Dynamic analysis and control of strip mill vibration under the coupling effect of roll and rolled piece

According to the “Hill rolling force formula”, taking particular account of the influence from horizontal vibration of rolled piece in roll gap, a dynamic rolling force model is analyzed. Considering the interaction between vibration of strip and roll, the dynamic vibration model of rolling mill is established. On this basis, the time delayed feedback is introduced to control the vibration of the roll system. The amplitude frequency response of the coupled vibration control equation is obtained by using the multiple scales method. Different time delay parameters are selected to test the control effect. Research results show that the unstable vibration of the roll system can be suppressed with appropriate time delay feedback parameters. Because it is simpler and has good control effect in solving nonlinear mechanical vibration, so these results will make a difference for the research of strip mill vibration, and provide theoretical basis for strip steel production

The Effect of Time-Delay Feedback Controller on an Electrically Actuated Resonator

This paper presents a study of the effect of a time-delay feedback controller on the dynamics of a Microelectromechanical systems (MEMS) capacitor actuated by DC and AC voltages. It is shown that negative time-delay feedback control gain can lead to an unstable system, even if AC voltage is relatively small compared to DC voltage. Perturbation method is utilized to present analytically the nonlinear dynamic characteristics of the MEMS capacitor. Agreements among the results of a shooting technique, long-time integration, basin of attraction analysis with the perturbation method are achieved

Cavity solitons in vertical-cavity surface-emitting lasers

We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a solitary localized structure that is stationary and stable in the absence of feedback. We focus our analysis on an experimentally relevant system namely the Vertical-Cavity Surface-Emitting Laser (VCSEL). In the absence of the delay feedback we present experimental evidence of stationary localized structures in a 80 $\mu$m aperture VCSEL. The spontaneous formation of localized structures takes place above the lasing threshold and under optical injection. Then, we consider the effect of the time-delayed optical feedback and investigate analytically the role of the phase of the feedback and the carrier lifetime on the self-mobility properties of the localized structures. We show that these two parameters affect strongly the space time dynamics of two-dimensional localized structures. We derive an analytical formula for the threshold associated with drift instability of localized structures and a normal form equation describing the slow time evolution of the speed of the moving structure.Comment: 7 pages, 5 figure

T-S Fuzzy H∞ Tracking Control of Input Delayed Robotic Manipulators

Time delays are often encountered by practical control systems while they are acquiring, processing, communicating, and sending signals. Time delays may affect the system stability and degrade the control system performance if they are not properly dealt with. Taking the classical robot control problem as an example, the significant effect of time delay on the closed-loop system stability has been highlighted in the bilateral teleoperation, where the communication delay transmitted through a network medium has been received widespread attention and different approaches have been proposed to address this problem (Hokayem and Spong, 2006). In addition, examples like processing delays in visual systems and communication delay between different computers on a single humanoid robot are also main sources that may cause time delays in a robotic control system (Chopra, 2009), and the issue of time delay for robotic systems has been studied through the passivity property. For systems with time delays, both delay dependent and delay independent control strategies have been extensively studied in recent years, see for example (Xu and Lam, 2008) and references therein. For the control of nonlinear time delay systems, model based Takagi- Sugeno (T-S) fuzzy control (Tanaka and Wang, 2001; Feng, 2006; Lin et al., 2007) is regarded as one of the most effective approach because some of linear control theory can be applied directly. Conditions for designing such kinds of controllers are generally expressed as linear matrix inequalities (LMIs) which can be efficiently solved by using most available software like Matlab LMI Toolbox, or bilinear matrix inequalities (BMIs) which could be transferred to LMIs by using algorithms like iteration algorithm or cone complementary linearisation algorithm. From the theoretical point of view, one of the current focus on the control of time delay systems is to develop less conservative approaches so that the controller can stabilise the systems or can achieve the defined control performance under bigger time delay

Postural control: learning to balance and responses to mechanical and sensory perturbations

The purpose of the current research was to examine how a novel balance task is learnt by individuals with a mature neurological system, and to investigate the responses of experienced hand balancers to mechanical and sensory perturbations. Balance in each posture was assessed by various techniques, including: traditional measures of centre of pressure, nonlinear time series analysis of centre of pressure, estimates of feedback time delay from cross correlations and delayed regression models, and calculation of small, medium, and large movement corrections. Data from this study suggests that the best balance metric for distinguishing between each of the balance conditions was the traditional balance measure of sway velocity. However, sway velocity cannot provide any further information on the underlying process of balance. Nonlinear measures of balance offer insight into the underlying deterministic processes that control balance, offering measures of system determinism, complexity, and predictability. Assessments of feedback time delay and movement corrections provide both an insight into the control of posture and help distinguish one condition from another. Both feedback time delay and movement corrections and magnitudes may be used simultaneously to delve further into the control of posture. Delayed regression models seem to be an appropriate and useful tool for estimating feedback time delays during balance. Findings support the use of the third term in the adapted regression model as a means of estimating the effect of passive stiffness on feedback time delay. Generally, with increased duration in handstand subjects displayed reduced sway as measured by traditional measures of balance. A more marked change in nonlinear measures of balance can be seen, with quicker reductions in variance for some nonlinear measures of balance than in the traditional measures. It may be that more pronounced changes in nonlinear measures represent changes in the subjects underlying process of postural control, whereas less pronounced changes in traditional measures relate more to their general ability or performance in the balance task

Prediction of the dynamic oscillation threshold in a clarinet model with a linearly increasing blowing pressure

14 pagesInternational audienceReed instruments are modeled as self-sustained oscillators driven by the pressure inside the mouth of the musician. A set of nonlinear equations connects the control parameters (mouth pressure, lip force) to the system output, hereby considered as the mouthpiece pressure. Clarinets can then be studied as dynamical systems, their steady behavior being dictated uniquely by the values of the control parameters. Considering the resonator as a lossless straight cylinder is a dramatic yet common simplification that allows for simulations using nonlinear iterative maps. In this paper, we investigate analytically the effect of a time-varying blowing pressure on the behavior of this simplified clarinet model. When the control parameter varies, results from the so-called dynamic bifurcation theory are required to properly analyze the system. This study highlights the phenomenon of bifurcation delay and defines a new quantity, the dynamic oscillation threshold. A theoretical estimation of the dynamic oscillation threshold is proposed and compared with numerical simulations

Reheat Turbine LFC of Power Systems with Multiple Delays Based on Sliding Mode Techniques

This paper considers the growing effect of reheat turbine delays in a power system with multiple delays and nonlinear disturbance. In order to improve the operating condition of the systems and avoid the destabilizing effects of time delay, a model representation for reheat turbine delay is developed where a multiple delayed nonlinear term is used to describe disturbances. On this basis, an admissible upper bound is provided based on the Lyapunov Razumikhin theorem and an acceptable ultimate bound is calculated for the load disturbance. An improved load frequency sliding mode control (SMC) is synthesized such that the controlled system is uniformly untimately stable even in the presence of time delays and nonlinear disturbances. Effectiveness of the proposed method is tested by simulation via an isolated power system supplying a service load

Using time delay in the nonlinear oscillations of magnetic levitation for simultaneous energy harvesting and vibration suppression

In this paper, the nonlinear oscillations of magnetic levitation in the presence of a time delay is investigated, with the purpose of simultaneous energy harvesting and vibration suppression. To harvest energy, a coil with seven layers of 36 gauge wire wound around the outer casing is utilized. Although the proposed control feedback consumes some power, the results show the harvestable power can be much larger than the consumed power, which makes the proposed concept feasible. The first-order perturbation method is utilized to examine the possibility of energy harvesting and vibration suppression for different selections of the delay parameters, the distances between the magnets and the external load resistances. In addition, the stability map of the time-delayed control is analytically determined. The influence of the time delay parameters chosen from Single Periodic Solutions (SPS) and Multiple Periodic Solutions (MPS) on the vibration and power amplitudes is studied. It is shown that a point chosen from the MPS region enables the system to harvest power over a broad range of excitation frequencies. Also, the effect of the distance between the magnets on the frequency response of the system is examined. In addition, to select the optimum value for the distance between the magnets for different values of the time delay parameters, a parameter called the Perfection Rate (PR), which reflects both the electrical and mechanical behavior of the system, is used. Finally, it is shown that the presence of the time delay and a point chosen from the MPS region enables the system to harvest more power over a broad range of excitation frequency and to suppress higher levels of vibration, than for a point chosen from the SPS region and without time delay