Nonlinear Control of Dynamic Systems Using Single Multiplicative Neuron Models

The paper presents an approach to nonlinear control of dynamic systems using artificial neural networks (ANN). A novel form of ANN, namely, single multiplicative neuron (SMN) model is proposed in place of more traditional multi-layer perceptron (MLP). SMN derives its inspiration from the single neuron computation model in neuroscience. SMN model is trained off-line, to estimate the network weights and biases, using a population based stochastic optimization technique, namely, particle swarm optimization (PSO). Both off-line training and on-line learning of SMN have been considered. The development of the control algorithm is illustrated through the hardware-in-the-loop (HIL) implementation of DC motor speed control in LabVIEW environment. The controller based on SMN performs better than MLP. The simple structure and faster computation of SMN have the potential to make it a preferred candidate for implementation of real-life complex control systems.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

Modeling and Control of an Infinitely Variable Speed Converter With Application to Wind Turbines

Traditional transmission in wind turbine applications has a constant output-to-input speed ratio, which needs a power converter to regulate the current frequency that can be fed into the grid. Different types of continuously variable transmission (CVT) have been developed for vehicle and wind turbine applications, which can generate constant-frequency current without using a power converter in a wind turbine. An infinitely variable speed converter (IVSC) is a specific type of CVT that can achieve a zero speed ratio and transmit a large torque at a low speed ratio. An IVSC with drivers that convert an eccentric motion of cams to a concentric motion of the output shaft through one-way bearings is introduced, and an active control system with a combined feedback and feed forward control that can automatically adjust the eccentricity of the outer cams to control the speed ratio of the transmission is developed. The kinematic model of the IVSC is derived and fitted by a polynomial function to serve as the feed forward function in the control law. The feedback control is used to reduce the system error. A dynamic model of the IVSC is derived to investigate the effect of the dynamic load on the input and output speeds. Static and dynamic tests were conducted to validate the kinematic model of the IVSC. The variation of the average output speed per revolution of the output shaft is 0.56% with respect to the desired output speed in the simulation and 0.91% in the experiments.

Spatial Actuation Effectiveness of Segmented Actuators on Parabolic Cylindrical Panels

With the distinct capability of line-focusing, open parabolic cylindrical panels are commonly used as key components of radar antennas, space reflectors, solar collectors, etc. These structures suffer unexpected vibrations from the fluctuation of base structure, non-uniform heating and air flow. The unwanted vibration will reduce the surface reflecting precision and even result in structure damages. To explore active vibration and shape control of parabolic cylindrical panels, this study focuses on actuation effectiveness induced by segmented piezoelectric patches laminated on a flexible parabolic cylindrical panel. The mathematical model of a parabolic cylindrical panel laminated with distributed actuators is formulated. The segmentation technique is developed and applied to parabolic cylindrical panels, and the piezoelectric layer is segmented uniformly in the meridional direction. The distributed actuator patches induced modal control forces are evaluated. As the area of actuator patch varies in the meridional direction, modal control force divided by actuator area, i.e., actuation effectiveness, is investigated. Spatial actuation effectiveness, including its membrane and bending components are evaluated with respect to design parameters: actuator size and position, shell curvature, shell thickness and vibration mode in case studies. The actuation component induced by the membrane force in the meridional direction mainly contributes to the total actuation effectiveness for lower modes. Average and cancellation effect of various actuator sizes and the optimal actuator position are also discussed. Results suggest that for odd vibration modes, the maximal actuation effectiveness locates at the ridge of the panel; while for even modes, the peak/valley closest to the ridge is the optimal position to obtain the maximal actuation effectiveness. A segmentation scheme of the meridian interval angle 0.0464rad for the investigated standard panel is a preferred tradeoff between the actuation effectiveness and practical feasibility. The modal actuation effectiveness increases with the shell curvature, whereas decreases when the shell thickens.

A Sensitivity Based Approach to Determining Non-Cooperative Solutions in Nash and Stackelberg Games

A sensitivity based approach is presented to determine Nash solution(s) in multiobjective problems modeled as a non-cooperative game. The proposed approach provides an approximation to the rational reaction set (RRS) for each player. An intersection of these sets yields the Nash solution for the game. An alternate approach for generating the RRS based on design of experiments (DOE) combined with response surface methodology (RSM) is also explored. The two approaches for generating RRS are compared on three example problems to find Nash and Stackelberg solutions. It is seen that the proposed sensitivity based approach (i) requires less computational effort than a RSM-DOE approach, (ii) is less prone to numerical errors than the RSM-DOE approach, (iii) is able to find all Nash solutions when the Nash solution is not a singleton, (iv) is able to approximate non linear RRS, and (v) is able to find better a Nash solution on an example problem than the one reported in the literature.

Simultaneous Time-Frequency Control of Multi-Dimensional Micro-Milling Instability

A novel control concept is presented for the online control of a high-speed micro-milling model system in the time and frequency domains concurrently. Micro-milling response at high-speed is highly sensitive to machining condition and external perturbation, easily deteriorating from bifurcation to chaos. When losing stability, milling time response is no longer periodic and the frequency response becomes broadband, rendering aberrational tool chatter and probable tool damage. The controller effectively mitigates the nonlinear vibration of the tool in the time domain and at the same time confines the frequency response from expanding and becoming chaotically broadband. The simultaneous time-frequency control is achieved through manipulating wavelet coefficients, thus not limited by the increasing bandwidth of the chaotic system — a fundamental restraint that deprives contemporary controller designs of validity and effectiveness. The feedforward feature of the control concept prevents errors from re-entering the control loop and inadvertently perturbing the sensitive micro-milling system. Because neither closed-form nor linearization is required, the innate, genuine features of the micro-milling response are faithfully retained.

Turning Dynamics: Part 1 — Experimental Analysis

The workpiece and tool vibrations in a lathe are experimentally studied to establish improved understanding of cutting dynamics that would support efforts in exceeding the current limits of the turning process. A Keyence laser displacement sensor is employed to monitor the workpiece and tool vibrations during chatter-free and chatter cutting. A procedure is developed that utilizes instantaneous frequency (IF) to identify the modes related to measurement noise and those innate of the cutting process. Instantaneous frequency is shown to thoroughly characterize the underlying turning dynamics and identify the exact moment in time when chatter fully developed. That IF provides the needed resolution for identifying the onset of chatter suggests that the stability of the process should be monitored in the time-frequency domain to effectively detect and characterize machining instability. It is determined that for the cutting tests performed chatters of the workpiece and tool are associated with the changing of the spectral components and more specifically period-doubling bifurcation. The analysis presented provides a view of the underlying dynamics of the lathe process which has not been experimentally observed before.

Dynamic Servo Control for Underactuated Mechanical Systems

Due to the lack of control inputs, the motion range and application areas of underactuated mechanical system are greatly limited. To overcome such difficulties, the arbitrary state point dynamic tracking problem named dynamical servo control is discussed in this paper. Considering simplicity and repeatability, periodic trajectory is the best way leading to the desired point. Virtual constraints concept is employed and a target oriented trajectory planning procedure is proposed, which can generate periodic dynamic compatible and desired point crossing trajectory. A Lyapunov based tracking controller is proposed to avoid the strict conditions for using a traditional LQR based method. Experiments are performed on an Acrobot prototype and verify the correctness of the proposed periodic trajectory generating method and the effectiveness of the tracking controller.

A Novel Acceleration/Deceleration Control Algorithm for High Precision Feed Motion System

The feed motion dynamic precision is determined by the properties of the CNC system, the servo control system and the mechanical structure. The Acceleration/Deceleration Control (ADC) in CNC system is widely used to smooth the motion trajectory, so as to reduce transient error caused by vibration. The performance of various ADC algorithms differ significantly, which indicates the importance of developing more effective ADC algorithm. In this paper a novel ADC algorithm called “Asymmetric Double S-shape type Algorithm” is introduced and validated by detailed mathematic deduction, and then its dynamic performance is compared with that of traditional ADC algorithms in both the time domain and frequency domain. The analytical and simulation results demonstrated that, the proposed novel ADC algorithm has notably advantage over the traditional ones in reducing the tracking error in both transient state and steady state, hence is capable of fundamentally improving the feed motion dynamic precision.

Nonlinear Parametric Instability of Functionally Graded Rectangular Plates in Thermal Environments

Geometrically nonlinear parametric instability of functionally graded (FG) rectangular plates in thermal environments is investigated via multi-modal energy approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to in-plane static and harmonic excitation in the frequency neighbourhood of twice the fundamental frequency is investigated. The boundary conditions are assumed to be simply supported movable. The plate displacements and rotations are expanded in terms of double series trigonometric functions and Lagrange equations are used to reduce the energy functional to a system of infinite nonlinear ordinary differential equations with time varying coefficients, and quadratic and cubic nonlinearities. In order to obtain the complete dynamic scenario, numerical analyses are carried out by means of pseudo arc length continuation and collocation technique to obtain frequency-amplitude and force-amplitude relations in the presence of temperature variation in the thickness direction. The effect of volume fraction exponent as well as temperature variation on the on-set of instability for both static and periodic in-plane excitation are fully discussed and the post-critical nonlinear responses are obtained.