2-DOF Model Research Articles

Design of a roll autopilot for a skid-to-turn guided missile

the design of autonomous systems is a growing research field which attract an increasing interest in various civilian and military applications. The design of control system can be considered a leading factor for developing any autonomous system. In this paper devoted to a missile autopilot which should achieve specific characteristics and performance criteria to ensure the overall system stability to track the desired commands in the presence of high dynamics and different uncertainties with high accuracy. The investigation of accurate missile 6DOF model is developed and linearization has been performed for designing the proper controllers for the pitch and roll channels and choose the optimum trim points based on system dynamic pressure. A design of lead compensator classical controller is presented to meet certain requirement of both time and frequency characteristic to ensure the system stability. The designed autopilot is evaluated using Matlab simulation is carried out for evaluating the proposed missile autopilot controller performance, the proposed controller presented sufficient performance during flight and simplicity, reliability, and availability for implementation in real time applications.

Robust static output feedback H∞-controller design for three degree of freedom integrated bus lateral, yaw, roll dynamics model

In this paper, a three-degree-of freedom (3 DOF) integrated vehicle lateral, yaw, roll dynamics model with optimal control design have been proposed to improve the bus lateral stability and handling performance. First, a 3 DOF vehicle model for a passenger bus is introduced. The 3 DOF model dynamics include the vehicle steering wheel angle, forward speed, yaw motion, sideslip angle, lateral acceleration and the rolling motion. Then, the presented 3 DOF model is used to design the robust static output feedback [Formula: see text] controller for both nominal system and uncertain system. The proposed controller is designed to improve the bus lateral stability and handling performance by controlling the yaw rate during normal driving and maneuvers. For the robust static output feedback [Formula: see text] controller, the norm bounded uncertainty is considered to simulate the variation of vehicle forward velocity uncertainty. The robust controller is designed to check the lateral stability of the bus at different forward velocity and at different velocity uncertainty. The controllers are synthesized within the [Formula: see text] control approach and the controllers’ design conditions are given within the Linear Matrix Inequalities (LMIs) framework. Numerical simulations have been carried out to demonstrate the effectiveness of the proposed controllers. The obtained simulation results show that the designed nominal and robust controllers enhance the lateral stability of the bus by reducing the amplitude of the yaw rate, lateral acceleration and rolling motion. Hence, the improvements in bus lateral stability and handling performance are achieved.

Modeling and performance evaluation of a heavy-duty vehicle based on the hydraulic power steering system

In most mathematical models that are presented for vehicle performance analysis, the dynamic role of the steering system is ignored and causes the steering effect on the vehicle overall response to be neglected. In this article, the main goal is the performance evaluation of a four-axle heavy-duty vehicle using the modeling and simulation of the vehicle and the hydraulic power steering (HPS) system. For this purpose, using Newton’s method, a 20-degrees-of-freedom (20-DOF) nonlinear model of the heavy vehicle is developed, and verified by the TruckSim software results. Then, the comprehensive 4-DOF model of the HPS system, including the steering handwheel angle, rack displacement, and left- and right-hand wheel angles, is presented. Finally, the dynamic model of the heavy-duty vehicle and the HPS system are combined and a 24-DOF dynamic model is simulated in MATLAB software. In order to evaluate the vehicle performance, the simulation on two maneuvers, namely parking and low-speed lane change maneuvers with load and no-load, are carried out. The simulation results demonstrate the desirable performances of the heavy vehicle based on the HPS system on the parking and low-speed maneuvering. Also, the research results provide a better understanding of the vehicle handling considering the nonlinear model of the heavy-duty vehicle based on the HPS system.

6-DOF motion blur synthesis and performance evaluation of light field deblurring

Motion deblurring is essential for reconstructing sharp images from given a blurry input caused by the camera motion. The complexity of this problem increases in a light field due to its depth-dependent blur constraint. A method of generating synthetic 3 degree-of-freedom (3-DOF) translation blur on a light field image without camera rotation has been introduced. In this study, we generate a camera translation and rotation (6-DOF) motion blur model that preserves the consistency of the light field image. Our experiment results show that the proposed blur model can maintain the parallax information (depth-dependent blur) in a light field image. Furthermore, we produce a synthetic blurry light field dataset based on the 6-DOF model. Finally, to validate the usability of the synthetic dataset, we conduct extensive benchmarking using state-of-the-art motion deblurring algorithms.

Similarity index: A procedure for comparing impact time histories validated with soft impact test

This paper describes the procedure developed to compare the dynamic behavior of a structure due to an impact load. The comparison procedure is especially useful for controlling the impact level and repeatability during testing, but it can also be used for fine-tuning the process of simplified models or finite element models. Both features provide important engineering value and permit the assessment of transient impact histories, qualitatively and quantitatively. More than 240 soft impacts, from a human impact against glass test campaign, have been used to develop and validate the comparison method.Three indicators have been defined in order to control the most significant impact parameters: the impact level (impulse), duration of the impact (stiffness), and maximum acceleration (peak system response). Based on the knowledge of the impact phenomena, the procedure defines a Similarity Index (SIn) that entails the weighted addition of the indicators. The SIn procedure assigns a numerical value to the difference between two time histories over the duration of the contact, and it is used to compare a series of data from a database of soft human impacts tests versus standard glass curves and curves obtained from a simplified 2DOF model.

Numerical study of a container ship model for the uncoupled parametric rolling

Parametric roll on ships is a resonance phenomenon whose onset causes heavy roll oscillations leading to dangerous situations for the ship, the cargo and the crew. It affects both small vessels with marginal stability and large container ships if four conditions are met simultaneously: the wave length and ship length are approximately equal, the frequency of encounter wave is twice the roll natural frequency, the ship’s roll damping is low enough and the wave height exceeds a limit value characteristic to each vessel. For a container ship, the first two conditions result in a time-varying geometry of the submerged hull and thus to a periodic variation of the transverse stability. In the last two decades, several mathematical models for parametric rolling have been proposed by scientists. In the paper, we cancelled the couplings terms between heave, pitch and roll in a 3 DOF model proposed by Neves and Rodriguez to obtain an uncoupled 1 DOF model for the parametric roll. Even if it seems too simplistic, such a model based on Mathieu type equation is a good start to capture the basic features of the analysed phenomenon. There are no less than seven parameters that can influence the ship stability and the appearance of large roll amplitudes. By modifying two of these parameters one by one and keeping the others constant, a series of colour plots have been drown that capture the role played by the ship’s parameters in obtaining dangerous roll amplitudes or too short times to take countermeasures. Analysing the instability regions suggested by these colour plots, one can imagine control measures to reduce the roll amplitudes, such as changing the forward velocity or the heading angle. The data used in the paper have been obtained from experiments with a container ship model in a towing tank followed by expansion to a full scale ship.

EXPERIMENT AND MODELING OF SEATED HUMAN BODY EXPOSED TO LARGE-MAGNITUDE VIBRATION IN SIX SINGLE DIRECTIONS

This paper is to perform experiment, modeling and parameter identification for the seated human bodies to provide insight into transmissibilities to the thigh and the chest, and estimate the indistinct spring and damping constants at human-seat interface. A test bench was designed, and a series of experiments was conducted with 15-seated subjects exposed to low-frequency and large-magnitude vibrations individually in roll, pitch, yaw, fore-and-aft, lateral and vertical axes. Transmissibilities were measured for each subject over the frequency range 0.5–8[Formula: see text]Hz. A 12-degree-of-freedom (DOF) biomechanical model was proposed and was subsequently simplified to six 2-DOF models to describe the experimental results in the corresponding directions. Translational and rotational spring and damping coefficients in six directions were identified via a genetic algorithm. Sensitivity tests were carried out and the influences of the spring and damping coefficients on the principal resonance frequencies and the peak moduli of the transmissibilities were exhibited.

The ride comfort optimization of mining dump truck based on eight degree of freedom

The working environment of mining dumping truck is poor and in order to improve the vibration reduction effect of mining dump trucks, a vehicle damping adjustable semi-active suspension based on connected hydro-pneumatic suspension is proposed. The 8 DOF model of hydro-pneumatic suspension and complete vehicle was established for mining dump truck. The fuzzy PID control method is used to optimize the smoothness of the vehicle by controlling the vertical acceleration of the truck, pitch angle acceleration and seat vertical acceleration. The damping performance of semi-active suspension is analyzed by Matlab/Simulink software. The simulation results show that compared with the passive suspension under the condition of random road power spectrum input, the root mean square values of the vertical acceleration of the truck and the vertical acceleration of the seat of the semi-active suspension are reduced by 25.76% and 48.7%. At the same time, the effect of vehicle vibration reduction is also obvious under the different speeds.

Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances

In order to stabilize multiple-input–multiple-output uncertain strict feedback nonlinear systems with time-varying full-state constraints and external disturbances, an adaptive neural dynamic surface control method is investigated in this paper. A new compensator is proposed, which combines approximation error based adaptive radial basis function neural networks (RBFNNs) and nonlinear disturbance observer (NDOB) to improve the compensate performance of unmodeled dynamics and external disturbances. To prevent that the time-varying full state constraints are violated, the controller is designed via asymmetric time-varying barrier Lyapunov function (ATBLF). Meanwhile, the dynamic surface control is established to avoid the problem of “explosion of complexity” in traditional backstepping design. All closed-loop signals are proved to be semiglobally uniformly ultimate bounded through stability analysis. Finally, the simulation for six degrees of freedom (6-DOF) model unmanned airship are given to illustrate the effectiveness of the proposed control method.

A direct displacement-based design procedure for base-isolated building structures with lead rubber bearings (LRBs)

This paper proposes a direct-displacement based design (DDBD) procedure, to make base-isolated building structure with lead-rubber bearing (LRBs) satisfy the performance objectives prescribed by displacement thresholds. To this end, the DDBD for regular building structures is incorporated with the two-degree-of-freedom (2DOF) model of base-isolated building structures. Fundamentals of the standard DDBD procedure is briefed at first. The equivalent linearized 2DOF model of a base-isolated building structure is then detailed. Modal analysis and response spectrum analysis of this 2DOF model has been carried out, which suggests a simplistic and readily-invertible closed-form relationship from structural characteristics to seismic displacements. Given the displacement requirements, the relationship facilitates the solution of the structural parameters of the base-isolated building structure. Following the basic steps of DDBD but utilizing this 2DOF model as the substitute for the original nonlinear structural model, an alternative DDBD procedure is then developed and detailed. This DDBD procedure is verified by numerical examples, in which the nonlinear time-history analysis of the designed structures yields seismic displacement results matching the preset target thresholds well. The design solutions of the proposed procedure are also compared with those given by an existing one. Numerical results indicate that the proposed DDBD procedure is reliable, straightforward, and convenient for the seismic design of base-isolated building structures with LRBs.

Model analysis, design and experiment of a fan-wing underwater vehicle

Abstract In order to achieve 5 degrees of freedom (DOFs) movement in an underwater space with only two moving parts, a new kind of unmanned underwater vehicle, Fan-wing Underwater Vehicle (FUV), is proposed. The FUV is driven by two fan-wings which are adapted from the fan-wings for aircraft. The features of the underwater fan-wing are analyzed by 2D computational fluid dynamic (CFD) simulations. In order to analyze the movement of the FUV, a 6-DOF hydrodynamics mathematical model is built. The model is simplified for analyzing two kinds of common conditions movements. According to the simplified model of the ideal straight-line depth-keeping cruise with constant velocity condition, a general procedure to design the FUV is put forward. Some 3D CFD simulations are added to solve the mathematical model in the procedure of the FUV design. Then, according to the design procedure, a control system and a mechanical structure of the FUV are designed. Finally, a real FUV is manufactured, and an underwater test is completed. The experiment shows that the real FUV can achieve 5 DOFs movement in an underwater space, and the results match the design proposes.

A Weighted Set Cover Problem for Product Family Design to Maximize the Commonality of Products

AbstractIn product family design, the commonality of products and performance are competing objectives when designers build platforms. The commonality makes it efficient to manufacture products while it will cause performance loss of products. In this paper, we assume that performance functions evaluate the performance of a product. Targets of performance functions are set for each product depending on the product's property. The designs that satisfy the target of performance functions are denoted as ‘good’ design points. By using ‘good’ design points, a weighted set cover problem (WSC) is applied to formulate the combinatorial optimization problem, which maximizes the commonality by minimizing the number component attributes. A recursive greedy algorithm is proposed to handle the general cost function in the problem for product family design. The formulation and the algorithm are tested for a linear three-degree-of-freedom (3DOF) model. In numerical experiment, the proposed method determines optimal values of the components which are suspensions, stabilizer bars, and tires in the vehicle model.

The Effect of Displacement Constraints on the Failure of MEMS Tuning Fork Gyroscopes under Shock Impact.

Displacement constraints such as stops are widely used in engineering to improve the shock resistance of microelectromechanical system (MEMS) tuning fork gyroscopes. However, in practical applications, it has been found that unexpected breakage can occur on MEMS tuning fork gyroscopes with stops. In this paper, the effects of two displacement constraints on the failure mode of MEMS tuning fork gyroscopes are studied. The MEMS tuning fork gyroscope is simplified to a two-degree-of-freedom (2DOF) model, then finite element analysis (FEA) is used to study the effects of displacement constraint on the gyroscope. The analysis proves that even if the displacement constraint of direct contact with the weak connecting beam is not established, the equivalent stiffness of the gyroscope can be enhanced by limiting the displacement of the movable mass, thereby improving the shock resistance of the gyroscope. However, under the shock of high-g level, displacement constraint with insufficient spacing will cause multiple collisions of the small-stiffness oscillating frame and lead to an increase in stress. The cause of failure and shock resistance of a MEMS tuning fork gyroscope are verified by the shock test. By comparing the results, we can get a conclusion that is consistent with the theoretical analysis.

Controlling the Altitude Dynamics of Quadcopter using Robust Output Feedback Controller

This paper deals with observer based controlling and stabilization of the nonlinear dynamics of the quadcopter and in order to explore the complex dynamics of the quadcopter, the only altitude of the quadcopter is considered. A nonlinear model of the altitude is extracted from the six DOF model of the quadcopter and the same is linearized. A robust controller is implemented in the design to cater to the nonlinear nature of the quadcopter at hover by using both Sliding mode control and model predictive controller. The soft instrument, observer, is designed here for the state estimation purpose to bring the simulated system more closely to realistic values. Effectiveness of the designed system is ensured by trajectory tracking of the quadcopter. Simulation results presented show that output feedback based controller designed having optimum performance in estimating the states of the targeted system with almost negligible error. Also, the nonlinear controller designed having superior performance as compared to a controller designed with the linearized system.

EFFECTS OF HUMAN-STRUCTURE INTERACTIONS ON THE DYNAMIC PROPERTIES OF BUILDING FLOORS SUSCEPTIBLE TO VIBRATIONS

Excessive vibrations of building floors due to human movements have become an important vibration serviceability problem for building designers and owners. A series of vibration tests on a full-scale laboratory floor with different numbers of humans in various postures were conducted. Using this data, the dynamic properties of a two-degree-of-freedom (2-DOF) dynamic system representing groups of people in different postures were computed. A 3-DOF model representing the floor and humans was developed and its dynamic properties were defined in terms of non-dimensional parameters. The dynamic properties of the floor were measured when occupied by groups of people in different postures and compared to those predicted using the 3-DOF dynamic model considering the identified human models. The results showed that the predicted properties were within the range of those found from the measurements, which validated the identified human dynamic models. This study also showed how the presence of humans can affect the natural frequency and damping ratio of a floor system.

Changes in surge and pitch decay periods of floating wind turbines for varying wind speed

Recently published experimental results show variations in surge and pitch decay periods of floating wind turbines (FWTs) subjected to different incident wind velocities. This paper explores the external loads acting on a FWT, with special attention to nonlinearities which affect its low-frequency global motions. The period variations in surge and pitch are found to have different sources. In surge, the mooring system nonlinearities dominate, while for pitch the relative phase between the nacelle velocity and the thrust induced in the rotor leads to an “apparent inertia/damping” effect. Simplified 2-DOF models using linearized stiffness coefficients for surge and modified inertia and damping matrices for pitch are developed. Comparisons with state-of-the-art aero-hydro-servo-elastic time-domain simulations show excellent agreement for three distinct catenary-moored FWT designs.

Seven Degrees-of-Freedom Model for the Roll Stabilization of Unstable Ships

As demonstrated by the 2014 MV Sewol incident, the prevention of top heavy ship capsize is necessary to protect life and property aboard a ship. The goal of this paper is to prevent the capsize of ships, which lack a restoring torque about the roll axis, by using a feedback-controlled pendulum actuator. A seven degrees-of-freedom (7DOF) model is developed for a ship equipped with a pendulum actuator. The model is used to conduct parameter analyses on the pendulum length, pendulum mast height, pendulum mass, ship center of mass (COM) height, and the pendulum controller's proportional feedback gain. The results of these analyses are depicted via time responses and phase plots. Key points for designing a pendulum actuator summarize simulation results, stating that the pendulum mass should be 3–7% of the total ship mass, and the pendulum moment of inertia should be 0.5–1.0 times the roll moment of inertia of the ship.

Analytical solution of seismic response of base‐isolated structure with supplemental inerter

SummaryClosed‐form solutions are derived for the modal characteristics and seismic response of a base‐isolated structure equipped with additional inerters. By simplifying the structure‐isolator‐inerter system in terms of the two‐degree‐of‐freedom (2DOF) model, the modal frequencies, mode shapes, damping ratios, and participation factors of the system are derived. Consequently, analytical seismic response solutions are formulated by the modal superposition method. Utilizing these analytical solutions, an extensive parametric study has been carried out to investigate the effect of supplement inerters on both the modal characteristics and seismic response of the structure‐isolator‐inerter system. There is a critical inertance leading to the zero second modal participation factor (ie, the disappearance of the second modal response). The associated critical inertance ratio is derived in closed form as well. Moreover, it is observed that the reduction of deformation of isolators by increasing the inertance may be offset by the increase in relative displacements of the superstructure. To circumvent this adverse effect, an optimal range of inertance is identified whereby both the deformation of isolators and the relative displacement of the superstructure are mitigated concurrently.

Static and Dynamic Coefficient Measurements for a Thrust Collar Used in an Integrally Geared Compressor

This paper introduces a test facility specifically designed to measure the axial stiffness and damping coefficients of an oil-lubricated thrust collar (TC). The geometry, load, and speeds of the test facility are representative of a production integrally geared compressor (IGC). Separate electric motors spin the shafts according to an assumed gear ratio; a pneumatic air piston loader provides a noncontacting, static thrust force; a remotely controlled impact hammer delivers a perturbation force; and eddy-current motion probes record the resulting vibration. The paper uses a one degree-of-freedom (1DOF) axial motion model that neglects the static and dynamic stiffness of the bull wheel (BW) and presents estimates of the TC oil-film dynamic coefficients for pinion spin speeds between 5 and 10 krpm, and static loads between 200 and 400 N, using time-domain (log-dec and damped period) and static load-deflection techniques. The measurements show that the TC oil-film develops appreciable stiffness (tens of MN/m), and the 1DOF model used here is inadequate for higher loads. Axial runout on the interfacing surfaces of the test facility TC and BW complicates parameter identification, but time-domain averaging effectively attenuates the runout while preserving the transient vibration that results from the impact hammer. Measurements of the TC oil-film stiffness, damping, and virtual mass coefficients are useful to machinery original equipment manufacturers (OEMs) or end-users seeking to predict or diagnose subsynchronous vibration in their machine that might be TC-related.

Control of stress and damage in structures by piezoelectric actuation: 1D theory and monofrequent experimental validation.

SummaryThis contribution presents novel results on feed‐forward control of stress in piezoelectric structures by means of piezoelectric actuation. For that sake, we focus on a one‐dimensional benchmark problem, a piezoelectric transducer that is excited by a piezoelectric stack actuator. We investigate the following problem: Is it possible to actuate the piezoelectric transducer in such a manner that the dominant axial stress component is nullified. In order to find a theoretical solution for this question, we discretize our system as a two‐degree‐of‐freedom (2DOF) model. The equations of motion are transformed into the differential equations for the inner forces by taking advantage of the constitutive relations, which relate displacement, stress, and electric field. Finally, we find a mathematical relation for the piezoelectric transducer excitation in order to annihilate the transducer force. A static and a frequency‐dependent approximate solution for the transducer actuation signal are derived. The latter solution reduces the inner force drastically in a certain frequency range. After numerical results for the force‐control algorithm are presented, we finally experimentally verify our theory: First, the force‐controlled configuration is exposed to a monofrequent harmonic excitation test run for 30 min, showing no sign of fatigue or material failure, because the transducer force is below the ultimate tensile strength. Then, the system is excited by the same harmonic excitation again, but the control signal for the piezoelectric transducer is turned off. The result is a visible damage of the piezoelectric transducer, leading to a significant change of the first eigenfrequency.