scholarly journals Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Douglas Domingues Bueno ◽  
Luiz Carlos Sandoval Góes ◽  
Paulo José Paupitz Gonçalves
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Control Surface ◽  
Space Representation ◽  
Linear Matrix ◽  
Limit Cycle Oscillation ◽  
Aerodynamic Forces ◽  
Control Gain ◽  
Takagi Sugeno ◽  
Three Degrees Of Freedom

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen’s theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov’s stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Sliding Mode Control of a Three Degrees of Freedom Anthropoid Robot by Driving the Controller Parameters to an Equivalent Regime

2000 ◽  
Vol 122 (4) ◽  
pp. 632-640 ◽  
Author(s):  
M. Onder Efe ◽  
Okyay Kaynak ◽  
Xinghuo Yu
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Tracking Error ◽  
Variable Structure ◽  
Mathematical Representation ◽  
Dynamic Complexity ◽  
Variable Structure Systems ◽  
Sliding Motion ◽  
Three Degrees Of Freedom

Noise rejection, handling the difficulties coming from the mathematical representation of the system under investigation and alleviation of structural or unstructural uncertainties constitute prime challenges that are frequently encountered in the practice of systems and control engineering. Designing a controller has primarily the aim of achieving the tracking precision as well as a degree of robustness against the difficulties stated. From this point of view, variable structure systems theory offer well formulated solutions to such ill-posed problems containing uncertainty and imprecision. In this paper, a simple controller structure is discussed. The architecture is known as Adaptive Linear Element (ADALINE) in the framework of neural computing. The parameters of the controller evolve dynamically in time such that a sliding motion is obtained. The inner sliding motion concerns the establishment of a sliding mode in controller parameters, which aims to minimize the error on the controller outputs. The outer sliding motion is designed for the plant. The algorithm discussed drives the error on the output of the controller toward zero learning error level, and the state tracking error vector of the plant is driven toward the origin of the phase space simultaneously. The paper gives the analysis of the equivalence between the two sliding motions and demonstrates the performance of the algorithm on a three degrees of freedom, anthropoid robotic manipulator. In order to clarify the performance of the scheme, together with the dynamic complexity of the plant, the adverse effects of observation noise and nonzero initial conditions are studied. [S0022-0434(00)01704-4]

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

2021 ◽  
Author(s):  
Renan F. Corrêa ◽  
Flávio D. Marques
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Equations Of Motion ◽  
Mechanical Vibration ◽  
Nonlinear Behavior ◽  
Limit Cycle Oscillation ◽  
Restoring Force ◽  
Aeroelastic System ◽  
Technical Literature ◽  
Practical Applications

Abstract Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.

Multibody Modeling and Simulation of Monocopter Micro Air Vehicle

2015 ◽  
Vol 772 ◽  
pp. 401-409
Author(s):  
Mehrdad Ebrahimi Dormiyani ◽  
Afshin Banazadeh ◽  
Fariborz Saghafi
Keyword(s):  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Model Simulation ◽  
Static Stability ◽  
Flight Simulation ◽  
Control Surface ◽  
Free Flight ◽  
Nonlinear Simulation ◽  
Multibody Model ◽  
Air Vehicle

In the current paper, seven degrees of freedom multibody model of a monocopter air vehicle is developed based on the Newton-Euler approach along with nonlinear simulation in different flight phases. Aerodynamic forces and moments are modeled using blade element momentum theory. The sole control surface is modeled like a conventional flap on a wing. Free flight simulation is performed in MATLAB Simulink environment to evaluate the behavior of the system and to demonstrate the effectiveness and applicability of the proposed model. Simulation results show harmonic oscillations in Euler angles, linear and angular velocities that are consistent with the physics and mathematical foundations. Static stability of the vehicle is evident in free flight by careful choice of initial conditions. The presented multibody model is useful for comparative study and design purposes.

A class of C∞-integrable Hamiltonian systems

1989 ◽  
Vol 113 (3-4) ◽  
pp. 293-314 ◽  
Author(s):  
W. M. Oliva ◽  
M. S. A. C. Castilla
Keyword(s):  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
First Integrals ◽  
Integrable Hamiltonian Systems ◽  
Integral Of Motion ◽  
Toda System ◽  
Nonnegative Coefficients ◽  
Special Case ◽  
Three Degrees Of Freedom

SynopsisWe discuss the C∞ complete integrability of Hamiltonian systems of type q = —grad V(q) = F(q), in which the closure of the cone generated (with nonnegative coefficients) by the vectors F(q), q ϵ ℝn, does not contain a line. The components of the asymptotic velocities are first integrals and the main aim is to prove their smoothness as functions of the initial conditions. The Toda-like system with potential V(q)=ΣNi=1 exp(fi∣ q) is a special case of the considered systems ifthe cone C(f1,…,fN)={ΣNi=1cifi,ci≧0} does notcontain a line. In any number of degrees of freedom, if C(f1,…,fN) has amplitude not too large (ang (fi, fj ≦π/2i,j=1,2,…, N), the first integrals are C∞ functions. In two degrees of freedom, without restriction on the amplitude of the cone, C∞-integrability is proved even in a case in which it is known that there is no other meromorphic integral of motion independent of energy. In three degrees of freedom the C∞-integrability of a deformation of the classic nonperiodic Toda system is proved. Some other examples are also discussed.

Deterministic Chaos in the Dynamics of a Freely Jointed Chain with Three Degrees of Freedom

1993 ◽  
Vol 48 (4) ◽  
pp. 584-594
Author(s):  
Georg R. Siegert ◽  
Roland G. Winkler ◽  
Peter Reineker
Keyword(s):  
Degrees Of Freedom ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Deterministic Chaos ◽  
Power Spectra ◽  
Constrained System ◽  
Rigid Rods ◽  
End Distance ◽  
Poincaré Surfaces Of Section ◽  
Three Degrees Of Freedom

Abstract The dynamics of a short freely jointed chain of three segments is investigated numerically. The chain consists of mass points connected by massless rigid rods, its initial and final points being fixed. Thus the chain represents a holonomically constrained system with three degrees of freedom. It is shown that the motion of the mass points can be chaotic; the occurrence of chaos depends on the initial conditions of the motion, the end-to-end distance of the chain, and the angular momentum about the axis of the stretching direction. Moreover, the chain more likely exhibits regular than chaotic behavior. The numerical results are presented in the form of Poincare surfaces of section, including the use of a slice technique, as well as in the form of power spectra.

Further Results on T-S Fuzzy Controller Design Subject to Input Constraint

2008 ◽  
Vol 12 (2) ◽  
pp. 190-197 ◽  
Author(s):  
Hugang Han ◽  
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Input Constraint ◽  
Initial State ◽  
Control Gain ◽  
Matrix Variable ◽  
Takagi Sugeno

In general, when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system, the state feedback control gain can be obtained by solving some linear matrix inequalities (LMIs). In this paper, we consider a class of nonlinear systems with input constraint (saturation). To obtain the control gain, we require to employ certain extra LMIs besides the general ones. As a result, all the LMIs are more conservative. At the same time, one of the extra LMIs confines the initial state to a region, which is referred to as an ellipsoid, and is relevant to a matrix variable in the LMIs. Therefore, the goals of this paper are: 1) making the ellipsoid as large as possible so that the initial state can be confined to the region easily and; 2) making all the LMIs more feasible to obtain the control gain.

Move blocking Model Predictive Control of a helicopter with three degrees of freedom

2020 ◽  
Author(s):  
Rogério Toniere Giovanelli ◽  
Rubens Junqueira Magalhães Afonso
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Degrees Of Freedom ◽  
Stable Region ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Control Law ◽  
Matrix Inequalities ◽  
Blocking Algorithm ◽  
Three Degrees Of Freedom

This work presents the use of a move blocking algorithm in the Model Predictive Control (MPC) of a helicopter with three degrees of freedom (3DoF). Considerations about the feasibility of the MPC solutions and robustness of the control law are developed to propose an internal feedback gain array using Linear Matrix Inequalities (LMIs). The objective of this structure is to grant adjustment  exibility of the plant dynamics through a D-stable region and to reduce the computational complexity of the problem.

scholarly journals Control of a Variable Blade Pitch Wind Turbine Subject to Gust Wind and Actuators Saturation

2021 ◽  
Vol 11 (17) ◽  
pp. 7865
Author(s):  
Chokri Sendi
Keyword(s):  
Wind Turbine ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Gain ◽  
Dynamics And Control ◽  
Takagi Sugeno ◽  
And Control ◽  
The Mathematical Model

This paper examines the dynamics and control of a variable blade pitch wind turbine during extreme gust wind and subject to actuators saturation. The mathematical model of the wind turbine is derived using the Lagrange dynamics. The controller is formulated using the Takagi–Sugeno fuzzy model and utilizes the parallel distributor compensator to obtain the feedback control gain. The controller’s objective is to obtain the generator electromagnetic torque and the blade pitch angle to attenuate the external disturbances. The (T–S) fuzzy controller with disturbances rejection properties is developed using the linear matrix inequalities technic and solved as an optimization problem. The efficacy of the proposed (T–S) fuzzy controller is illustrated via numerical simulations.

scholarly journals Active Disturbance Rejection for a Three Degrees of Freedom Gyroscope

2018 ◽  
Vol 51 (13) ◽  
pp. 372-377 ◽  
Author(s):  
Juan E. Andrade García ◽  
Alejandra Ferreira de Loza ◽  
Luis T. Aguilar ◽  
Ramón I. Verdés
Keyword(s):  
Disturbance Rejection ◽  
Degrees Of Freedom ◽  
Active Disturbance Rejection ◽  
Three Degrees Of Freedom
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