Lumped Delay Research Articles

Non-fragile robust output feedback control of uncertain active suspension systems with stochastic network-induced delay

The vehicle active suspension has attracted considerable attention owing to its great contributions to the vertical dynamics of vehicle. This paper investigates the non-fragile output feedback control problem of the uncertain vehicle active suspension with stochastic network-induced delay. Firstly, taking the variation of sprung and unsprung masses into consideration, an interval type-2 (IT-2) Takagi–Sugeno (T–S) fuzzy model is introduced to describe the nonlinear characteristics of active suspension systems (ASSs). Secondly, to ensure that the control strategy is practicable when some states are unmeasured, a novel output feedback method is proposed by employing a variable substitution approach. Meanwhile, in order to approximate the real physical conditions of the control system, the gain perturbations are taken into account. Thirdly, with regard to the complexity of signal transmission delay in network control process, a more generalized lumped delay form is employed to represent the network-induced delay. Moreover, to describe the stochasticity of lumped delay, a Markovian process is introduced. Finally, both numerical simulations and experimental tests are carried out to examine the effectiveness and practicability of the proposed controller.

Robust Gain-Scheduling Path Following Control of Autonomous Vehicles Considering Stochastic Network-Induced Delay

This paper concerns the robust gain-scheduling control issue for autonomous path following systems with stochastic network-induced delay. Firstly, to effectively approximate the highly nonlinear tire dynamics, the linear fractional transformation formulations are employed to describe the tire cornering stiffness with a norm-bounded uncertainty. Secondly, by taking the data dropout and delay encountered in signal computation and transmission into account, a more generalized lumped delay form is proposed to unify the time-varying data dropout and network-induced delay. Moreover, a Markovian process is presented to describe the lumped delay as a stochastic distribution. Thirdly, to address the issue of varying vehicle velocity, a linear parameter varying model is established to capture vehicle lateral behaviors. Based on the stochastic stability theory, a new robust gain-scheduling path following control method is proposed for the autonomous vehicles. Finally, the experimental study is presented to bridge the gap between the theoretical and practical investigations on path following control of autonomous vehicles, and results validate the superior performance of the proposed method compared with existing works.

Complete stability assessment of LTI systems with multiple constant-coefficient distributed delays using the improved frequency sweeping framework

The stability problem of linear time-invariant systems with multiple constant-coefficient distributed delays is investigated from a new perspective. We present an equivalent system with multiple lumped delays and then apply the Dixon resultant to determine the exact upper bound of the projected imaginary spectra of the system. We then adopt the improved frequency sweeping framework over the obtained range to get the kernel and offspring hypersurfaces (KOH). Furthermore, the singularity at the zero characteristic root is scrutinised, leading to what we call the stationary root boundary (SRB) in the domain of the delays. With these, we resort to the Cluster Treatment of Characteristic Roots (CTCR) paradigm to determine the complete stability map of the system with the complete knowledge of the KOH and SRB. Finally, the effectiveness of our proposed procedure is shown by two case studies.

RWRoute: An Open-source Timing-driven Router for Commercial FPGAs

One of the key obstacles to pervasive deployment of FPGA accelerators in data centers is their cumbersome programming model. Open source tooling is suggested as a way to develop alternative EDA tools to remedy this issue. Open source FPGA CAD tools have traditionally targeted academic hypothetical architectures, making them impractical for commercial devices. Recently, there have been efforts to develop open source back-end tools targeting commercial devices. These tools claim to follow an alternate data-driven approach that allows them to be more adaptable to the domain requirements such as faster compile time. In this paper, we present RWRoute, the first open source timing-driven router for UltraScale+ devices. RWRoute is built on the RapidWright framework and includes the essential and pragmatic features found in commercial FPGA routers that are often missing from open source tools. Another valuable contribution of this work is an open-source lightweight timing model with high fidelity timing approximations. By leveraging a combination of architectural knowledge, repeating patterns, and extensive analysis of Vivado timing reports, we obtain a slightly pessimistic, lumped delay model within 2% average accuracy of Vivado for UltraScale+ devices. Compared to Vivado, RWRoute results in a 4.9× compile time improvement at the expense of 10% Quality of Results (QoR) loss for 665 synthetic and six real designs. A main benefit of our router is enabling fast partial routing at the back-end of a domain-specific flow. Our initial results indicate that more than 9× compile time improvement is achievable for partial routing. The results of this paper show how such a router can be beneficial for a low touch flow to reduce dependency on commercial tools.

Quasi-Synchronization of Heterogeneous LC Circuits in Grid-Connected Systems With Intentionally Time-Varying Lumped Delays

This article is concerned with quasi-synchronization of grid-connected systems in electrical networks, where heterogeneous Inductance-Capacitance (LC) oscillators are coupled via electrical inductance subject to time-varying delays. Note that complete synchronization fails to be accomplished due to the existence of nonidentical parameters and quasi-synchronization cannot be achieved via non-delayed inductive coupling. A configuration of multiple heterogeneous LC oscillators with inductive coupling subject to time-varying lumped delay is first constructed by introducing an active delay intentionally. Then the complete-type Lyapunov-Krasovskii functionals (LKF) are constructed to investigate the exponential convergence of quasi-synchronization of LC oscillators in the presence of parameter mismatches utilizing the positive effects of interval time-varying delays. Some feasible synchronization criteria are derived. The gain matrix can be designed by solving a set of linear matrix inequalities combining an optimization algorithm. Finally, a numerical example of five LC oscillators in photovoltaic grid-connected system is given to demonstrate the effectiveness of the proposed method.

Stability criteria for a class of stochastic distributed delay systems

Abstract In the paper linear distributed delay stochastic systems are considered. Using theory of stochastic differential equations sufficient conditions for different kinds of stability are formulated and proved. The article attempts to generalise results presented in the paper [1] and thus theorems proved in [1] become a special case of a generalised approach. The considered class is wider - the function that influence dynamics of a problem can be a real solution of N-degree linear deterministic differential equation. Therefore the generalised reduction technique of distributed delay to lumped delay has to be applied. Criteria for numerous properties of the aforementioned class followed Mao theory designed for point delay systems [2, 3]

Relative controllability of nonlinear neutral systems with distributed and multiple lumped delays in control

In this paper we study the relative controllability of nonlinear neutral system with distributed and multiple lumped time varying delays in control. Using Schauder's fixed point theorem sufficient conditions for relative controllability in a given time interval are formulated and proved. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 565-570

Point delay methods applied to the investigation of stability for a class of distributed delay systems

The main target of this paper is to present criteria (adapted from the point delay systems) for the different kinds of stability, boundedness and existence of a stochastic attractor for a class of distributed delay differential stochastic equations. The new results are based on a technique of reduction of distributed delay to a lumped delay and Mao criteria for point delay equations.

Time delay systems applications in textile industry - Modelling of sliver drafting process

The paper deals with the textile sliver drafting process. It is shown that this process can be modelled as a non-linear time delay system with distributed delays. This model is linearized and distributed delays are converted into equivalent lumped delay system. An easy to apply method of distributed delay to lumped delay reduction is outlined as a by-product of this procedure. The main result of the paper is a model of important textile engineering process with time delays that has never been described in control engineering literature and that can be used as a basis for controller design. Thus, the paper opens a way of time delay systems theory applications to the field of textile engineering.

High-level DSP synthesis using concurrent transformations, scheduling, and allocation

This paper addresses high-level synthesis methodologies for dedicated digital signal processing (DSP) architectures used in the iterative Loop-based Minnesota Architecture Synthesis (MARS) design system. We present a novel concurrent scheduling and resource allocation algorithm which exploits inter-iteration and intra-iteration precedence constraints. The novel algorithm implicitly performs algorithmic transformations, such as pipelining and retiming, on the data-flow graphs during the scheduling process to produce solutions which are as good as those previously published and which executes in less time. MARS is capable of producing optimal and near-optimal schedules in fractions of seconds. Previous synthesis systems have focused on DSP algorithms which have single or lumped delays in the recursive loops. In contrast, MARS is capable of generating valid architectures for algorithms which have randomly distributed delays. MARS exploits these delays to produce more efficient architectures and allows our system to be more general. We are able to synthesize architectures which meet the iteration bound of any algorithm by unfolding, retiming, and pipelining the original data-flow graph.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>