Lateral Motion Control Invariance Helicopter on the Roll Angle. Analytical Synthesis

2021 ◽  
Vol 22 (6) ◽  
pp. 331-336
Author(s):  
N. E. Zubov ◽  
V. N. Ryabchenko
Keyword(s):  
Matrix Equation ◽  
Mimo System ◽  
Dynamic Properties ◽  
Control Object ◽  
Singular Values ◽  
Roll Angle ◽  
Lateral Motion ◽  
The Matrix ◽  
Fourth Order Model ◽  
Invariant Control

For the linearized fourth-order model of the isolated lateral motion of a single-rotor helicopter as a MIMO system containing two inputs, the control is analytically synthesized, which ensures the invariance of the roll angle motion in the presence of disturbances in the control channels, as well as the required placement of the poles of the closed-loop system, given any specific values from the area of their stability. The approach to the synthesis of invariant control consists in finding a matrix of feedback coefficients of a linear system that satisfies the invariance conditions, which are a system of power matrix equations of a certain design. The synthesis is based on the application of theor ems based on the use of the regularization condition of the matrix equation and the invariance conditions under disturbances in the control channels, as well as theorems that make it possible to place the poles of the MIMO system using the original decomposition of the control object. Regularization of a matrix equation is understood as a solution to the problem of providing a given set of singular values for an inverted symmetric square matrix. The invariance of the MIMO system is considered with respect to unmeasured disturbances inthe control channels. The use of such an approach to the synthesis of invariant control made it possible to obtain an analytical solution that is versatile and can be applied in various flight modes of single-rotor helicopters with different dynamic properties. The results of the numerical synthesis of the lateral motion of a singlerotor helicopter using the obtained laws of invariant control, which confirm the reliability of the analytical expressions, areshown.

scholarly journals Convergence analysis of gradient-based iterative algorithms for a class of rectangular Sylvester matrix equations based on Banach contraction principle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Adisorn Kittisopaporn ◽  
Pattrawut Chansangiam ◽  
Wicharn Lewkeeratiyutkul
Keyword(s):  
Spectral Radius ◽  
Matrix Equation ◽  
Iterative Algorithms ◽  
Banach Contraction Principle ◽  
Contraction Principle ◽  
Convergence Factor ◽  
Sylvester Matrix ◽  
Iteration Matrix ◽  
Banach Contraction ◽  
The Matrix

AbstractWe derive an iterative procedure for solving a generalized Sylvester matrix equation $AXB+CXD = E$ A X B + C X D = E , where $A,B,C,D,E$ A , B , C , D , E are conforming rectangular matrices. Our algorithm is based on gradients and hierarchical identification principle. We convert the matrix iteration process to a first-order linear difference vector equation with matrix coefficient. The Banach contraction principle reveals that the sequence of approximated solutions converges to the exact solution for any initial matrix if and only if the convergence factor belongs to an open interval. The contraction principle also gives the convergence rate and the error analysis, governed by the spectral radius of the associated iteration matrix. We obtain the fastest convergence factor so that the spectral radius of the iteration matrix is minimized. In particular, we obtain iterative algorithms for the matrix equation $AXB=C$ A X B = C , the Sylvester equation, and the Kalman–Yakubovich equation. We give numerical experiments of the proposed algorithm to illustrate its applicability, effectiveness, and efficiency.

Solution of the matrix equation AX + XB = C [F4]

1972 ◽  
Vol 15 (9) ◽  
pp. 820-826 ◽  
Author(s):  
R. H. Bartels ◽  
G. W. Stewart
Keyword(s):  
Matrix Equation ◽  
The Matrix

scholarly journals Ranks of Hermitian and skew-Hermitian solutions to the matrix equation AXA∗=B

2009 ◽  
Vol 431 (12) ◽  
pp. 2359-2372 ◽  
Author(s):  
Yonghui Liu ◽  
Yongge Tian ◽  
Yoshio Takane
Keyword(s):  
Matrix Equation ◽  
The Matrix

A matrix realignment method for recognizing entanglement

2003 ◽  
Vol 3 (3) ◽  
pp. 193-202
Author(s):  
K. Chen ◽  
L.-A. Wu
Keyword(s):  
Kronecker Product ◽  
Singular Values ◽  
Quantum Systems ◽  
Entangled States ◽  
Approximation Technique ◽  
Separable State ◽  
Simple Method ◽  
Bipartite Quantum Systems ◽  
The Matrix ◽  
Degree Of Entanglement

Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any separable state, the sum of the singular values of the matrix should be less than or equal to $1$. This condition provides a very simple, computable necessary criterion for separability, and shows powerful ability to identify most bound entangled states discussed in the literature. As a byproduct of the criterion, we give an estimate for the degree of entanglement of the quantum state.

scholarly journals Weak Fault Detection of Tapered Rolling Bearing Based on Penalty Regularization Approach

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 184 ◽  
Author(s):  
Qing Li ◽  
Steven Liang
Keyword(s):  
Vibration Signal ◽  
Singular Values ◽  
Rolling Bearing ◽  
L1 Norm ◽  
Detection Approach ◽  
The Matrix ◽  
Noisy Observation ◽  
Weak Fault ◽  
Convex Regularization ◽  
Fault Information

Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estimates non-zero singular values (i.e., fault component) accurately and (2) it maintains the convexity of the proposed objective cost function (OCF) by restricting the parameters of the non-convex regularization. Specifically, the AHNPR model is expressed as the L1-norm minus a generalized Huber function, which avoids the underestimation weakness of the L1-norm regularization. Furthermore, the convexity of the proposed OCF is proved via the non-diagonal characteristic of the matrix BTB, meanwhile, the non-zero singular values of the OCF is solved by the forward–backward splitting (FBS) algorithm. Last, the proposed method is validated by the simulated signal and vibration signals of tapered bearing. The results demonstrate that the proposed approach can identify weak fault information from the raw vibration signal under severe background noise, that the non-convex penalty regularization can induce sparsity of the singular values more effectively than the typical convex penalty (e.g., L1-norm fused lasso optimization (LFLO) method), and that the issue of underestimating sparse coefficients can be improved.

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