Covariance Control of Nonlinear Dynamic Systems via Exact Stationary Probability Density Function

2004 ◽  
Vol 126 (1) ◽  
pp. 71-76 ◽  
Author(s):  
O. Elbeyli ◽  
J. Q. Sun
Keyword(s):  
Present Method ◽  
Stochastic Systems ◽  
Control Method ◽  
Solution Process ◽  
Maximum Entropy Principle ◽  
Nonlinear Feedback ◽  
Feedback Controls ◽  
Approximate Methods ◽  
Covariance Control ◽  
Special Cases

This paper presents a method for designing covariance type controls of nonlinear stochastic systems. The method consists of two steps. The first step is to find a class of nonlinear feedback controls with undetermined gains such that the exact stationary PDF of the response is obtainable. The second step is to select the control gains in the context of the covariance control method by minimizing a performance index. The exact PDF makes the solution process of optimization very efficient, and the evaluation of expectations of nonlinear functions of the response very accurate. The theoretical results of various orders of response moments by the present method have been compared with Monte Carlo simulations. Special cases are studied when the approximate methods based on the maximum entropy principle or other closure schemes leads less accurate response estimates, while the present method still works fine.

scholarly journals A Covariance Feedback Approach to Covariance Control of Nonlinear Stochastic Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Salman Baroumand ◽  
Amir Reza Zaman ◽  
Mohammad Reza Mahmoudi
Keyword(s):  
Nonlinear Systems ◽  
Linear Approximation ◽  
Feedback Linearization ◽  
Control Algorithm ◽  
Stochastic Systems ◽  
Control Method ◽  
Nonlinear Case ◽  
Nonlinear Stochastic Systems ◽  
Covariance Control ◽  
Feedback Algorithm

In this paper, the covariance control algorithm for nonlinear stochastic systems using covariance feedback is studied. Covariance control of nonlinear systems scenario involves the theory of covariance control based on the idea of the covariance feedback. Therefore, the proposed covariance control algorithm is derived for our case, firstly by applying the covariance control method and linear approximation of nonlinear systems, and then it is achieved by adopting this method for a class of nonlinear stochastic systems by using feedback linearization idea and a covariance feedback controller. The effectiveness of the proposed covariance feedback algorithm is studied using numerous simulations concerning different nonlinear case studies.

Composite Nonlinear Feedback for Vehicle Active Front Steering

2014 ◽  
Vol 663 ◽  
pp. 127-134 ◽  
Author(s):  
M.H. Che Hasan ◽  
Y.M. Sam ◽  
Ke Mao Peng ◽  
Muhamad Khairi Aripin ◽  
Muhamad Fahezal Ismail
Keyword(s):  
Control Method ◽  
Actuator Saturation ◽  
External Disturbance ◽  
Reference Signal ◽  
Stability Control ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Active Front Steering ◽  
Yaw Stability ◽  
Fast Settling

In this paper, Composite Nonlinear Feedback (CNF) is applied on Active Front Steering (AFS) system for vehicle yaw stability control in order to have an excellent transient response performance. The control method, which has linear and nonlinear parts that work concurrently capable to track reference signal very fast with minimum overshoot, fast settling time, and without exceed nature of actuator saturation limit. Beside, modelling of 7 degree of freedom for typical passenger car with magic formula to represent tyre nonlinearity behaviour is also presented to simulate controlled vehicle as close as possible with a real situation. An extensive computer simulation is performed with considering a various profile of cornering manoeuvres with external disturbance to evaluate its performance in different scenarios. The performance of the proposed controller is compared to conventional Proportional Integration and Derivative (PID) for effectiveness analysis.

An Efficient Operational Matrix Technique for Multidimensional Variable-Order Time Fractional Diffusion Equations

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
M. A. Zaky ◽  
S. S. Ezz-Eldien ◽  
E. H. Doha ◽  
J. A. Tenreiro Machado ◽  
A. H. Bhrawy
Keyword(s):  
Present Method ◽  
Operational Matrix ◽  
Solution Process ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Variable Order ◽  
Algebraic Equations ◽  
Global Approximation ◽  
Fractional Diffusion Equations ◽  
Accurate Numerical Algorithm

This paper derives a new operational matrix of the variable-order (VO) time fractional partial derivative involved in anomalous diffusion for shifted Chebyshev polynomials. We then develop an accurate numerical algorithm to solve the 1 + 1 and 2 + 1 VO and constant-order fractional diffusion equation with Dirichlet conditions. The contraction of the present method is based on shifted Chebyshev collocation procedure in combination with the derived shifted Chebyshev operational matrix. The main advantage of the proposed method is to investigate a global approximation for spatial and temporal discretizations, and it reduces such problems to those of solving a system of algebraic equations, which greatly simplifies the solution process. In addition, we analyze the convergence of the present method graphically. Finally, comparisons between the algorithm derived in this paper and the existing algorithms are given, which show that our numerical schemes exhibit better performances than the existing ones.

Design and control of 2-DoF joystick using MR-fluid rotary actuator

2021 ◽  
pp. 1045389X2110639
Author(s):  
Bao Tri Diep ◽  
Quoc Hung Nguyen ◽  
Thanh Danh Le
Keyword(s):  
Pid Controller ◽  
Force Feedback ◽  
Control Method ◽  
Open Loop ◽  
Friction Torque ◽  
Feedback Controls ◽  
Loop Control ◽  
Fuzzy Logic Algorithm ◽  
Experimental Apparatus ◽  
Close Loop Control

The purpose of this paper is to design a control algorithm for a 2-DoF rotary joystick model. Firstly, the structure of the joystick, which composes of two magneto-rheological fluid actuators (shorten MRFA) with optimal configuration coupled perpendicularly by the gimbal mechanism to generate the friction torque for each independent rotary movement, is introduced. The control strategy of the designed joystick is then suggested. Really, because of two independent rotary movements, it is necessary to design two corresponding controllers. Due to hysteresis and nonlinear dynamic characteristics of the MRFA, controllers based an accurate dynamic model are difficult to realize. Hence, to release this issue, the proposed controller (named self-turning fuzzy controllers-STFC) will be built through the fuzzy logic algorithm in which the parameters of controllers are learned and trained online by Levenberg-Marquardt training algorithm. Finally, an experimental apparatus will be constructed to assess the effectiveness of the force feedback controls. Herein, three experimental cases are performed to compare the control performance of open-loop and close-loop control method, where the former is done through relationship between the force at the knob and the current supplied to coil while the latter is realized based on the proposed controller and PID controller. The experimental results provide strongly the ability of the proposed controller, meaning that the STFC is robust and tracks well the desirable force with high accuracy compared with both the PID controller and the open-loop control method.

A B-Spline Higher-Order Panel Method Applied to Two-Dimensional Lifting Problem

2003 ◽  
Vol 47 (04) ◽  
pp. 290-298
Author(s):  
Chang-Sup Lee ◽  
Justin E. Kerwin
Keyword(s):  
Present Method ◽  
Gaussian Quadrature ◽  
Solution Process ◽  
Higher Order ◽  
Panel Method ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Kutta Condition ◽  
B Spline ◽  
Panel Methods

A higher-order panel method based on B-spline representation for both the geometry and the solution is developed for the solution of the flow around two-dimensional lifting bodies. The influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts; then the former is integrated analytically, whereas the latter is integrated using Gaussian quadrature. Through a desingularization process, the accuracy of the present method can be increased without limit to any order by selecting a proper numerical quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with far fewer panels than existing low-order panel methods.

Elastic Fields in Double Inhomogeneity by the Equivalent Inclusion Method

2000 ◽  
Vol 68 (1) ◽  
pp. 3-10 ◽  
Author(s):  
H. M. Shodja ◽  
A. S. Sarvestani
Keyword(s):  
Elastic Constants ◽  
Present Method ◽  
Present Theory ◽  
Actual Distribution ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Ellipsoidal Inhomogeneity ◽  
Equivalent Inclusion ◽  
Comparison Results ◽  
Special Cases

Consider a double-inhomogeneity system whose microstructural configuration is composed of an ellipsoidal inhomogeneity of arbitrary elastic constants, size, and orientation encapsulated in another ellipsoidal inhomogeneity, which in turn is surrounded by an infinite medium. Each of these three constituents in general possesses elastic constants different from one another. The double-inhomogeneity system under consideration is subjected to far-field strain (stress). Using the equivalent inclusion method (EIM), the double inhomogeneity is replaced by an equivalent double-inclusion (EDI) problem with proper polynomial eigenstrains. The double inclusion is subsequently broken down to single-inclusion problems by means of superposition. The present theory is the first to obtain the actual distribution rather than the averages of the field quantities over the double inhomogeneity using Eshelby’s EIM. The present method is precise and is valid for thin as well as thick layers of coatings, and accommodates eccentric heterogeneity of arbitrary size and orientation. To establish the accuracy and robustness of the present method and for the sake of comparison, results on some of the previously reported problems, which are special cases encompassed by the present theory, will be re-examined. The formulations are easily extended to treat multi-inhomogeneity cases, where an inhomogeneity is surrounded by many layers of coatings. Employing an averaging scheme to the present theory, the average consistency conditions reported by Hori and Nemat-Nasser for the evaluation of average strains and stresses are recovered.

Sign in / Sign up

Export Citation Format

Share Document