and influences the achievable stability regions. The effect of different types of non-dominant poles and the corresponding stability regions are obtained for nine test-bench processes indicating different levels of open-loop damping and lag to delay ratio. Next, we investigate which expression yields a wider stability region in the design parameter space by using Monte Carlo simulations while uniformly sampling a chosen design parameter space. The accepted data-points from the stabilizing region in the design parameter space can then be mapped on to the PID controller parameter space, relating these two sets of parameters. The widest stability region is then used to find out the most robust solution which are investigated using an unsupervised data clustering algorithm yielding the optimal centroid location of the arbitrary shaped stability regions. Various time and frequency domain control performance parameters are investigated next, as well as their deviations with uncertain process parameters, using thousands of Monte Carlo simulations, around the robust stable solution for each of the nine test-bench processes. We also report, PID controller tuning rules for the robust stable solutions using the test-bench processes while also providing computational complexity analysis of the algorithm and carry out hypothesis testing for the distribution of sampled data-points for different classes of process dynamics and non-dominant pole types.KH acknowledges the support from the University Grants Commission (UGC), Govt. of India under its Basic Scientific Research (BSR) schem

Stability of delayed systems in structural control applications

This analyses the applicability of a quite novel methodology of experimental testing socalled Real-Time Dynamic Substructuring Test (RTDST) in the assessment of protection systems for natural hazards mitigation. RTDST allows testing critical components of structures at full-scale under realistic extreme loading conditions. Only those components where the nonlinearity behavior is concentrated are physically tested, whilst the remainder of the structure is simulated numerically. The main drawback of this technique lies in the unavoidable delays associated to the loop feeding back some experimental measurements to the numerical model. Such delays may cause instability during the test. This work is focused on testing passive control systems based on large-scale non linear fluid viscous dampers. Throughout a careful explicit stability analysis, we present a complete set of closed-form expressions to describe the dynamics of the main complex delay-induced phenomena exhibited for the delayed system. This analysis is addressed in the context of both classic stability theory for non-linear systems and the qualitative theory of Piecewise Smooth Dynamical Systems. The results obtained are also useful for other kind of mechanical systems where the response of some components is arriving with delay and may cause harmful effects on system behaviour. Semi-active control by MR dampers are examples of such systems. The theoretical results obtained were confirmed experimentally. When carrying out the experimental campaign, in fact, unexpected selfsustained oscillations were detected. This was caused by delays in the feedback loop, even when they are very small, unavoidably lead the system to self-sustained oscillations at high frequency