Sharif Digital Repository

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration analysis of single and double tapered beams on elastic foundation. Geometric nonlinearity is considered using the condition of inextensibility of neutral axis. Moreover, the elastic foundation consists of a linear and cubic nonlinear parts together with a shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the second-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the nonlinear... 

The main purpose of this paper is to design a decentralized controller for some car-like (wheeled) multi robots to follow and hunt a moving target. Considering geometric dimensions, mass and moment of inertia, robots are very similar to actual cars in which the outputs of the controller are steering and driving wheel torques. All robots are equipped with range and bearing sensors along with antenna, to communicate radio wave signals. A Kalman filter is implemented to estimate relative position, state variables of the target and state variables of other robots. The controller is designed to carry out the group maneuver of the system, based on the system dynamics analysis of inertial agents,... 

In this paper, chaos in spatial attitude dynamics of a triaxial rigid satellite in an elliptic orbit is investigated analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers (i.e. the initial values needed to have a chaotic attitude motion) based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincaré maps and the maximum value of the Lyapunov exponents. The rotational–translational Hamiltonian of the system is first derived. This Hamiltonian has six degrees of freedom. Choosing a proper set of coordinates and given the fact that the... 

In this paper, chaos in spatial attitude dynamics of a triaxial rigid satellite in an elliptic orbit is investigated analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers (i.e. the initial values needed to have a chaotic attitude motion) based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincaré maps and the maximum value of the Lyapunov exponents. The rotational–translational Hamiltonian of the system is first derived. This Hamiltonian has six degrees of freedom. Choosing a proper set of coordinates and given the fact that the... 

In this paper, we analytically and numerically investigate chaos in attitude dynamics of a flexible satellite composed of a rigid body and two identical rigid panels attached to the main body with springs. Flexibility, viewed as a perturbation, can cause chaos in the satellite. To show this, first, we use a novel approach to define this perturbation. Then, we employ canonical transformation to transform the Hamiltonian of the system from five to three degrees of freedom. Next, we approximate the system by a second-order differential equation with a time quasiperiodic perturbation. Finally, we apply Melnikov–Wiggins’ method near the heteroclinic orbits to prove the existence of chaos. Using... 

This paper focuses on the observer design for a 2D nano-positioner. In order to position the stage with a desired accuracy, it is required to adjust the stage displacements with a closed-loop control system. Since displacement and velocity of the main stage are not measured directly in the designed nano-positioning system, some observers should be designed to estimate these state variables using data provided by measurable variables. To this end, three different observers were designed based on neural, fuzzy and adaptive neuro fuzzy inference system (ANFIS) networks. With the purpose of obtaining data for training the observer model, a reference model is required. For this reason, the... 

This study presents a novel method for observation of stage position in a 2D nano-positioning system based on a hybrid Kalman filter. The proposed method obviates the need to measure the stage position directly using complex and costly capacity sensors. Instead, traditional piezo actuators equipped with strain gauge sensors are utilized to measure the deection of the magnification system at the position of actuators. Then, a powerful estimation algorithm called Kalman filter was employed to observe stage displacements. The designed hybrid Kalman filter uses dynamical equations of motion in the prediction step. The piezo actuators deections are measured and exploited to correct the predicted... 

In this study tracking problem of tip of a micro cantilever, actuated by electrostatic, is investigated. Dynamic model of the system is a PDE. Using electrostatic actuation.introduced significant nonlinearity in dynamic model of the system. Control goals are achieved by means of backstepping for SI and feedback linearization for MI system. Performance of control system is inspected for some assumptions and simplifications. The results are in according to numerical simulations  

The chaotic dynamics of roto-translatory motion of a triaxial Kelvin-type gyrostat satellite under gravity gradient perturbations is considered. The Hamiltonian approach is used for modelling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation using the Serret- Andoyer variables. Therefore, this reduction leads to the derivation of the perturbation form of the Hamiltonian that can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos phenomenon. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate... 

In this study tracking problem of tip of a micro cantilever, actuated by electrostatic, is investigated. Dynamic model of the system is a PDE. Using electrostatic actuation introduced significant nonlinearity in dynamic model of the system. Control goals are achieved by means of backstepping for SI and feedback linearization for MI system. Performance of control system is inspected for some assumptions and simplifications. The results are in according to numerical simulations  

Quasi-periodic and chaotic behavior, along with the control of chaos for a Gyrostat satellite (GS), is investigated in this work. The quaternion-based dynamical model of the GS is first derived, and then the influences of the reaction wheels in the GS structure, under the gravity gradient perturbation that causes a route to chaos through quasi-periodicity mechanism, is investigated. For the suppression of chaos in the system, a chaos control system with the quaternion feedback is designed for the GS based on the extension of the Ott-Grebogi-Yorke (OGY) method using the linearization of the Poincaré map. In the extended OGY controller, the Poincaré map is estimated using the Least Square... 

Piezoelectric transducers (sensors and actuators) are widely used to produce motion or to sense displacement. One of the most applicable types of the piezo-electric transducers is a transducer in which the piezo stacks are sandwiched between two vibrating masses by a connecting stud. These types of the piezo-electric transducers which are utilized for sensing applications are known as Tonpilz. A piezo-electric transducer is usually designed to work in the resonant frequency, and modeling and simulating its dynamics behavior to check the desired performance are very important. In this study, by considering the concept of the admittance expression, the dynamics model of a piezo-electric... 

In this paper a linear delayed feedback control is proposed and experimentally applied to eliminate chaos in a nonlinear electrical circuit which is known as Sprott circuit. The chaotic behavior of the system is suppressed by stabilizing one of its first order Unstable Periodic Orbits (UPOs) by a controller designed based on so-called Pyragas method. The effectiveness of this method, firstly, is numerically investigated by stabilizing the unstable first order periodic orbit and then verified experimentally by a laboratory setup. ©2007 IEEE  

In this paper, design, simulation and optimization of a novel electrothermally-activated polymeric microactuator capable of generating combination of bidirectional lateral and rotational motions are presented. The composite structure of this actuator is consisted of a symmetric meandered shape silicon skeleton, a SU8 thermal expandable polymer and a thin film chrome layer heater. This actuator is controlled by applying appropriate voltages on its four terminals. With the purpose of dimension optimization, a numerical parametric study is executed. The modeled actuator which is 1560 ?m long, 156 ?m wide and 30 ?m thick, demonstrates a remarkable lateral displacement of 23 ?m at power... 

A method for controlling chaos when the mathematical model of the system is unknown is presented in this paper. The controller is designed by the pole placement algorithm which provides a linear feedback control method. For calculating the feedback gain, a neural network is used for identification of the system from which the Jacobian of the system in its fixed point can be approximated. The weights of the neural network are adjusted online by the gradient descent algorithm in which the difference between the system output and the network output is considered as the error to be decreased. The method is applied on both discrete-time and continuous-time systems. For continuous-time systems,... 

Variational principle is used to derive the nonlinear response of the floating roof of cylindrical liquid storage tanks due to harmonic base excitations. The formulation accounts for nonlinearity due to large deflections of the floating roof. The derived nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating the response of the nonlinear model for increasing amplitudes of near resonance harmonic excitations gives rise to the appearance of sub and... 

The fusion of the optical and inertial tracking systems seems an attractive solution to solve the shadowing problem of the optical tracking systems, and remove the time integration troubles of the inertial sensors. We developed a fusion algorithm for this purpose, based on the Kalman filter, and examined its efficacy to improve the position and orientation data, obtained by each individual system. Experimental results indicated that the proposed fusion algorithm could effectively estimate the 2 seconds missing data of the optical tracker  

Paraplegic users of mechanical walking orthoses, e.g. advanced reciprocating gait orthosis (ARGO), often face high energy expenditure and extreme upper body loading during locomotion. We studied the effect of kinematical pattern on the mechanical performance of paraplegic locomotion, in search for an improved gait pattern that leads to lower muscular efforts. A three-dimensional, four segment, six-degrees-of-freedom skeletal model of the advanced reciprocating gait orthosis-assisted paraplegic locomotion was developed based on the data acquired from an experimental study on a single subject. The effect of muscles was represented by ideal joint torque generators. A response surface analysis... 

In non-classical micro-beams, the strain energy of the system is determined by the non-classical continuum mechanics. In this study, we consider a closed-loop control methodology for suppressing the vibration of non-classical microscale Euler-Bernoulli beams with nonlinear electrostatic actuation. The non-dimensional form of the governing nonlinear partial differential equation of the system is introduced and converted into a set of ordinary differential equations using the Galerkin projection method. In addition, we prove the observability of the system and we design a state estimation system using the extended Kalman filter algorithm. The effectiveness and performance of the proposed... 

During the drug delivery process in chemotherapy, both of the cancer cells and normal healthy cells may be killed. In this paper, three mathematical cell-kill models including log-kill hypothesis, Norton-Simon hypothesis and Emax hypothesis are considered. Three control approaches including optimal linear regulation, nonlinear optimal control based on variation of extremals and H∞-robust control based on μ-synthesis are developed. An appropriate cost function is defined such that the amount of required drug is minimized while the tumor volume is reduced. For the first time, performance of the system is investigated and compared for three control strategies; applied on three nonlinear models...