Aria Alasty

Closed-form approximation and numerical validation of the influence of van der Waals force on electrostatic cantilevers at nano-scale separations

In this paper the two-point boundary value problem (BVP) of the cantilever deflection at nano-scale separations subjected to van der Waals and electrostatic forces is investigated using analytical and numerical methods to obtain the instability point of the beam. In the analytical treatment of the BVP, the nonlinear differential equation of the model is transformed into the integral form by using the Greens function of the cantilever beam. Then, closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. In the numerical method, the BVP is solved with the MATLAB BVP solver, which implements a collocation method for obtaining the solution of the BVP. The large deformation theory is applied in numerical simulations to study the effect of the finite kinematics on the pull-in parameters of cantilevers. The centerline of the beam under the effect of electrostatic and van der Waals forces at small deflections and at the point of instability is obtained numerically. In computing the centerline of the beam, the axial displacement due to the transverse deformation of the beam is taken into account, using the inextensibility condition. The pull-in parameters of the beam are computed analytically and numerically under the effects of electrostatic and/or van der Waals forces. The detachment length and the minimum initial gap of freestanding cantilevers, which are the basic design parameters, are determined. The results of the analytical study are compared with the numerical solutions of the BVP. The proposed methods are validated by the results published in the literature.

Adaptive chaos synchronization in Chua's systems with noisy parameters

Using the Lyapunov stability theory an adaptive control is proposed for chaos synchronization between two Chua systems which have stochastically time varying unknown coefficients. The stochastic variations of the coefficients around their unknown mean values are modeled through Gaussian white noise produced by the Wiener process. It is shown that using the proposed adaptive control the mean square of synchronization error converges to an arbitrarily small bound around zero depending on the controller feedback gain. Simulation results indicate that the proposed adaptive controller has a high performance in synchronization of chaotic Chua circuits in noisy environment.

Parameter estimation and interval type-2 fuzzy sliding mode control of a z-axis MEMS gyroscope

This paper reports a hybrid intelligent controller for application in single axis MEMS vibratory gyroscopes. First, unknown parameters of a micro gyroscope including unknown time varying angular velocity are estimated online via normalized continuous time least mean squares algorithm. Then, an additional interval type-2 fuzzy sliding mode control is incorporated in order to match the resonant frequencies and to compensate for undesired mechanical couplings. The main advantage of this control strategy is its robustness to parameters uncertainty, external disturbance and measurement noise. Consistent estimation of parameters is guaranteed and stability of the closed-loop system is proved via the Lyapunov stability theorem. Finally, numerical simulation is done in order to validate the effectiveness of the proposed method, both for a constant and time-varying angular rate.

Effects of Rotary Inertia and Shear Deformation on Nonlinear Free Vibration of Microbeams

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the doubly clamped microbeam. Shear deformation and rotary inertia have significant effects on the large amplitude vibration of thick and short microbeams.

Equations of Motion of a Single-Wheel Robot in a Rough Terrain

In this article, dynamic equations of a single wheel robot, known as Gyrover, through Lagrange method applying a new approach will be addressed. There is no simplification on the dynamic analysis. Considering any possible differentiable function for the road’s curve, the effect of the road’s roughness is completely described in the dynamic equation evaluation. Although there are complicated relations between the wheel and rough terrain, due to the efficient generalized coordinate selection, closed form dynamic equation of the motion is derived. Because of the closed form formulation, required time for simulation will be reduced. From the proposed complete model a simplified model for the controller design could be extracted

Design and real-time experimental implementation of gain scheduling PID fuzzy controller for hybrid stepper motor in micro-step operation

In this paper, design and real time experimental implementation of fuzzy gain scheduling of PID controller for hybrid stepper motor in micro-stepping operation is described that was developed to track the desired positioning problem. The control problems characterized by mathematical models exhibit significant nonlinearity and uncertainty. The good performance of proposed fuzzy PID controller is shown.

Adaptive critic-based neuro-fuzzy controller in multi-agents: Distributed behavioral control and path tracking

In this paper, we follow two control tasks in a leader following frame with undirected network and local communications. As the first goal, distributed behavioral imitation, which is necessary to fit agents with complicated motion equations in kinematic frames, is discussed. Providing real agents with behavioral controller makes them capable to act as a kinematic particle. The second goal is to design an active leading strategy for the LA to move the group on a predefined path. Both problems can be mathematically modeled in an affine form, which is the reason behind using a unique adaptive controller to solve them. The controller is based on a neuro-fuzzy structure with critic-based leaning structure. It is shown that the proposed controller can successfully handle both tasks.

Kinematic and dynamic sensitivity analysis of a three-axis rotary table

Three-axis rotary table is a flight motion simulator (FMS) used in the hardware in the loop (HWIL) simulation. Geometrical modeling of 3-axis rotary tables is described and then three possible geometrical layouts are driven. Kinematic and dynamic modelings of a 3-axis rotary table are developed in this paper. Denavit-Hartenberg (D-H) method, recursive Newton-Euler (RNE) and Lagrange methods are used, respectively, in kinematic and dynamic modeling. A kinematic error analysis is applied to determine the orientation and position accuracy of the table. Dynamic sensitivity analysis is also performed and the first-order sensitivity functions are derived corresponding several dynamic and control system parameters.

Control of a Nonlinear Boiler-Turbine Unit Using Two Methods: Gain Scheduling and Feedback Linearization

To achieve a good performance of a boiler-turbine unit, dynamic variables such as steam pressure, water level of drum and electric output of turbine must be controlled. In this paper a nonlinear model of the boiler-turbine unit is considered in which the inputs are the valve positions of fuel flow, steam control, and feed-water flow. Using two control methods, feedback linearization and gain scheduling, a PI controller is designed. It is shown that by applying both methods, system goes from one operating point to another with an appropriate specification of time response. Results show that system with a controller designed based on gain scheduling method has a better time response from a nominal operating point to a far operating point. In addition, applying any of these control approaches guarantees robustness of the system against the uncertainties associated with dynamic model.Copyright

On the control of chaos via fractional delayed feedback method

In this paper the problem of controlling unstable fixed points (in discrete systems) and periodic orbits (in continuous system) is investigated via a new scheme involving fractional derivatives. This method is based on applying feedback of measured states and using the period of fixed points and periodic orbits. In this method there is no need of information for fixed point and periodic orbits, just the period is enough. The effectiveness of this method is investigated via some demonstrative example.