Two-degree-of-freedom Research Articles

Stability and post-critical behavior of a two-degrees of freedom aero-elastic system in a cross flow

The linear deterministic approach of aero-elastic stability of a slender prismatic beam in a cross flow has been widely investigated in the past. Due to character of the system and regulations in practice (civil engineering, aircraft design, etc.) it can be used for determination of the lowest flow velocity of various types of instability onset. Several two degrees of freedom (TDOF) theoretical models have been worked out and experimentally validated. Nevertheless, it comes to light that a random component appearing in an external excitation can influence significantly the effective aeroelastic stability of this system. Combination of deterministic and random types of external excitation is taken into account regarding simultaneous vortex shedding and turbulence in the shear layer around the profile. Additive excitation includes deterministic (more or less harmonic) and random parts. Multiplicative excitation has a random character only and acts as a perturbation of aeroelastic and elastic parameters of the system. Some attempts for investigation of such a system have been done in the past considering noises as Gaussian white noises. Experimental measurements, however, show that these noises have character of narrow band random processes with distinctly expressed maximum in relevant spectral density. To overcome the limitation of white noises in the Fokker-Planck equation, an extended definition of correlation coefficients is used when constructing the Ito system. Then the original narrow band processes emerge in the relevant Ito system only as a couple of input process spectral density values in significant points of the system resonance curves.

An implementation of movement classification for prosthesis control using custom-made EMG system

Electromyography (EMG) is a well known technique used for recording electrical activity produced by human muscles. In the last few decades, EMG signals are used as a control input for prosthetic hands. There are several multifunctional myoelectric prosthetic hands for amputees on the market, but so forth, none of these devices permits the natural control of more than two degrees of freedom. In this paper we present our implementation of the pattern classification using custom made components (electrodes and an embedded EMG amplifier). The components were evaluated in offline and online tests, in able bodied as well as amputee subjects. This type of control is based on computing the time domain features of the EMG signals recorded from the forearm and using these features as input for a Linear Discriminant Analysis (LDA) classifier estimating the intention of the prosthetic user.

Optimal design of two-degree-of-freedom control scheme for non-minimum phase processes with time delay

This paper proposes an analytical two-degree-of-freedom (TDOF) control scheme for non-minimum phases systems with time delay, which leads to remarkable improvement of regulator capacity for both of reference input tracking and input load disturbance rejection. All controllers that make the closed-loop system internally stable and have no steady-error have been employed firstly. Then, the set-point tracking controller and the disturbance rejection controller are analytically derived in terms of the integral squared error performance specifications. The nominal set-point response is decoupled from the load disturbance response in the adopted TDOF control scheme. In consequence, both of the set-point tracking performance and load disturbance rejection performance can be optimised simultaneously and separately. Finally, an illustrative example is included to demonstrate the superiority of the proposed method.

Optimal design of two-degree-of-freedom control scheme for non-minimum phase processes with time delay

This paper proposes an analytical two-degree-of-freedom (TDOF) control scheme for non-minimum phases systems with time delay, which leads to remarkable improvement of regulator capacity for both of reference input tracking and input load disturbance rejection. All controllers that make the closed-loop system internally stable and have no steady-error have been employed firstly. Then, the set-point tracking controller and the disturbance rejection controller are analytically derived in terms of the integral squared error performance specifications. The nominal set-point response is decoupled from the load disturbance response in the adopted TDOF control scheme. In consequence, both of the set-point tracking performance and load disturbance rejection performance can be optimised simultaneously and separately. Finally, an illustrative example is included to demonstrate the superiority of the proposed method.

Analytical Investigation on the Damping Performance of Atorque Converter in an Automotive Driveline Model

Torque converters are avital part of automatic transmission vehicles. In this paper the influence of a torque converter on the lowest mode of driveline vibrations (shuffle mode) is investigated. The automotive driveline is modelled by lumped parameter models, in which a steady-state torque converter model is inserted between the engine and the gearbox. A detailed mathematical model of a two-degree of freedom and a three-degree of freedom dynamic systemis given. The resulting nonlinear differential equations are linearized to obtain system transfer functions and to study damping characteristics of the torque converter.Additionally, a dynamic system model with nonlinear equations is developed in MATLAB/Simulink to verify the linearized system. The simulations show that the high frequency vibrations from the engine side are damped due to the torque converter and the linearized model predicts the system response accurately.

Accuracy analysis of geometrical and numerical approaches for two degrees of freedom robot manipulator

Analysis of algorithms to determine the accuracy of aiming direction using two inverse kinematic approaches i.e. geometric and numeric has been done. The best method needs to be specified to precisely and accurately control the aiming direction of a two degrees of freedom (TDOF) manipulator. The manipulator degrees of freedom are azimuth (Az) and elevation (El) angles. A program has been made using C language to implement the algorithm. Analysis of the two algorithms was done using statistical approach and circular error probable (CEP). The research proves that accuracy percentage of numerical method is better than geometrical method, those are 98.63% and 98.55%, respectively. Based on the experiment results, the numerical approach is the right algorithm to be applied in the TDOF robot manipulator.

Optimal disturbance rejection controller design for integrating processes with dead time based on algebraic theory

ABSTRACTIn this paper, an H2 optimal input-load disturbance rejection (ILDR) controller for integrating processes with dead time is proposed based on the internal model control principle. The main contribution of this work is that the optimal solution under ILDR criterion for integrating processes with dead time and input constant disturbances has been derived based on algebraic theory. To further improve the performance for both set-point tracking and input disturbance rejection, a two-degree-of-freedom (TDOF) control design method has also been developed. Compared with previous advanced control methods, the proposed design method has three main advantages. First, the optimal ILDR controller is derived systematically on the basis of algebraic theory. The designed controller is given in an analytical form. Second, a simple tune principle is developed. The set-point tracking performance specification and robustness stability specification can be quantitatively achieved by monotonously tuning the performance degree in the designed controller. Finally, both optimal set-point tracking performance and input disturbance rejection can be achieved by the proposed TDOF control structure. Numerical simulations are given to illustrate the effectiveness of the proposed method.

Investigation of two degrees of freedom on vortex-induced vibration under the wake interference of an oscillating airfoil

The vortex formation and shedding process behind an isolated cylinder under the wake interference of an oscillating airfoil at different oscillating frequencies and amplitudes have been studied numerically. The “2S” and “P+S” mode are found in the drag-producing von Kármán vortex wake and thrust-producing inverted von Kármán vortex wake, respectively. For the “2P” case, the pairs of vortices with different sizes are laterally parallel to each other. For the “2P+2S” case, the merged single vortices do not appear between the vortex pairs, but they only emerge after every two pairs of vortices.For the two-degree of freedom (2-DOF) VIV in the wake of the steady flow, seven types of the phase portraits of the displacement shapes are observed. In the range of small reduced velocity (Vr<5), the body trajectories are mainly characterized by an “8-shape” with some differences in phase. At the peak amplitude, the body trajectories have changed into two shapes: i.e., the half “8-shape” (initial stage) and the crescent-shape (final stage). When Vr=6, the body trajectories have also shown to have two shapes: i.e., the “8-shape” (initial stage) and the half “8-shape” (final stage). When Vr arrives at the low branch (Vr>7), the body trajectories will become irregularly shaped like a cone-net.

Self-Paced Reaching after Stroke: A Quantitative Assessment of Longitudinal and Directional Sensitivity Using the H-Man Planar Robot for Upper Limb Neurorehabilitation.

Technology aided measures offer a sensitive, accurate and time-efficient approach for the assessment of sensorimotor function after neurological insult compared to standard clinical assessments. This study investigated the sensitivity of robotic measures to capture differences in planar reaching movements as a function of neurological status (stroke, healthy), direction (front, ipsilateral, contralateral), movement segment (outbound, inbound), and time (baseline, post-training, 2-week follow-up) using a planar, two-degrees of freedom, robotic-manipulator (H-Man). Twelve chronic stroke (age: 55 ± 10.0 years, 5 female, 7 male, time since stroke: 11.2 ± 6.0 months) and nine aged-matched healthy participants (age: 53 ± 4.3 years, 5 female, 4 male) participated in this study. Both healthy and stroke participants performed planar reaching movements in contralateral, ipsilateral and front directions with the H-Man, and the robotic measures, spectral arc length (SAL), normalized time to peak velocities (TpeakN), and root-mean square error (RMSE) were evaluated. Healthy participants went through a one-off session of assessment to investigate the baseline. Stroke participants completed a 2-week intensive robotic training plus standard arm therapy (8 × 90 min sessions). Motor function for stroke participants was evaluated prior to training (baseline, week-0), immediately following training (post-training, week-2), and 2-weeks after training (follow-up, week-4) using robotic assessment and the clinical measures Fugl-Meyer Assessment (FMA), Activity-Research-Arm Test (ARAT), and grip-strength. Robotic assessments were able to capture differences due to neurological status, movement direction, and movement segment. Movements performed by stroke participants were less-smooth, featured longer TpeakN, and larger RMSE values, compared to healthy controls. Significant movement direction differences were observed, with improved reaching performance for the front, compared to ipsilateral and contralateral movement directions. There were group differences depending on movement segment. Outbound reaching movements were smoother and featured longer TpeakN values than inbound movements for control participants, whereas SAL, TpeakN, and RMSE values were similar regardless of movement segment for stroke patients. Significant change in performance was observed between initial and post-assessments using H-Man in stroke participants, compared to conventional scales which showed no significant difference. Results of the study indicate the potential of H-Man as a sensitive tool for tracking changes in performance compared to ordinal scales (i.e., FM, ARAT).

Fast consensus algorithm of multi-agent systems with double gains regulation

ABSTRACTTwo novel fast consensus algorithms based on local information of first-order discrete multi-agent systems under a directed network are proposed in this paper. By applying matrix theory and the frequency-domain analysis methods, two sufficient conditions about the convergence rate of the systems are presented, respectively, where the proportional-like gain feedback and incremental proportional–integral–differential gains feedback only with local information are added. Finally, a numerical example is given to show the double gains regulation algorithm proposed in this paper has much faster consensus rate compared with the classical consensus algorithm in the same condition for its two-degree freedom parameters.

Pitch motion problem induced by dynamic positioning system for new sandglass-type floating body

In this paper, a new concept of sandglass-type floating body, which can overcome the performance limitations of traditional ship-type and cylindrical FDPSO (floating drilling production storage and offloading), is proposed as research subject. In the general design of dynamic positioning systems, it is adequate to deal with a three-degree of freedom problem in the horizontal plane. However, the new floating body with small water-plane area and low metacentric height may cause an unintentional coupling phenomenon between the pitch and surge motions by the thruster system. Therefore, first by numerical boundary element method (BEM) based on wave potential theory and experiments, the pitch motion characteristic of the sandglass-type model is studied and meanwhile the numerical method of this paper is validated. Furthermore, two dynamics models with and without consideration for the additional pitch moment by the thruster systems are introduced and numerically simulated, which can show the problem of pitch motion induced by the positioning thrusters. Then by the mass-spring-damper systems with two-degree of freedom, the influence of additional pitch moment by the thrusters on the pitch and surge motion performances is theoretically analyzed. Finally, based on the essential reason of pitch motion problem, a control law considering pitch inertia effect has been used and proven to be effective to decrease the pitch motion response.

Vibration power flow and force transmission behaviour of a nonlinear isolator mounted on a nonlinear base

The vibrational power flow and force transmission characteristics of a two-degree-of-freedom (TDOF) nonlinear system are investigated to examine the performance of a nonlinear isolator. The system consists of a harmonically-excited mass, mounted on a single-degree-of-freedom (SDOF) nonlinear flexible base structure through a nonlinear isolator. Both the isolator and the base exhibit damping and stiffness nonlinearities characterized by cubic damping and cubic restoring forces, respectively. The steady-state response of the system is obtained by using the method of averaging and numerical integrations. The bisection method is developed to solve coupled nonlinear frequency response equations. The time-averaged input, dissipated and transmitted powers of the system in the steady-state motion are formulated. Power transmission ratio is proposed as an isolation performance index and compared with force transmissibility. It is found that softening stiffness nonlinearity in the isolator can reduce power transmission ratio, and suppress the peak values of time-averaged power flow and force transmissibility. In comparison, the hardening stiffness in the isolator can lead to a larger power transmission ratio and larger force transmissibility in the high-frequency range. It is shown that power transmission ratio can be reduced by the damping nonlinearity in the isolator, but is enlarged by that in the base. It is also shown that softening nonlinear isolator may provide a better performance than a hardening isolator when the base is of either hardening or softening stiffness nonlinearity. The paper provides a better understanding of the effects of nonlinearities on the performance of nonlinear vibration isolators and demonstrates their potential application to enhance vibration mitigation.

Non-linear 2DOF system for efficient seismic analysis of vertical soil-nailed walls

New non-linear analysis of a two-degree of freedom (2DOF) system is proposed to evaluate the seismic deformation of soil-nailed structures. The proposed method satisfactorily predicted the deformation of a soil-nailed structure under earthquake action and saved computational time for analysis of a practical problem in comparison with full non-linear time-history analysis developed within the finite difference approach. The 2DOF model is calibrated using a non-linear static procedure and the calibrated 2DOF model is used for non-linear time history analysis. The Non-linear static analysis was performed by applying a vertical load pattern behind the reinforced block at the top boundary of finite difference model. By applying the aforementioned load pattern, additional lateral pressure was mobilised behind the reinforced block. This additional lateral pressure allowed examination of the lateral resistance of the reinforced block and provided the non-linear system characteristics required to simulate the seismic response. Two models were selected and subjected to five different excitations with two amplitude scale factors to verify the proposed method using fully dynamic analysis. The results show that the elastic fundamental period of a structure with respect to the predominant period of input motion and the level of excitation control the level of deformation.

Comparison of two models for human-structure interaction

This paper studies the vibratory characteristics of human-structure interaction. The two-degree-of-freedom (TDOF) system is developed to describe the coupled vibration of the body and the structure, in which one degree is from the structure and the other degree from the body. Two kinds of modelling methods are used to develop the TDOF system, respectively. One method is called as the separative modelling, which firstly models the structure and the body separately to be independent single-degree-of-freedom (SDOF) systems and then physically combines the two SDOF systems to form a TDOF system. The other method is called as the integrative modelling, which considers the body and the structure as an inseparable whole to develop the coupled TDOF system. It is shown that the present integrative modelling method is more reasonable than the conventional separative modelling method. The differences between two kinds of models are checked in detail when the human body is considered as a two-segment elastic bar with four kinds of typical mass and stiffness distributions.

Chaos control and impact suppression in rotor-bearing system using magnetorheological fluid

In this paper a general dynamic model of a rotor-bearing system using magnetorheological fluid (MR) is presented. The mathematical model of the rotor-bearing system results from a Jeffcott rotor with two-degrees of freedom and discontinuous supports. The effect of magnetorheological fluid on vibration is investigated based on a model of a modified LuGre dynamical friction model. A comparison with equivalent rotor-bearing system is made to verify the contribution of MR in this system. In this study two different implementations of the control procedure are presented, one eliminating the chaotic behavior and the second suppressing the unbalancing vibration so as to avoid impact in rotor-bearing system. First, to control the undesirable chaos in rotor-bearing system a damped passive control methodology is used. On the other hand, to suppressing the impact vibration, the Fuzzy Logic Control is considered. Results demonstrate that undesirable behaviors of rotor can be avoided by varying the damping force.

Longitudinal stability and control augmentation with robustness and handling qualities requirements using the two degree of freedom controller

This paper presents a practical design of longitudinal stability and control augmentation system (SCAS) using a two degree of freedom (TDOF) controller. It is based on the linear quadratic regulator (LQR) technique in the frequency domain, via spectral factorization. The controller exhibits robustness to plant uncertainties, related with variation due to different operation conditions, and incorporates various aircraft handling qualities (HQ) requirements to comply with certification authority’s requests. The project results in an unique set of fixed gain TDOF controller for a plant dynamics which changes with a $$V_{\text {CAS}}\times x_{\text {cg}}$$ envelope. The project is done aiming at the industrial implementation of TDOF controller in fly-by-wire aircrafts.

Design of GA Tuned Two-degree Freedom of PID Controller for an Interconnected Three Area Automatic Generation Control System

In this paper an innovative controller named parallel two-degree freedom of PID controller has deliberated and employed in an interconnected three area reheat thermal power system. The optimal controller gains obtained by using Genetic algorithm and the Integral Time Squared Error (ITSE) employed as an objective function. To realize the system practically, physical constraints like generator rate constraints and governor dead band nonlinearities have considered. To compensate the loss of kinetic energy during sudden load increase Superconducting Magnetic Energy Storage used in each area. The results gained by using GA tuned parallel two-degree freedom PID controller has compared with the conventional Ziegler’s Nichols tuned PID controller and genetically tuned PID controller. The GA tuned parallel two-degree freedom of PID controller produces better transient response characteristics for frequency and tie line power deviations under step load perturbations. The system simulation have realized by means of MATLAB/SIMULINK software.

Time-Delayed Control of SISO Systems for Improved Stability Margins

While time delays typically lead to poor control performance, and even instability, previous research shows that time delays can, in some cases, be beneficial. This paper presents a new benefit of time-delayed control (TDC) for single-input single-output (SISO) linear time invariant (LTI) systems: it can be used to improve robustness. Time delays can be used to approximate state derivative feedback (SSD), which together with state feedback (SF) can reduce sensitivity and improve stability margins. Additional sensors are not required since the state derivatives are approximated using available measurements and time delays. A systematic design approach, based on solution of delay differential equations (DDEs) using the Lambert W method, is presented using a scalar example. The method is then applied to both single- and two-degree of freedom (DOF) mechanical systems. The simulation results demonstrate excellent performance with improved stability margins.

Oscillators: Phenomenological mappings and analogies: Second part: Structural analogy and chains

New analytical and numerical results of dynamics for both linear and nonlinear system with two degrees of freedom are presented. For the mechanical chain system with two degrees of freedom, oscillations are investigated analytically and numerically with corresponding comparison between free and forced oscillatory dynamics of linear and nonlinear system. Using the Mihailo Petrovic's theory of elements of mathematical phenomenology, the phenomenological mappings in vibrations, signals, resonances and dynamical absorptions in models with two degrees of freedom-abstractions of different real system dynamics are identified, as well as in eigen time functions of multi-deformable coupled body system dynamics, and presented. Mathematical description of a chain mechanical system with two mass particles coupled by linear and nonlinear elastic springs and with two degree of freedom is given. By the analysis of corresponding solutions for free and forced vibrations, series of related two-frequency regimes and resonant states, as well as dynamical absorption states, are identified. Phenomenological mappings are used to explain dynamics in two deformable body (beams, plates or membranes) systems. In short, new analytical and numerical results of linear and non-linear dynamics of a system with two-degrees of freedom in analogy with eigen time functions oscillations of transversal vibrations of two body system dynamics are presented. Structural analogies are identified between eigen time functions of different multi-coupled deformable body transversal vibrations (plates, beams, belts or membranes). Mathematical phenomenology elements and phenomenological mappings are applied in the scientific results integration. Mathematical analogy and phenomenological mappings of linear and nonlinear singular phenomena in discrete and multi-body system vibrations (torsional system, multi-pendulum system, coupled electrical circuit and multi-deformable-body oscillations-beams, plates, membranes) are performed. Structural analogy is used to explain phenomenological mappings between displacements of the mass particles in discrete system and eigen time functions in one eigen amplitude mode of dynamics in two coupled deformable body (beams, plates or membranes) systems.

Periodic Motions and Bifurcation Trees in a Buckled, Nonlinear Jeffcott Rotor System

In this paper, analytical solutions for period-m motions in a buckled, nonlinear Jeffcott rotor system are obtained. This nonlinear Jeffcott rotor system with two-degrees of freedom is excited periodically from the rotor eccentricity. The analytical solutions of period-m solutions are developed, and the corresponding stability and bifurcation are also analyzed by eigenvalue analysis. Analytical bifurcation trees of period-1 motions to chaos are presented. The Hopf bifurcations of periodic motions cause not only the bifurcation tree but quasi-periodic motions. The quasi-periodic motion can be stable or unstable. Displacement orbits of periodic motions in the buckled, nonlinear Jeffcott rotor systems are illustrated, and harmonic amplitude spectrums are presented for harmonic effects on periodic motions of the nonlinear rotor. Coexisting periodic motions exist in such a buckled nonlinear Jeffcott rotor.