Deflection Control of Electrostatically Actuated Micro Cantilevers via Fuzzy Controller

2016 ◽  
Author(s):  
Mohammad Khadembashi ◽  
Hamid Moeenfard ◽  
Amir H. Ghasemi
Keyword(s):  
Passive Control ◽  
Fuzzy Controller ◽  
Open Loop ◽  
Beam Deflection ◽  
The Novel ◽  
Lagrange Equations ◽  
Controlled System ◽  
Single Level ◽  
Electrostatically Actuated ◽  
Micro Structures

The objective of this paper is to develop a novel two-level supervised fuzzy controller to stabilize the response of electrostatically actuated microbeams beyond their pull-in range. To this end, Lagrange equations are utilized to derive the differential equations governing the dynamic behavior of the system. To investigate the possibility of using a passive control strategy, the static behavior of the system is studied in detail. Through some open loop simulations, the qualitative and quantitative dependence of the beam deflection to the applied voltage and system parameters are studied. Based on the understanding obtained from these studies, a single level fuzzy controller is designed to control the response of the microstructure. In order to enhance the performance of the closed-loop system, another higher level supervisory fuzzy controller is designed to tune the maximum allowable voltage the lower level controller can apply. Simulation results reveal that both single level and multi-level fuzzy controllers can extend the travel range of the microbeams beyond its pull-in range. However the rise time, overshoot and settling time in the multilevel controlled system is far better than that of a simple single level fuzzy controller. The novel controller presented in this paper can be applied in most intrinsically nonlinear nano/micro structures to help them to have more efficient regulations and command tracking maneuvers.

A Two-Level Adaptive Fuzzy Control Algorithm for Beyond Pull-In Stabilization of Electrostatically Actuated Microplates

2016 ◽  
Author(s):  
Moeen Radgolchin ◽  
Hamid Moeenfard ◽  
Amir H. Ghasemi
Keyword(s):  
Fuzzy Controller ◽  
Adaptive Fuzzy Control ◽  
Single Mode ◽  
Lagrange Equations ◽  
Dynamic Simulations ◽  
Positioning Systems ◽  
Electrostatically Actuated ◽  
Performance Specifications ◽  
Control Objective ◽  
Fuzzy Control Algorithm

The objective of this paper is to present an adaptive multi-level fuzzy controller to stabilize the deflection of an electrostatically actuated microplate beyond its pull-in range. Using a single mode approximation along with utilizing the Lagrange equations, the dynamic behavior of the microplate is described in modal space by an ordinary differential equation. By different static and dynamic simulations, the system and the dependence of the deflection to the input applied voltage is identified linguistically. Then, based on the linguistic description of the system, a fuzzy controller is designed to stabilize the microplate at the desired deflections. To improve the performance specifications of the closed-loop system, another fuzzy controller at a higher level is designed to adjust the parameters of the main controller in real time. The simulation results reveal that by using the proposed single level and adaptive two level controllers, the control objective is met effectively with good performance specifications. It is also observed that adding a supervisory level to the main controller can reduce the overshoot and the settling time in beyond pull-in stabilization of electrostatically actuated microplates. The qualitative knowledge resulting from this research can be generalized and used for development of efficient controllers for N/MEMS actuators and electrostatically actuated nano/micro positioning systems.

scholarly journals Study of the stability of fuzzy controllers by an estimation of the attraction regions: A Vector Norm approach

2002 ◽  
Vol 8 (3) ◽  
pp. 221-231 ◽  
Author(s):  
J.-Y. Dieulot ◽  
A. El Kamel ◽  
P. Borne
Keyword(s):  
Fuzzy Controller ◽  
Domain Of Attraction ◽  
Constant Term ◽  
Open Loop ◽  
Region Of Attraction ◽  
Open Loop System ◽  
Controlled System ◽  
Disjoint Sets ◽  
The Stability ◽  
Vector Norms

A fuzzy controller with singleton defuzzification can be considered as the association of a regionwise constant term and of a regionwise non linear term, the latter being bounded by a linear controller. Based on the regionwise structure of fuzzy controller, the state space is partitioned into a series of disjoint sets. The fuzzy controller parameters are tuned in order to ensure that theith set is included into the domain of attraction of the preceding sets of the series. If the first set of the series is included into the region of attraction of the equilibrium point, the overall fuzzy controlled system is stable. The attractors are estimated with the help of the comparison principle, using Vector Norms, which ensures the robustness with respect to uncertainties and perturbations of the open loop system.

Optimal Design of a Stable Fuzzy Controller for Beyond Pull-In Stabilization of Electrostatically Actuated Circular Microplates

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Mohsen Bakhtiari-Shahri ◽  
Hamid Moeenfard
Keyword(s):  
Noise Suppression ◽  
Fuzzy Controller ◽  
Single Mode ◽  
Open Loop ◽  
Positioning Systems ◽  
Electrostatically Actuated ◽  
Proposed Model ◽  
Linguistic Rules ◽  
The Stability ◽  
Stability Enhancement

The current paper aims to provide an optimal stable fuzzy controller to extend the travel range of a pair of flexible electrostatically actuated circular microplates beyond their pull-in limit. The single mode assumption is utilized to derive the equation of motion of the system based on a Lagrangian approach. The static behavior of the system is studied using the proposed model, and the utilized assumption and the relevant results are closely verified by nonlinear finite element simulations. The open-loop dynamic analysis is also performed to derive the linguistic rules governing the voltage-deflection behavior of the system. The mentioned rules are then employed for designing a fuzzy controller, which controls the deflection of the microplates. The controller is then optimized to provide better response specifications. The performance of the optimal fuzzy controller is compared with that of the optimal proportional–integral–derivative (PID) controller and obvious superiorities in terms of noise suppression and stability enhancement are observed. To guarantee the stability of the closed-loop system, another higher level controller is designed to oversee the behavior of the fuzzy controller. Simulation results reveal that the superintended fuzzy controller can prevent instability, while fairly extending the travel range of system and providing it with a better transient response. The suggested design approach proposed in this paper may be used to improve the performance of many nano/micro devices and nano/micro positioning systems.

Utilizing an Adaptive Controller (Azadi Controller) for Trajectory Planning of PUMA 560 Robot

2011 ◽  
Vol 403-408 ◽  
pp. 4880-4887
Author(s):  
Sassan Azadi
Keyword(s):  
Steady State ◽  
Trajectory Planning ◽  
Positive Feedback ◽  
Fuzzy Controller ◽  
Research Work ◽  
Adaptive Controller ◽  
The Novel ◽  
Transient Responses ◽  
Simulation Results ◽  
Good Substitute

This research work was devoted to present a novel adaptive controller which uses two negative stable feedbacks with a positive unstable positive feedback. The positive feedback causes the plant to do the break, therefore reaching the desired trajectory with tiny overshoots. However, the two other negative feedback gains controls the plant in two other sides of positive feedback, making the system to be stable, and controlling the steady-state, and transient responses. This controller was performed for PUMA-560 trajectory planning, and a comparison was made with a fuzzy controller. The fuzzy controller parameters were obtained according to the PSO technique. The simulation results shows that the novel adaptive controller, having just three parameters, can perform well, and can be a good substitute for many other controllers for complex systems such as robotic path planning.

Improving the efficiency of a wastewater treatment plant by fuzzy control and neural networks

2001 ◽  
Vol 43 (11) ◽  
pp. 189-196 ◽  
Author(s):  
M. Bongards
Keyword(s):  
Wastewater Treatment ◽  
Wastewater Treatment Plant ◽  
Municipal Wastewater ◽  
Fuzzy Controller ◽  
Control Strategies ◽  
Treatment Plant ◽  
Municipal Wastewater Treatment ◽  
Controlled System ◽  
Measurement Results ◽  
Predictive Controller

One of the main problems in operating a wastewater treatment plant is the purification of the excess water from dewatering and pressing of sludge. Because of a high load of organic material and of nitrogen it has to be buffered and treated together with the inflowing wastewater. Different control strategies are discussed. A combination of neural network for predicting outflow values one hour in advance and fuzzy controller for dosing the sludge water are presented. This design allows the construction of a highly non-linear predictive controller adapted to the behaviour of the controlled system with a relatively simple and easy to optimise fuzzy controller. Measurement results of its operation on a municipal wastewater treatment plant of 60,000 inhabitant equivalents are presented and discussed. In several months of operation the system has proved very reliable and robust tool for improving the system's efficiency.

scholarly journals Design and simulate of LQR-Fuzzy controller for unicycle robot with double flywheels

2018 ◽  
Vol 192 ◽  
pp. 02001 ◽  
Author(s):  
Surachat Chantarachit
Keyword(s):  
Angular Momentum ◽  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Taylor Series Expansion ◽  
Lagrange Equations ◽  
Main Structure ◽  
Structure Control ◽  
Controller Gain ◽  
Lqr Controller ◽  
Simulation Results

This research is focus on design and simulate unicycle robot with double flywheels model with LQR-Fuzzy controller. Roll balancing torque is generated by gyroscopic effect. Pitch balancing torque is applied by inverted pendulum concept. To control the heading of the robot, the angular momentum from both flywheel is applied to control this. The robot model is based on Euler-Lagrange equations. The non-linear model is linearization by Taylor series expansion. The simulation results conducted by MATLAB/Simulink. LQR-Fuzzy is combination algorithm between LQR and Fuzzy controller. The main structure control is the LQR controller and use the Fuzzy controller to adjust the close loop controller gain. The simulation results is simulated and compared with conventional LQR.

Static Analysis of Electrically Actuated Nano to Micron Scale Beams Using Nonlocal Theory

2011 ◽  
Author(s):  
Y. Alizadeh Vaghasloo ◽  
Abdolreza Pasharavesh ◽  
M. T. Ahmadian ◽  
Ali Fallah
Keyword(s):  
Size Effect ◽  
Algebraic Equation ◽  
Bending Moment ◽  
Nonlocal Theory ◽  
Nonlinear Ordinary Differential Equation ◽  
Beam Deflection ◽  
Electrostatically Actuated ◽  
Size Dependent ◽  
Electrically Actuated ◽  
The One

In this paper, size dependent static behavior of micro and nano cantilevers actuated by a static electric field including deflection and pull-in instability, is analyzed implementing nonlocal theory. Euler-bernoulli assumptions are made to model the relation between deflection of the beam and bending moment. Differential form of the constitutive equation of nonlocal theory is used to find the revised equation for bending moment and substituting in the equilibrium equation of electrostatically actuated beams final nonlinear ordinary differential equation is arrived. Also the boundary conditions for solving the equation are revised and to analyze the size effect better governing equation is nondimetionalized. The one parameter Galerkin method is used to transform this equation to a nonlinear algebraic equation. Arrived algebraic equation is solved utilizing Newton-Raphson method. Size effect on the maximum deflection and deflection shape for various applied voltages is studied. Also effect of beam size on the static pull-in voltage is studied. Results indicate that the dimensionless beam deflection decreases as size decreases while the pull-in voltage increases and specially change of deflection and pull-in voltage is significant for nanobeams.

scholarly journals Variational Calculus Approach to Optimal Interception Task of a Ballistic Missile in 1D and 2D Cases

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 148
Author(s):  
Dariusz Horla
Keyword(s):  
Parametric Analysis ◽  
Variational Calculus ◽  
Open Loop ◽  
Ballistic Missile ◽  
Control Law ◽  
Open Loop Control ◽  
Performance Indices ◽  
Lagrange Equations ◽  
Loop Control ◽  
Conservation Of Momentum

The paper presents the application of variational calculus to achieve the optimal design of the open-loop control law in the process of anti-ballistic missile interception task. It presents the analytical results in the form of appropriate Euler–Lagrange equations for three different performance indices, with a simple model of the rocket and the missile, based on the conservation of momentum principle. It also presents the software program enabling rapid simulation of the interception process with selected parameters, parametric analysis, as well as easy potential modification by other researchers, as it is written in open code as m-function of Matlab.

Nonlinear Dynamic Modeling of Elastic Beam Fixed on a Moving Cart and Carrying Lumped Tip Mass Subjected to External Periodic Force

2009 ◽  
Author(s):  
Fadi A. Ghaith
Keyword(s):  
Linear Model ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Open Loop ◽  
Beam Deflection ◽  
Mode Shapes ◽  
Euler Beam ◽  
Periodic Force ◽  
Assumed Mode Method ◽  
Tip Mass

In the present work, a Bernoulli – Euler beam fixed on a moving cart and carrying lumped tip mass subjected to external periodic force is considered. Such a model could describe the motion of structures like forklift vehicles or ladder cars that carry heavy loads and military airplane wings with storage loads on their span. The nonlinear equations of motion which describe the global motion as well as the vibration motion were derived using Lagrangian approach under the inextensibility condition. In order to investigate the influence of the axial movement of the cart on the response of the system, unconstrained modal analysis has been carried out, and accurate mode shapes of the beam deflection were obtained. The assumed mode method was utilized for approximating the beam elastic deformation based on the single unconstrained mode shapes. Numerical simulation has been carried out to estimate the open-loop response of the nonlinear beam-mass-cart model as well as for the simplified linear model under the influence of the periodic excitation force. Also a comparison study between the responses of the linear and nonlinear models was established. It was shown that the maximum values of the beam tip deflection estimated from the nonlinear model are lower than the corresponding values obtained via the linear model, which reveals the importance of considering nonlinear hardening term in formulating the equations of motion for such system in order to come with more accurate and reliable model.

Electrostatically Actuated Coupled MEMS Resonators

2011 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Kyle N. Taylor
Keyword(s):  
Nonlinear Response ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
System Structure ◽  
Lagrange Equations ◽  
Electrostatically Actuated ◽  
Beam System ◽  
Mems Resonators ◽  
The Mathematical Model ◽  
Steady State Solutions

This paper deals with the nonlinear response of an electrostatically actuated cantilever beam system composed of two micro beam resonators near natural frequency. The mathematical model of the system is obtained using Lagrange equations. The equations of motion are nondimensionalized and then the method of multiple scales is used to find steady state solutions. Both AC and DC actuation voltages of the first beam are considered, while the influence on the system of DC on the second beam is explored. Graphical representations of the influence of the detuning parameters are provided for a typical micro beam system structure.

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