scholarly journals Lyapunov Matrices Approach to the Parametric Optimization of a System with Two Delays

2016 ◽  
Vol 26 (3) ◽  
pp. 367-381
Author(s):  
Jozef Duda
Keyword(s):  
Time Delay ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Delay System ◽  
Delay Systems ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Two Delays ◽  
Lyapunov Matrix ◽  
Quadratic Performance

AbstractIn the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with two commensurate delays and a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of the Lyapunov functional for the initial function of time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix.

scholarly journals Lyapunov matrices approach to the parametric optimization of time-delay systems

2015 ◽  
Vol 25 (3) ◽  
pp. 279-288 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Time Delay ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Delay System ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Lyapunov Matrix ◽  
Quadratic Performance

AbstractIn the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix

scholarly journals Lyapunov matrices approach to the parametric optimization of a neutral system

2016 ◽  
Vol 26 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Jozef Duda
Keyword(s):  
Initial Function ◽  
Lyapunov Functional ◽  
Optimization Problem ◽  
Parametric Optimization ◽  
Neutral System ◽  
Quadratic Performance Index ◽  
Parametric Optimization Problem ◽  
Lyapunov Matrix ◽  
Quadratic Performance ◽  
Index Of Quality

In the paper a Lyapunov matrices approach to the parametric optimization problem of a neutral system with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the neutral system. The Lyapunov functional is determined by means of the Lyapunov matrix.

scholarly journals Parametric optimization of neutral linear system with two delays with P-controller

2011 ◽  
Vol 21 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Józef Duda
Keyword(s):  
Linear System ◽  
Performance Index ◽  
Lyapunov Functional ◽  
Parametric Optimization ◽  
Neutral Type ◽  
Neutral System ◽  
Initial State ◽  
Quadratic Performance Index ◽  
Two Delays ◽  
Quadratic Performance

Parametric optimization of neutral linear system with two delays with P-controller In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.

scholarly journals A Lyapunov functional for a system with both lumped and distributed delay

2017 ◽  
Vol 27 (4) ◽  
pp. 527-540
Author(s):  
Jozef Duda
Keyword(s):  
Time Delay ◽  
Lyapunov Functional ◽  
Distributed Delay ◽  
Delay System ◽  
Time Delay System ◽  
Method Of Determination ◽  
Lyapunov Matrix

AbstractIn the paper construction of a Lyapunov functional for time delay system with both lumped and distributed delay is presented. The Lyapunov functional is determined by means of the Lyapunov matrix. The method of determination of the Lyapunov matrix for time delay system with both lumped and distributed delay is presented. It is given the example illustrating the method.

Stabilizing Gain Regions of PID Controller for Time Delay Systems

2013 ◽  
Vol 313-314 ◽  
pp. 432-437
Author(s):  
Fu Min Peng ◽  
Bin Fang
Keyword(s):  
Stability Analysis ◽  
Time Delay ◽  
Pid Controller ◽  
Delay System ◽  
Nyquist Plot ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Frequency Range ◽  
Time Delay System ◽  
Key Points

Based on the inverse Nyquist plot, this paper proposes a method to determine stabilizing gain regions of PID controller for time delay systems. According to the frequency characteristic of the inverse Nyquist plot, it is confirmed that the frequency range is used for stability analysis, and the abscissas of two kind key points are obtained in this range. PID gain is divided into several regions by abscissas of key points. Using an inference and two theorems presented in the paper, the stabilizing PID gain regions are determined by the number of intersections of the inverse Nyquist plot and the vertical line in the frequency range. This method is simple and convenient. It can solve the problem of getting the stabilizing gain regions of PID controller for time delay system.

scholarly journals Enhanced Disturbance-Observer-Based Control for a Class of Time-Delay System with Uncertain Sinusoidal Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xinyu Wen
Keyword(s):  
Time Delay ◽  
Flight Control ◽  
Disturbance Observer ◽  
Delay System ◽  
Delay Systems ◽  
Flight Control System ◽  
Control Laws ◽  
Nonlinear Disturbance Observer ◽  
Dynamic Performances ◽  
Uncertain Disturbance

This paper is concerned with disturbance-observer-based control (DOBC) for a class of time-delay systems with uncertain sinusoidal disturbances. The disturbances are decomposed as precise and uncertain parts using nonlinear disturbance observer (DO) after appropriate coordinate transformation. And then the two parts can be compensated by corresponding controller, respectively, such that the classic DOBC method is extended to uncertain disturbance rejection. One novel feature of the proposed method is that even if the precise disturbance parameters are inaccessible, the merits of DOBC can be inherited. By integrating the disturbance observers with feedback control laws with time delay, the disturbances can be rejected and the desired dynamic performances can be guaranteed. Finally, simulations for a flight control system are given to demonstrate the effectiveness of the results.

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