Input Shaping for Flexible System With Nonlinear Spring and Damper

Input shaping suppresses residual vibration by destructive interference of the impulse responses. Because proper destructive interference requires superposition property of the linear system, traditional input shaper only applies to the linear flexible system. In this paper, the work and energy principle is used to derive input shaper for flexible system having nonlinear spring and damper. It was shown via simulation and experiment that this type of shaper performs well with nonlinear systems. Positive, robust, and negative input shapers are discussed.

Nonlinear Dynamic Behavior of a Rotor Bearing System With Nonlinear Viscous Damping Suspension

Nonlinear damping suspension has gained attention owing to its excellent vibration isolation performance. In this paper, a cubic nonlinear viscous damping suspension was introduced to a rotor bearing system for vibration isolation between the bearing and environment. The nonlinear dynamic response of the rotor bearing system was investigated thoroughly. First, the nonlinear oil film force was solved based short bearing approximation and half Sommerfeld boundary condition. Then the motion equations of the system was built considering the cubic nonlinear viscous damping. A computational method was used to solve the equations of motion, and the bifurcation diagrams were used to display the motions. The influences of rotor-bearing system parameters were discussed from the results of numerical calculation, including the eccentricity, mass, stiffness, damping and lubricating oil viscosity. The results showed that: (1) medium eccentricity shows a wider stable speed range; (2) rotor damping has little effect to the stability of the system; (3) lower mass ratio produces a stable response; (4) medium suspension/journal stiffness ratio contributes to a wider stable speed range; (5) a higher viscosity shows a wider stable speed range than lower viscosity. From the above results, the rotor bearing system shows complex nonlinear dynamic behavior with nonlinear viscous damping. These results will be helpful to carrying out the optimal design of the rotor bearing system.

Study on a Photovoltaic Lunar Dust Removal System Based on the Photovoltaic Effect of PLZT

The deposition of lunar dust on the surface of solar panels and optical elements is one of the most important problems need to be solved in lunar exploration. This paper will propose an initiative lunar dust removal system based on the photovoltaic effect of PbLaZrTi (PLZT), which is activated by the ultraviolet light extracted from sun light at the lunar surface. When ultraviolet light with a wavelength near 365nm illuminates on polarized PLZT materials, high voltages of several kilovolt per centimeter can be generated between two electrodes of PLZT. When two electrodes of PLZT are connected to a lunar dust collector (LDC) and the ITO film of protected surface respectively, an electrostatic field forms between LDC and the protected surface. Coulomb forces over particles will overcome gravitational force and surface forces, so the particles can be absorbed to LDC and removed by LDC finally. Based on the equivalent electrical model, mathematical model of electrostatic force is derived when the lunar removal electric field is acted either by single piece PLZT or by multi-pieces PLZT which are connected in parallel. Experimental platform is set up to prove the feasibility of this lunar dust removal system. In order to improve the removal efficiency, a novel configuration design of LDC based on multi-PLZT patched is proposed and its removal efficiency is evaluated by experiments.

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Analysis of Hybrid Programming Simulation Based on the Variable Stiffness Ring With Expanding Loop SMA Actuator

In the development of space craft design index, the requirements of hypersonic space craft control accuracy has been increasingly rigorous. Thin-walled structure is often employed in hypersonic craft to reduce the weight of the load and to save the room. During the flight of the craft, temperature field is produced along the surface and the dynamic properties of the craft structure are obviously changed. The decreasing elastic modulus of the structure material and the appearance of thermal stress lead to the decrease of integral rigidity and stability of the structure, then the thermal flutter appears and control difficulties increase. Shape Memory Alloy (SMA) has the advantages of the considerable driving force in the compact volume and the simple driving method. By the combination of actuator structure design and stiffness control, the smart structure is able to make active control to the thermal stiffness variation. In this paper, the apex high-temperature area is equivalent to a ring structure. Finite difference method is employed firstly to transform the governing partial differential equation into discrete finite difference equations. Then the elastic modulus change, thermal stress and tension along the circumference are considered comprehensively to propose the calculation formulas of equivalent young’s modulus. The discrete dynamic matrix model is obtained containing the control terms of SMA. To solve the big-matrix calculation and multiple iterated large data problem, hybrid program is developed with C++ and MATLAB. Finite element software is employed to make optimization analysis to design an expanding loop actuator containing SMA as driving source, variable thickness loops of spring steel as expanding units, and universal-ball pre-loading units. On the basis of that, the thermal stiffness variation active control system with smart structure is developed based on expanding loop SMA actuator. After the analysis of examples, the variation law of the needed SMA driving force is obtained. The distribution position and quantity of the driving source is optimized. This research provides reference for the Theoretical Analysis and Simulation of structure stiffness active control and adaptive control of the aircraft employing smart material. The research results have guiding significance for the smart structure design of hypersonic aircraft in the future.

Nonlinear Modeling of Cracked Beams for Impedance Based Structural Health Monitoring

One of the main objectives of the structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method is continuously damage detection applications. In present work impedance method of beam structure is considered and the effect of early crack using breathing crack modeling is studied. In order to model the effect of a crack in beam, the beam is connected with a rotational spring in crack location. The Rayleigh–Ritz method is used to generate ordinary differential equation of cracked beam. Firstly, only open crack is considered that this is leads to linear system equation. In linear system, time domain system equations are converted to frequency domain, and then impedance of PWAS in frequency domain is calculated. Secondly, the breathing crack is modeled to be fully open or fully closed. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using pseudo-arc length continuation scheme and collocation method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect early crack using breathing crack modeling on PWAS impedance. At the first, frequency response of breathing crack in the frequency range with its sub-harmonics is calculated. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

Casimir Effect on Voltage Response of Superharmonic Resonance of NEMS Resonators

This paper investigates the voltage response of superharmonic resonance of the second order of electrostatically actuated nano-electro-mechanical system (NEMS) resonator sensor. The structure of the NEMS device is a resonator cantilever over a ground plate under Alternating Current (AC) voltage. Superharmonic resonance of second order occurs when the AC voltage is operating in a frequency near-quarter the natural frequency of the resonator. The forces acting on the system are electrostatic, damping and Casimir. To induce a bifurcation phenomenon in superharmonic resonance, the AC voltage is in the category of hard excitation. The gap distance between the cantilever resonator and base plate is in the range of 20 nm to 1 μm for Casimir forces to be present. The differential equation of motion is converted to dimensionless by choosing the gap as reference length for deflections, the length of the resonator for the axial coordinate, and reference time based on the characteristics of the structure. The Method of Multiple Scales (MMS) and Reduced Order Model (ROM) are used to model the characteristic of the system. MMS transforms the nonlinear partial differential equation of motion into two simpler problems, namely zero-order and first-order. ROM, based on the Galerkin procedure, uses the undamped linear mode shapes of the undamped cantilever beam as the basis functions. The influences of parameters (i.e. Casimir, damping, fringe, and detuning parameter) were also investigated.

Vibration of Rectangular Single-Layered Black Phosphorus

Two-dimensional layered crystal material black phosphorus (BP) has attracted extensive attention due to its excellent property and practical applications. Single-layered BP has a characteristic puckered structure which leads to two anisotropic in-plane directions. The vibration properties of this puckered structure material would be very interesting. Thermal vibration of a rectangular single-layered BP is studied by using continuum orthotropic plate models together with molecular dynamics (MD) simulation. Five elastic constants including two bending moduli, two Poisson’s ratios, and one shear modulus of BP are calculated by using MD method. The natural frequencies of BP are obtained by orthotropic plate models and MD simulation via fast Fourier transformation (FFT). The result of MD simulation shows that continuum orthotropic plate models can predict the natural frequencies well.

Exploration of the Response of Electrically Actuated MEMS Arches Under the Effect of Mechanical Shock Loads

This work investigates the modeling and simulation of the dynamic response of MEMS shallow arches under the combined effects of mechanical shock waves and electrostatic actuating forces. The possible instabilities and/or failures that can be considered in any reliability study of such bi-stable structures are numerically examined. The results demonstrate that the simultaneous effects of shock loads and the actuating force can make the bi-stability and/or the instability thresholds of electrically actuated MEMS arches devices much lower than the predicted values when considering their effects independently. The outcomes of this investigation can be very useful to design smart MEMS bi-stable sensors/accelerometers activated at a pre-programmed level of shock and/or abrupt change in the acceleration.

Adaptive Backstepping Control of the Gripping Process of Heavy Manipulators

A valve-controlled asymmetrical cylinder model was established to study the gripping hydraulic drive system of the grip device of heavy manipulator. Due to the strong nonlinear characteristics and uncertain parameters of the model, the Lyapunov stability principle was used to design a multistage inversion adaptive controller based on backstepping method and by introducing the virtual control parameter. The simulation results reveal that the tracking control and adaptive of uncertain parameters are very effective, which confirm that the designed controller can guarantee the stability of the closed-loop clamping hydraulic drive system.