Underdamped Second-order System Research Articles

Dynamic Soft Tissue Artifacts during Impulsive Loads: Measurement Errors Vary With Wearable Inertial Measurement Unit Sensor Design.

Characterize and model Inertial Measurement Unit (IMU) errors due to transient dynamic soft tissue artifacts excited by impulsive loads, such as foot strikes during running and jumping. We instrumented 10 participants (5 female, 5 male) with IMUs on the dominant leg. An ankle IMU measured reference vertical accelerations during impulsive loads and was cross-validated against vertical force measures. Two IMUs on the posterior shank and anterior shank were used to characterize errors caused by dynamic soft tissue artifacts with respect to the reference. Shank sensors' masses were varied to explore their effect on dynamic soft tissue artifacts. Both the posterior IMU and anterior IMU overestimated peak vertical accelerations during the impulsive load (gain of 2.18 ± 0.63 and 1.55 ± 0.35 respectively). The post- impulsive load oscillation duration and natural frequency varied with sensor mass according to an underdamped second-order system, with posterior IMU and anterior IMU durations of 326 ± 75ms and 151 ± 50ms respectively and natural frequencies of 9.79 ± 2.68Hz and 18.22 ± 12.10Hz respectively. Low-pass filtering reduced overestimation of peak vertical accelerations, but also attenuated the reference measure. Our study suggests dynamic soft tissue artifacts result in transient, but substantial measurement errors that may not be appropriately mitigated through low-pass filtering. However, these dynamic soft tissue artifacts can be modeled using an underdamped second-order system and used to estimate material properties of underlying soft tissue. We demonstrate that dynamic soft tissue artifacts can be modeled and potentially mitigated to improve accuracy in applications necessitating measurement of impulsive loads such as foot strikes.

Non-fragile control associated with exponential stability for unmanned surface vessels with the rudder failure and dynamic event-trigger

In this paper, non-fragile control associated with exponential stability for unmanned surface vessels(USVs) with the rudder failure and dynamic event-trigger is presented. To begin with, the event trigger and switch system are introduced, taking into account the distribution characteristics of faults and resource efficiency, and a class of independence-distributed random failure models are built. Furthermore, acknowledging the practical challenges associated with parameter uncertainties, USVs are used as uncertain Nomoto model(NM) and the rudder system is described with uncertain second-order underdamped system(UDS). Then, in the presence of dynamic disturbances, an appropriate non-fragile controller is proposed to demonstrate that the closed-loop system states can be exponentially stabilized through the application of the Lyapunov–Krasovskii functions(LKF) and Linear Matrix Inequalities (LMIs). Lastly, the simulation results confirmed that control design methods proposed are effective.

Gain Scheduled PI controller design using Multi-Objective Reinforcement Learning

Gain scheduling, a widely adopted control design approach, performs tasks by decomposing into sub-problems. It has found successful applications across diverse fields, including aerospace and industrial process control (Leith and Leithead (2000)). Reinforcement Learning (RL) has become increasingly significant in process control applications, thanks to the advancement of sophisticated algorithms and the rise in computational speeds. An attempt has been made to enhance the performance of a Proportional-Integral (PI) controller by integrating the benefits of both gain scheduling and RL. The manuscript focuses on designing a Gain Scheduled PI controller using Multi-Objective RL (GS-MORL). Proposing the training of multiple RL-based PI controllers with distinct objectives with customized reward functions to derive tuning parameters for each goal. The switching between these parameter sets is facilitated by a gain schedule variable. The controller parameters are adjusted based on the error between actual and desired responses. The aim is to enhance overall performance across various performance indices, including the integral of absolute error and time response specifications. The performance improvement from the proposed work has been demonstrated using two simulation case studies, one involving an underdamped second-order system and an integrating type steam turbine system. Comparative analysis against existing literature revealed superior performance across all indices.

A novel non-fragile [formula omitted] fault-tolerant course-keeping control for uncertain unmanned surface vehicles with rudder failures

This paper investigates the problem of non-fragile H∞ fault-tolerant course-keeping control (NFC) for uncertain unmanned surface vehicles (UUSV) with rudder failures. Firstly, due to the inevitable parameter perturbations in practice, the unmanned surface vehicles (USV) is modeled as a kind of uncertain Nomoto model, and an uncertain second-order under-damped system is used to describe the rudder system. Next, considering the distribution characteristic of failures, a distribution-dependent stochastic failure model is established and incorporated into the controller design. In order to investigate the fragile problems of the controller, a new non-fragile fault-tolerant scheme is given against multiplicative and additive controller gain perturbations. Finally, the effectiveness of the proposed methods is verified via two numerical examples.

Rolling Bearing Fault Diagnosis by Aperiodic Stochastic Resonance Under Variable Speed Conditions

The fault characteristic of rolling bearings under variable speed condition is a typical non-stationary stochastic signal. It is difficult to extract due to the interference of strong background noise makes the applicability of traditional noise reduction methods less. In this paper, an aperiodic stochastic resonance (ASR) method is proposed to study the fault diagnosis of rolling bearings under variable speed conditions. Based on numerical simulation, the effect of noise intensity and damping coefficient on the ASR of the second-order underdamped system is discussed, and an appropriate damping coefficient is found to reach the optimal ASR. The proposed method enhances the fault characteristic information of bearing fault simulation signal. Corresponding to rising-stationary and the stationary-declining running conditions, the method is verified by both simulated and experimental signals. It provides reference for fault diagnosis under variable speed condition.

Multivariable predictive functional control of a compound power-split hybrid electric vehicle

The Corun hybrid system (CHS) is a deeply coupled multiple-input–multiple-output (MIMO) hybrid system. The two inputs are the torques of the two motors. The two outputs are the carrier speed and transmission output torque. Using the traditional control method, the multi-objective control quality cannot be guaranteed because of the adopted static decoupling method and proportional–integral–derivative (PID) controllers. In this paper, the problems of the traditional control method are carefully analyzed, and a new control method is proposed. Instead of static decoupling, dynamic decoupling is adopted to improve the decoupling control effect. A predictive functional controller instead of a PID controller is adopted to deal with the pure delay caused by controller area network (CAN) communication. The tracking effect of the target value is further improved by predictive functional controllers. For the two decoupled subsystems, that is, the integral system and the second-order underdamped system, two predictive functional controllers are designed. The new control method was verified by simulations and tests. The results show that the new control method is superior to the traditional control method for CHS.

Genetic algorithm for dynamic parameters estimation of the machine tool worktable using the residual vibration signal

In this article, the residual vibration signal of the worktable of the machine tool is used to identify its dynamic parameters. By analyzing the time-domain characteristics of the residual vibration signal, it is found that the signal has the similar attenuation characteristics to the impulse response of the second-order underdamped system, so a new method for identifying the dynamic parameters of the worktable is proposed. In this method, the impulse response model of the second-order underdamped system is used to describe the residual vibration signal, so the parameter identification problem based on the time-domain signal is transformed into the optimization problem of the model parameters. Then, the dynamic parameters can be determined by using the genetic algorithm. The results of the genetic algorithm are compared with the results of the autoregressive moving average method, which is a commonly used parameter identification method based on the time-domain signal. It was found that the results of the model-based method proposed in this article are more accurate than the autoregressive moving average method.

Trajectory linearization-based robust course keeping control of unmanned surface vehicle with disturbances and input saturation

This article addresses the problem of course keeping for unmanned surface vehicle (USV) subject to rudder servo characteristics, disturbances, uncertainties and rudder saturation. A double loop robust compound control strategy is developed by incorporating finite-time uncertainty observer (FUO) and auxiliary dynamic system into trajectory linearization control (TLC). TLC is an effective robust control technique with simple design structure, which is used in the course control experiment of USV for the first time. In each loop, the FUO and auxiliary system are designed to compensate unknown lumped disturbances and input saturation, respectively. A nonlinear tracking differentiator (NTD) is concurrently introduced to realize differentiation and filtering for the reference command. Strict stability analysis indicates that the entire system is uniformly ultimately bounded (UUB). Results from simulations and experiments are presented to validate the developed strategy.

Reduced-Order Modeling and Design of Single-Stage LCL Compensated IPT System for Low Voltage Vehicle Charging Applications

In this paper, single-stage LCL inductive power transfer (IPT) system is proposed in low voltage vehicle charging applications to minimize the system complexity, and its reduced-order modeling and design approach is presented. To deal with the high-order resonant tank, the reduced-order methodology is applied throughout the paper, with which the behavior of resonant tank is investigated under multiple scales. Using the reduced-order time-domain model, the resonant waveform within switching period is accurately described with only one cycle's numerical computation. A novel parameter design principle for realizing ZVS condition and high averaged efficiency within full load range is then proposed and serves as parametric basis. Next, the low-order linear frequency-domain model is deduced using Extended Describing Function (EDF). It is found that six-order LCL-type system behaves as second-order underdamped system within frequency range of interest. Compared to existing models, the proposed reduced-order model features much more simplicity as it provides intuitive understanding into both steady and dynamic characteristic of the converter while facilitating the parameter and controller design. Through above work, the overall design consideration towards a single-stage LCL IPT system is elaborated. Finally, experimental results are given to verify accuracy of the models as well as the effectiveness of designed parameters and controller.

Generalized Optimal and Explicit PI/PID Tuning Formulas for Underdamped Second-order Systems

This study aims to propose generalized formulas in an explicit form to optimally tune the gains of the proportional-integral (PI) and proportional-integral-derivative (PID) controllers of an underdamped second-order system. Unlike other methods used in literature, the controller gains are tuned explicitly based on the known system parameters of the second-order system, namely: the damping ratio and the natural frequency. The proposed accurate and one-step formulas do not need any further effort to effectively control any given second-order system while keeping the desired performance indices within near-optimal specifications. The proposed work relies on a restricted deadbeat response criterion and cascaded surface curve fitting procedure to end by near-optimal controller gains tuning formulas. A particle swarm optimization (PSO) method is employed to optimize the primary tuned gains for wide-range of system frequency. The proposed formulas are tested and simulated to demonstrate their effectiveness with comparisons with the closest common related gains tuning methods. Based on the comprehensive analysis, the proposed work ensures 2% maximum percentage overshoot when the proposed formulas are adopted to tune the gains of the PID controllers. Different comparisons are carried out to show the effectiveness of the proposed work.

Effects of external perturbations on dynamic performance of carbon dioxide transcritical power cycles for truck engine waste heat recovery

Carbon dioxide transcritical power cycle (CTPC) systems are dynamically tested on a constructed test bench using an expansion valve. Effects of external perturbations of pump speed, expansion valve opening and engine conditions on dynamic performance of the CTPC systems are investigated with step changes. Dynamic characteristics are identified with rise time, settling time and overshoot. Results show that both a basic CTPC system and a CTPC system with a recuperator (R-CTPC) behave as a second-order underdamped system with the perturbations of pump speed and expansion valve opening. Overshoot or undershoot tends to appear in pressures when pump speed changes, while overshoot or undershoot occurs more noticeably in temperatures when expansion valve opening varies. Although the CTPC systems respond slowly with the perturbations of engine conditions, they have the ability to operate safely and produce power continuously. Therefore, the CTPC systems are robust when facing narrow fluctuations of heat sources while swift when required to make adjustments, showing great potential for truck engine waste heat recovery. Overall, current research gives a full understanding of the dynamic performance of the CTPC systems, which will provide references for dynamic model validation and possible control strategy identification.

Instability Analysis and Oscillation Suppression of Enhancement-Mode GaN Devices in Half-Bridge Circuits

This paper analyzes the problem of instability in enhancement-mode gallium nitride (GaN) transistors based half-bridge circuits. The instability may cause sustained oscillation, resulting in overvoltage, excessive electromagnetic interference (EMI), and even device breakdown. GaN devices operate in the saturation region when they conduct reversely during the dead time. Under the influence of parasitic parameters, the GaN-based half-bridge circuit exhibits positive feedback under certain conditions, thus, resulting in sustained oscillation. A small-signal model is proposed to study this positive feedback phenomenon. Like the second-order under-damped system, damping ratio is defined to determine the system's stability. Based on the model, the influence of circuit parameters on instability is investigated and guidelines to suppress the oscillation are given. Reducing the common-source inductance, increasing the gate resistance of the inactive switch or connecting a diode in parallel to the inactive switch are some effective ways to suppress the oscillation. Finally, the analyses are verified by both simulation and experiment.

Stochastic Resonance in Second-Order Underdamped System With Exponential Bistable Potential for Bearing Fault Diagnosis

Stochastic resonance (SR) as effective approach for weak signal detection has been widely used in bearing fault signal diagnosis. In this paper, a new method was proposed to detect fault signals, which consists of an exponential bistable potential model generalized by using a harmonic Potential (HP) model, a Gaussian potential (GP) model and second-order underdamped system. As the classical bistable SR (CBSR) has the disadvantage of output saturation, which will suppress the optimal signal-to-noise ratio (SNR) of the system, therefore, underdamped SR with exponential potential (UESR) and underdamped SR with classical bistable potential (UCSR) are applied to detect fault signal, respectively. Under the adiabatic condition, the analytical expression of the SNR is calculated for the UESR system driven by Gaussian white noise and periodic signal. Then, the effects of system parameters and the damping factor on analytical expression of SNR as a function of noise intensity for different parameters are studied, respectively. Finally, the proposed method is applied to detect simulated fault signals and actual bearing fault signals. The experimental results show that the proposed UESR method is superior to the UCSR method in fault signal diagnosis, such as larger output SNR and higher spectrum peaks at fault characteristic frequencies.

Periodic Signal Tracking for Lightly Damped Systems

The focus of this paper is on the development of time-delay filters to accomplish tracking of periodic signals with zero phase errors. The class of problems addressed include systems whose dynamics are characterized by lightly damped modes. A general approach for the zero-phase tracking of periodic inputs is presented followed by an illustration of single harmonic tracking of underdamped second-order systems with relative degree two. A general formulation of the approach is then posed for higher-order systems and systems including zeros. The paper concludes with the illustration of enforcing constraints to desensitize the time-delay filter to uncertainties in the location of the poles of the system and forcing frequencies. A numerical practical design case based on a medical X-ray system is used to illustrate the potential of the proposed technique.

Direct and parametric synchronization of a graphene self-oscillator

We explore the dynamics of a graphene nanomechanical oscillator coupled to a reference oscillator. Circular graphene drums are forced into self-oscillation, at a frequency fosc, by means of photothermal feedback induced by illuminating the drum with a continuous-wave red laser beam. Synchronization to a reference signal, at a frequency fsync, is achieved by shining a power-modulated blue laser onto the structure. We investigate two regimes of synchronization as a function of both detuning and signal strength for direct (fsync≈fosc) and parametric locking (fsync≈2fosc). We detect a regime of phase resonance, where the phase of the oscillator behaves as an underdamped second-order system, with the natural frequency of the phase resonance showing a clear power-law dependence on the locking signal strength. The phase resonance is qualitatively reproduced using a forced van der Pol-Duffing-Mathieu equation.

Poststimulus response characteristics of the human cone flicker electroretinogram

At certain temporal frequencies, the human cone flicker electroretinogram (ERG) contains multiple additional responses following the termination of a flicker train. The purpose of this study was to determine whether these poststimulus responses are a continuing response to the terminated flicker train or represent the oscillation of a resonant system. ERGs were recorded from 10 visually normal adults in response to full-field sinusoidally modulated flicker trains presented against a short-wavelength rod-saturating adapting field. The amplitude and timing properties of the poststimulus responses were evaluated within the context of a model of a second-order resonant system. At stimulus frequencies between 41.7 and 71.4 Hz, the majority of subjects showed at least three additional ERG responses following the termination of the flicker train. The interval between the poststimulus responses was approximately constant across stimulus frequency, with a mean of 14.4 ms, corresponding to a frequency of 69.4 Hz. The amplitude and timing characteristics of the poststimulus ERG responses were well described by an underdamped second-order system with a resonance frequency of 70.3 Hz. The observed poststimulus ERG responses may represent resonant oscillations of retinal ON bipolar cells, as has been proposed for electrophysiological recordings of poststimulus responses from retinal ganglion cells. However, further investigation is required to determine the types of retinal neurons involved in the generation of the poststimulus responses of the human flicker ERG.

Discuss about Fast Response Performance of under-Damped Second-Order System in Time Domain

Influence of the damping ratio on the response fast performance to under-damped second-order system in the time domain has been discussed. The relationship between peak time and the input signal, the adjust time, and the system type has been analyzed. The response’s fast performance indicators are relative, and it is related to the input signal, the response of the system, and the type of system and its initial states. In conclusion, the peak time and the adjust time cannot reach a minimum at the same time. The fast response issue must be discussed in relation to specific cases, and it cannot be generalized.

Underdamped Second-Order Systems Overshoot Control

The paper addresses the problem of decreasing the overshoot for underdamped second-order systems. A new technique to control the overshoot is proposed, which is based on Posicast control and proportional integral and derivative (PID) control, which performs switching between two controllers. The aim is to use open-loop feedforward control to increase tracking performance and PID control to deal with disturbance rejection. It has been shown that the proposed control scheme can have some advantages over the classical approaches without switching capabilities.

Passive leg motion changes in cerebral palsied children after whole body vertical acceleration

Reports on a pilot study designed to quantify changes in spasticity in children with spastic cerebral palsy following whole body vertical accelerations. Ten subjects, ranging in age from 5 to 18 years, were selected from the Cerebral Palsy Clinic of the Alfred I. duPont Institute. Most of the subjects were independent ambulators, although two used wheelchairs for long distances and one used a wheelchair full time. Passive leg motion changes, as seen in leg drop pendulum tests performed before and after vertical accelerations, are reported here. These changes are based on the comparison of 13 parameters, some of which are derived based on the assumption that normal limbs, when subjected to the leg drop pendulum test, behave as an underdamped second-order system. The vertical acceleration consisted of 15 min of up and down motion on a specially constructed platform capable of rating and lowering both the subject and his or her seating device. Amplitude of oscillation was set at 8.90 cm and the frequency of oscillation was commonly 1.57 Hz. Position of the leg was recorded with an electromagnetic position sensing device. Results of the study showed that 9 of the 10 subjects made a statistically significant improvement in one or more of the 13 attributes, with the highest achiever making improvements in 11 of the 13 attributes. Trends in the data show that the less severely involved clients made the most improvements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Thermal Response of a Metallic Mold to Thermoelastic Interactions at Its Inner Boundary—System Approach

The system theory is used to analyze the thermoelastic interaction at the casting-mold interface and to develop a simplified model for the thermal response of the mold. It is revealed that due to the interaction at the interface, the surface layer at the inner boundary of the mold behaves thermally as an underdamped second-order system and not as an overdamped one. The latter would be the case if the thermoelastic interaction were neglected. This finding is verified experimentally, using molds of different materials and melts of different compositions. The effect of this thermoelastic interaction on the transient temperature field within the mold wall is demonstrated using a finite element model for a spherical mold of a uniform wall thickness.