This research work presents an H control design based on cluster sensing and actuation to suppress acoustic modes of a distributed panel structure which is subjected to excitation with varying frequency. A state–space model of the planar structure is obtained based on cluster sensing and cluster actuation. Uncertainty sources are considered for robustness of the control system. The eigenvalues of the structure's acoustic power modes are assumed to vary with the excitation frequency in order to consider sound radiation from the vibrating panel structure. The proposed controller design covers the uncertainties caused by varying disturbance frequencies and inhomogeneities of the structure.

Motion-induced vibration can be greatly reduced by properly shaping the reference command. Input shaping is one type of reference shaping method that is based largely on linear superposition. In this paper we document the impact of nonlinear crane dynamics on the effectiveness of input shaping. As typical bridge cranes are driven using Cartesian motions, they behave nearly linearly for low- and moderate-velocity motions. On the other hand, the natural rotational motions of tower cranes make them more nonlinear. The nonlinear equations of motion for both bridge and tower cranes are presented and experimentally verified using two portable cranes. The effectiveness of input shaping on the near-linear bridge crane is explained. Then, a command-shaping algorithm is developed to improve vibration reduction during the more nonlinear slewing motions of the tower crane. Experimental results demonstrate the effectiveness of the proposed approach over a wide range of operating conditions.

Recently, the design of active magnetic bearings (AMBs) for miniaturized industrial applications puts much emphasis on small size and low-power consumption as well as low-cost system production. In this paper, a novel hybrid type three-pole AMB system is proposed, which is divided into two bearing parts: a three-pole radial AMB and an axial permanent magnet bearing. The radial AMB consists of three active main poles with three coil windings, three sub-poles with radial permanent magnets, generating bias flux, and three Hall diodes, measuring the rotor position. The permanent magnet bearing is made of two facing axially polarized ring-type permanent magnets for passive stability in the axial and angular motion. Compared with the conventional four- or eight-pole AMB, the hybrid three-pole AMB system reduces the power consumption with fewer power amplifiers and is suitable for smaller-sized AMBs. The primary problem in modeling and control of the three-pole AMB in the conventional Cartesian coordinates is the strong coupling in magnetic flux generated by three main and sub-poles. Consequently, the system becomes strongly nonlinear with respect to control inputs as well as states. To resolve this difficulty in treating the strong nonlinearity in the conventional Cartesian coordinates, we introduce the redundant coordinates along with three-pole configuration for modeling and design of controller. Based on the redundant coordinates, three identical decoupled proportional–derivative controllers can be applied, which is very simple compared with previous nonlinear control algorithms developed for three-pole AMBs. Experiments are also carried out with a prototype AMB system to validate the proposed design and control concept based on the redundant coordinates.

An analytical solution to the equation of motion of a beam controlled with piezoceramic (PZT – lead zirconate titanate) sensor and actuator patches is proposed. The contribution of the mass and stiffness of the piezoceramic patches to the piezo structure are taken into account. The equation of motion for the controlled structure includes Heaviside functions and derivatives of the Heaviside function due to finite patch lengths making the equation of motion difficult to solve using conventional methods. In the present study, an integral equation is introduced where the eigensolutions of the integral equation are eigensolutions of the differential equation of motion for the controlled beam. A finite element model of the controlled beam is also formulated. The model contains modified beam element mass and stiffness matrices to account for the piezo patches and control effect. Two case studies are presented and the first three natural frequencies and mode shapes are found using the integral equation and finite element solutions. The results from the integral equation solution match very closely the results from the finite element solution.

Chatter suppression is essential for achieving high precision and surface quality in machining processes. In this paper, a control strategy is presented for chatter suppression in cutting process in the presence of tool wear and parameter uncertainties. A single-degree-of-freedom model of a turning process in the orthogonal cutting configuration is used to set up the nonlinear delay differential equation of motion that includes the effects of tool flank wear. Uncertainties in cutting velocity, tool wear size and parameters of the dynamic model are included in the model of the cutting process. The force provided by a piezo-actuator is taken as the control input of the system. A sliding mode control scheme is used and an effective control law is derived that suppresses chatter. Results of stability analysis and sliding mode control for two distinct cases of sharp and worn tools are presented and compared, which show the effectiveness of the approach.

Introducing an independent four-wheel-steering (4WS) system, we are able to design an autodriver to keep an autonomous vehicle on a given road. The kinematic condition of steering can be used to set the steer angles such that the kinematic center of rotation be at any desired point. The road and tire characteristics, along with the dynamics of a moving vehicle cause the vehicle to turn about an actual point that is not necessarily at the road curvature center. The position of the dynamic turning center can be controlled by adjusting the steer angles such that it coincides with the road curvature center. Such a vehicle will move on the desired road autonomously.

Free vibration analysis of annular sector plate is studied using an eight-node curvilinear domain. The method of discrete singular convolution (DSC) is used for computations. Radial edges of plates are simply supported; however, various edge conditions are taken into account for circumferential edge. In the proposed approach, an irregular physical domain is transformed into a rectangular domain by using geometric coordinate transformation. The DSC procedures are then applied to discretization of the transformed set of governing equations and boundary conditions. The effects of mode numbers, vertex angle, boundary conditions and outer-to-inner radius ratio on the vibration frequencies are investigated. It is seen that the results obtained by DSC method shows very good agreement with that of other available analytical and numerical solutions for the plate problems under investigation.

Rotating machinery support excitations can occur if a machine is installed on a base prone to ground motions or on-board moving systems such as ships and aircraft. This paper presents a formulation for the dynamic analysis of rigid rotors subject to base excitations plus mass imbalance. The formulation allows for six motions at the machine base and takes into account the linear/nonlinear spring characteristics of the supporting bearings. Equations of motion are derived using Lagrange's equations. For rotor–linear bearing systems subject to mass imbalance plus harmonic excitations along or around lateral directions, analytical solutions for equations of motion are derived and analytical results in the time domain are compared with their counterparts obtained by numerical integration using the Runge–Kutta method and typical agreement is obtained. The system natural frequencies as affected by rotor speed are obtained using the QR algorithm using the DAMRO-1 program and compared with those obtained by MATLAB and excellent agreement is obtained. The frequency response (maximum amplitude of vibrations against the base excitation frequency) is characterized by peaks at natural frequencies of the rotating gyroscopic system. This necessitates extreme precaution when we design such rotating systems that are prone to base motions and mass imbalance. For systems with bearing cubic nonlinearity, results are obtained by numerical integration and discussed with regards to the time domain, fast Fourier transform (FFT) and Poincaré map. Periodic and quasi-periodic disk/bearings motions are observed. For systems with support cubic nonlinearity and subject to mass imbalance and base excitation, the FFT of disk horizontal and vertical vibrations is marked with sum and difference tones, ±nf_b ± f_s (n + m is always odd) where f_s is the rotating unbalance frequency and f_b is base excitation frequency.

H full information control method for structural vibration suppression with control delay is proposed within a discrete-time framework. Firstly, the continuous-time system equation with control delay is discretized by precise computation of matrix exponentials. By introducing an appropriate extended state vector, the time-delay system is transformed into standard discrete forms without time delays. Then a controller is designed based on the discrete time H full information control theory. The controller consists of a regular feedback closed-loop and a feed-forward compensator which utilizes external excitation signals measured in real time. The feed-forward plus feedback controller has better performance than feedback only controllers. The feedback loop of the deduced controller contains linear combinations of former control inputs besides the current state feedback terms. Thus the proposed method is applicable to large time-delay cases. Considering the complexity of the transformed system, a 2^N algorithm is introduced to search the optimal attenuation level and evaluate the control law. The present algorithm can be executed parallel, which makes the design of H controllers very convenient. Finally, numerical simulations of a three-story structure control are implemented. Time-delay effects on the optimal attenuation level are given to show that it is an important factor for system stability. Simulation results demonstrate the feasibility and effectiveness of the proposed control method.

The present work deals with stability analysis of a spinning non-symmetric shaft with a non-central disk mounted on a rotating (precessing) base, where the spin axis and the precession axis intersect at right angles. The nutation speed is zero and the spin and precession speeds are considered to be uniform. The motion of the rotor is such that it undergoes small elastic deformation superposed on rigid body rotation. The shaft-disk system is assumed to be axially and torsionally stiff. A four-degree- of-freedom model is considered for the stability analysis. A non-symmetric shaft (e.g., shaft with rectangular or elliptic cross-section, shaft with a keyway, cracked shaft etc.) of a rotor has dissimilar stiffness in two perpendicular transverse planes. The governing equations for such a rotor are expressed in the precessing but non-spinning frame. Since the governing equations of motion are found to have periodic stiffness terms, a variant of Hill's method is adopted for stability analysis. The stability borderlines are constructed with respect to the spin speed and precession speed.

A control method for achieving zero compliance to direct disturbance is proposed for a vibration isolation system. The structure of the proposed zero-compliance system is as follows. A middle mass is suspended by a spring from the base. The isolation table is suspended and moved by a linear actuator that is fixed to the middle mass. When direct disturbance acts on the isolation table, the middle mass begins to move in the same direction as the disturbance. The actuator operates to move the isolation table in the opposite direction to cancel the displacement of the middle mass to the base. To verify the effectiveness of this principle, a single-axis apparatus was fabricated. In this apparatus, the isolation table and the middle mass are guided to move horizontally to study characteristics without the influence of gravity. A voice coil motor (VCM) is installed between the isolation table and the middle mass, and integral–proportional–derivative (I-PD) control is implemented to achieve displacement cancellation control. Another VCM is installed between the middle mass and the base, and PD control is implemented for realizing the prescribed stiffness and damping. The efficacy of the designed control system is confirmed experimentally.

In this paper we deal with compensation for controller windup due to actuator saturation in the integral sliding mode control. It is shown that the actuator saturation in the integral sliding mode control causes windup problem similar to the so-called integrator windup, which often takes place in linear control systems with integral action. A simple modification for the switching function is presented in order to reduce the discontinuous component of the control input during saturation. This can be seen as a variable switching function. Furthermore, the proposed anti-windup compensation is applied to a power-assisted manipulator with a single degree of freedom. Simulation and experimental results show the effectiveness of the proposed method.

In this paper we propose a design method for a three-dimensional active isolation system with a low-stiffness isolation table assumed to be a large-size, lightweight isolation system. The lightweight, large-size isolation tables have been designed to be flexible. Owing to this, multi-modal vibrations appeared on the isolation table in the lower-frequency region. Therefore, a control system for considering multi-modal vibrations should be developed. We constructed a five-degree-of-freedom lumped model of the isolation table using a reduced-order physical-modeling method that is effective for controlling multi-modal vibrations. In the controller design, the performance of vibration control is obtained using a feedback controller designed using the linear–quadratic (LQ) control theory. Moreover, a feed-forward controller for a multi-input multi-output system has been added in order to obtain a high-isolation performance. Thus, a two-degree-of-freedom controller combined with LQ feed-forward controllers is designed. The usefulness of the proposed modeling method and controller are confirmed through numerical simulations and experimental results.

This paper leads with the phenomenon of the bouncing of a vehicle due to an irregularity being on a road or on a bridge deck. Attention is focused on the determination of the critical velocity for which the vehicle loses touch with the road's or the bridge-deck's surface following a missile's orbit and then striking the road or the bridge during landing. If the vehicle moves with a velocity greater than the critical one, we determine the corresponding time (and thus the point of the bridge) at which touch is lost. Afterwards, we determine also the landing point of the vehicle. Solving firstly the above problem for a vehicle moving on a road, it is easy next to proceed to the solution of the same problem for a vehicle moving on a bridge. The theoretical formulation is based on a continuous approach in addition to the use of a two degrees of freedom model associated with the mass of the moving load.

Anti-swing control is a well-known term in gantry crane control. It is designed to move the payload of gantry crane as fast as possible while the payload swing angle should be kept as small as possible at the final position. A number of studies have proposed anti-swing control using the well-known proportional, integral, derivative (PID) control method. However, PID controllers cannot always effectively control systems with changing parameters. Some studies have also proposed intelligent-based control including fuzzy control. However, the designers often have to face the problem of tuning many parameters during the design to obtain optimum performance. Thus, a lot of effort has to be taken in the design stage. In this paper Fuzzy-tuned PID controller design for anti-swing gantry crane control is presented. The objective is to design a practical anti-swing control which is simple in the design and also robust. The proposed Fuzzy-tuned PID utilizes fuzzy system as PID gain tuners to achieve robust performance to parameters' variations in the gantry crane. A complex dynamic analysis of the system is not needed. PID controller is firstly optimized in MATLAB using a rough model dynamic of the system which is identified by conducting a simple open-loop experiment. Then, the PID gains are used to guide the range of the fuzzy outputs of the Fuzzy-tuned PID controllers. The experimental results show that the proposed anti-swing controller has satisfactory performance. In addition, the proposed method is straightforward in the design.

An analytical approximate technique for nonlinear problems, namely the homotopy analysis method, is employed to propose an approach for the aeroelastic system of a two-dimensional airfoil with a cubic nonlinearity. The frequency and amplitude of the limit cycle oscillation are expanded as power series of an embedding parameter. A series of algebraic equations governing the coefficients of the series are then derived. All the equations are linear except the first one. This provides us with a simple iteration scheme to seek high-order approximations. The frequency and amplitude of the limit cycle oscillation are obtained with a high degree of accuracy. It turns out that the frequency is independent of the coefficient of the cubic nonlinearity, and that the amplitude is in inverse proportion to the square root of this coefficient.

The dynamic behavior of a high speed unbalanced rotor supported on roller bearings with damping has been studied, focusing particular attention on its nonlinear aspects. The non-linearity in the rotor bearing system has been considered mainly due to Hertzian contact, unbalanced rotor effect and radial internal clearance. This is modeled as an oscillating spring-mass-damper system. Various techniques like Time Response curves, Poincaré maps, Orbits plots, fast Fourier transformation, Hopf bifurcation and Phase Trajectory are used to study the nature of response. The motion of an unbalanced rotor is categorized with respect to the ratio of the Forcing/Natural frequency of the system as Harmonic, Sub-harmonic, Quasi periodic and Chaotic. The results show the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. Period doubling and mechanism of intermittency have been observed that lead to chaos. The outcomes illustrate the appearance of instability and chaos in the dynamic response as the speed of the rotor-bearing system is changed. This work differs from the previous studies in the way that the complex model simulates nonlinear vibrations, considering that both the lubricated nonlinear contact stiffness and damping correspond to the conservative and dissipative energies, respectively. The comprehensive model developed in this investigation is a useful tool to predict the system behavior and for performance evaluation of a rotor bearing system.

In the authors' previous study, we proposed a novel shock vibration control method using the active momentum exchange impact damper (AMEID). By using this method, the shock vibration of the vibratory system is greatly reduced by transferring part of its momentum to the damper mass. This feature is effective for suppressing the first large peak value of the acceleration response due to a shock load. However, the validity of AMEID for actual implementations has not yet been investigated. In this paper, the active control of shock vibration using AMEID under real conditions is evaluated by simulation and experiment. A one-degree-of-freedom vibratory system is used as the controlled object. The controller is designed using the linear quadratic regulator optimal control theory. Reductions in the acceleration response and transmitted force to the base are investigated using simulations. Experiments are carried out to verify the simulation results.

We consider a right cylinder composed of a physically dipolar thermoelastic material for which one plane end is subjected to an excitation which is harmonic in time. By using a measure of Toupin type associated with the corresponding steady-state vibration and assuming that the exciting frequency is lower than a certain critical frequency, we obtain a spatial decay estimate, similar to that of Saint-Venant type.

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important to know the natural frequencies of the coupled beam–mass system for a proper design of the structural elements. There is plenty of literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring–mass system and Bernoulli–Euler multi-span beams carrying multiple spring–mass systems, but less is available regarding Reddy–Bickford multi-span beam carrying multiple spring–mass systems with/without axial force effect. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of Reddy–Bickford beams. The model allows the influence of the shear effect and spring–mass systems on the dynamic behavior of the beams to be analyzed by using Reddy–Bickford beam theory. The effects of the attached spring–mass systems on the free vibration characteristics of one to four span beams are studied. The calculated natural frequencies of Reddy–Bickford and Timoshenko multi-span beams using a secant method for nontrivial solution of the different values of axial force are given. The mode shapes of Reddy–Bickford multi-span beams are also presented.

This paper presents a computational technique for the solution of a class of nonlinear singular boundary value problems arising in physiology. The approach is based on a pseudospectral Legendre method in which Legendre–Gauss–Lobatto nodes are used to construct the Nth degree polynomial interpolation to approximate the solution. The method is easy to implement and yields accurate results. Illustrative examples are included to demonstrate the capability of the proposed method, and a comparison is made with existing methods in the literature.

In this paper the authors propose a modification to the known force identification procedure based on modal filtration. The modification consists of replacing the modal vectors with the Ritz vectors. The latter seem to be more accurate because they take into account the static deformation of the structure and are less sensitive to truncation error. After the main idea- the algorithm modification- is presented, it is verified and then compared with the original solution. Two sets of data are used for this purpose, firstly simulation data from the numerical model, and then physical data recorded during a laboratory experiment.