Some Notes on the Grassmann Manifolds and Nonlinear System

2013 ◽  
Vol 419 ◽  
pp. 611-615
Author(s):  
Chun Na Zeng ◽  
Peng Tao
Keyword(s):  
Differential Geometry ◽  
Control System ◽  
Nonlinear System ◽  
Control Theory ◽  
Boundary Problem ◽  
Periodic Solutions ◽  
Grassmann Manifold ◽  
Quotient Space ◽  
Point Boundary ◽  
The Matrix

The differential geometry as a new tool has been introduced to research the control system, especially the nonlinear system. In this paper, by considering how to construct a manifold from a quotient space, we investigate the structure of Grassmann manifold concretely. This is beneficial to study the problem of finding periodic solutions of the matrix Riccati equations of control theory and the two point boundary problem.

A Technique of Quasi-Optimum Control

1966 ◽  
Vol 88 (2) ◽  
pp. 437-443 ◽  
Author(s):  
B. Friedland
Keyword(s):  
Nonlinear System ◽  
Analytic Solution ◽  
Control Variable ◽  
Control Law ◽  
System Of Equations ◽  
Point Boundary ◽  
Optimum Control ◽  
Bounded Control ◽  
Linear System Of Equations ◽  
The Matrix

To find the optimum control law u = u(x) for the process x˙ = f(x, u), the Hamiltonian H = p′f is formed. The optimum control law can be expressed as u = u* = σ(p, x), where u* maximizes H. The transformation from the state x to the “costate” p entails the analytic solution of the nonlinear system: x˙ = f(x, σ(p, x)); p˙=−fx′p with boundary conditions at two points. Since such a solution generally can not be found, we seek a quasi-optimum control law of the form u = σ(P + Mξ, x), where x = X + ξ with ‖ξ‖ small, and X, P are the solutions of a simplified problem, obtained by setting ξ = 0 in the above two-point boundary-value problem. We assume that P(X) is known. It is shown that the matrix M satisfies a Riccati equation, −M˙ = MHXP + HPXM + MHPPM + HXX, and can be computed by solving a linear system of equations. A simple example illustrates the application of the technique to a problem with a bounded control variable.

scholarly journals Periodic solutions of systems with asymptotically even nonlinearities

2000 ◽  
Vol 13 (1) ◽  
pp. 41-50
Author(s):  
Peter E. Kloeden ◽  
Alexander M. Krasnosel'skii
Keyword(s):  
Control Theory ◽  
Boundary Value Problem ◽  
Periodic Solutions ◽  
Vector Fields ◽  
Boundary Value ◽  
General Theorem ◽  
Linear Part ◽  
Periodic Problem ◽  
Scalar Equation ◽  
Point Boundary

New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate “next order” terms are obtained for the 2π-periodic problem for the scalar equation x″+n2x=g(|x|)+f(t,x)+b(t) with bounded g(u) and f(t,x)→0 as |x|→0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory.

Robust Two-degree-of-freedom Control Based on H∞ Method for PMSM Drive System

2020 ◽  
Vol 13 (4) ◽  
pp. 496-506
Author(s):  
Qixin Zhu ◽  
Lei Xiong ◽  
Hongli Liu ◽  
Yonghong Zhu ◽  
Guoping Zhang
Keyword(s):  
Control System ◽  
Control Theory ◽  
Position Control ◽  
Dynamic Performance ◽  
Servo System ◽  
Degree Of Freedom ◽  
Trade Off ◽  
Standard Design ◽  
Position Controller ◽  
Two Degree Of Freedom

Background: The conventional method using one-degree-of-freedom (1DOF) controller for Permanent Magnet Synchronous Motor (PMSM) servo system has the trade-off problem between the dynamic performance and the robustness. Methods: In this paper, by using H∞ control theory, a novel robust two-degree-of-freedom (2DOF) controller has been proposed to improve the position control performance of PMSM servo system. Using robust control theory and 2DOF control theory, a H∞ robust position controller has been designed and discussed in detail. Results: The trade-off problem between the dynamic performance and robustness which exists in one-degree-of-freedom (1DOF) control can be dealt with by the application of 2DOF control theory. Then, through H∞ control theory, the design of robust position controller can be translated to H∞ robust standard design problem. Moreover, the control system with robust controller has been proved to be stable. Conclusion: Further simulation results demonstrate that compared with the conventional PID control, the designed control system has better robustness and attenuation to the disturbance of load impact.

Modeling and Simulation of Improved Vector Control System for PMSM

2014 ◽  
Vol 548-549 ◽  
pp. 819-823
Author(s):  
Xi Juan Wang ◽  
Tao Zhou ◽  
Jing Xiao Feng ◽  
Yu Peng Pei
Keyword(s):  
Control System ◽  
Control Theory ◽  
Modeling And Simulation ◽  
Vector Control ◽  
System Model ◽  
Excellent Performance ◽  
Matlab Simulink ◽  
Ac Motor ◽  
Control System Model ◽  
Vector Control System

In the AC control system, vector control theory is very popular as it makes the AC motor achieve the performance as perfect as DC motor [1]. In the paper, the vector control theory is briefly introduced, and then a vector control system model is builded in the matlab/simulink, and the SVPWM technique is adopted. The results show that the improved vector control sytem of PMSM has a excellent performance.

scholarly journals Solvency control of the enterprise in the bankruptcy prevention system

2020 ◽  
Vol 4 (2) ◽  
pp. 14-23
Author(s):  
Hanna Sytnyk ◽  
Inna Olesenko
Keyword(s):  
Control System ◽  
Financial Management ◽  
Financial Responsibility ◽  
Coverage Ratio ◽  
Total Capital ◽  
Logical Sequence ◽  
The Matrix ◽  
Control Procedures ◽  
Recent Trends ◽  
Control Circuits

Introduction. Recent trends in the economy, in particular the situation with COVID-19 epidemic, will contribute to the deterioration of the level of solvency, financial security of enterprises, and, as consequence, increasing the number of bankruptcies. Constant monitoring of the solvency level is a necessary element of anti-crisis financial management and a tool to prevent bankruptcy. That is why the development of methodological bases and methodological approaches to solvency control is an important area of research. Aim and tasks. The aim of the article is to substantiate the solvency control system of the enterprise, which would cover the identification of the main control indicators, methods of control over individual control circuits, the formation of a clear structural and logical sequence of this process. Results. The tendency of increasing the share of current liabilities in the total capital of the enterprise, decreasing the value of the financial autonomy ratio and total coverage ratio, which indicates a problematic state of solvency of Ukrainian enterprises was investigated. The solvency control system elements of the enterprise were determined: objects, subject, purpose, functions, functional directions, components of the control according to the management contours. The characteristic of solvency control according to the management contours (strategic, current, operational) was described more detailed. The gradation of the deviation scales in a solvency condition of the enterprise was improved and the matrix of decisions in which directions of the reaction on type and scale of deviations were defined was composed. Conclusions. In order to avoid bankruptcy, the enterprise must adhere to the financial discipline, be aware of financial responsibility and constantly improve management mechanisms, especially preventive anti-crisis methods, which should include a solvency control. The proposed approach to controlling is expected to provide a comprehensive nature of solvency control as an important component of preventive anti-crisis management aimed at preventing bankruptcy. Complexity is achieved by the consistency of the control procedures on the control contours, differentiation of the control tools, identification of possible deviations and ways to respond to them.

scholarly journals Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Longchuan Guo ◽  
Chuanping Zhou ◽  
Xiaoqing Tian ◽  
Huawei Ji ◽  
Yudong Peng
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
Control Problem ◽  
Growth Condition ◽  
Output Feedback ◽  
Controller Design ◽  
Polynomial Function ◽  
Growth Conditions ◽  
Simulation Software ◽  
Tracking Controller

This paper mainly studies the output feedback control problem of the stochastic nonlinear system based on loose growth conditions and applies the research results to the valve control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. First, the concept of randomness is introduced to study the actual tracking control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general polynomial function growth conditions, and propose a combination of static and dynamic output feedback practices. The design of the tracking controller makes all the states of the system meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Second, the system is extended to the parameter-uncertain system, and the output feedback tracking controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Further, the time-delay factor is introduced, and the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to cleverly construct a set of Lyapunov functions and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Stability. Finally, through the ocean library in the Simulation X simulation software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness of the controller design.

scholarly journals A Quasilinear Two Point Boundary Problem

1994 ◽  
Vol 24 (3) ◽  
pp. 1117-1134
Author(s):  
Victor L. Shapiro
Keyword(s):  
Boundary Problem ◽  
Point Boundary
Sign in / Sign up

Export Citation Format

Share Document