On the stability properties of a third order system

1968 ◽  
Vol 78 (1) ◽  
pp. 91-103 ◽  
Author(s):  
G. P. Szegö ◽  
C. Olech ◽  
A. Cellina
Keyword(s):  
Order System ◽  
Third Order ◽  
Stability Properties ◽  
The Stability

scholarly journals Modeling and Designing a Hydrostatic Transmission With a Fixed-Displacement Motor

1998 ◽  
Vol 120 (1) ◽  
pp. 45-49 ◽  
Author(s):  
N. D. Manring ◽  
G. R. Luecke
Keyword(s):  
Order System ◽  
Axial Piston Pump ◽  
Third Order ◽  
Stability Range ◽  
Hydrostatic Transmission ◽  
Control Gain ◽  
Variable Displacement ◽  
Linearized System ◽  
The Stability ◽  
Axial Piston

This study develops the dynamic equations that describe the behavior of a hydrostatic transmission utilizing a variable-displacement axial-piston pump with a fixed-displacement motor. In general, the system is noted to be a third-order system with dynamic contributions from the motor, the pressurized hose, and the pump. Using the Routh-Hurwitz criterion, the stability range of this linearized system is presented. Furthermore, a reasonable control-gain is discussed followed by comments regarding the dynamic response of the system as a whole. In particular, the varying of several parameters is shown to have distinct effects on the system rise-time, settling time, and maximum percent-overshoot.

scholarly journals Subharmonic oscillation in third order non-linear systems

1979 ◽  
Vol 1 (3-4) ◽  
pp. 12-20
Author(s):  
Nguyen Van Dao
Keyword(s):  
Order Equation ◽  
Exciting Force ◽  
Order System ◽  
Subharmonic Solution ◽  
Third Order ◽  
The Third ◽  
The Family ◽  
Subharmonic Oscillation ◽  
Non Linear Systems ◽  
The Stability

In this paper the subharmonic oscillation with frequency n times smaller than that of exciting force is considered. The first paragraph is devoted to the formulation of problem. Here an example of third order equation in which there exists pure subharmonic solution is given. In the second paragraph the condition (2.5), (2.7) for the existence of pure odd subharmonic oscillation in the dynamical system governed by equation (2.1) are derived. The mixed subharmonic oscillation is studied in the third paragraph. The family of tow parameters solutions (3.2) of equation (3.1) with subharmonic term is found by means of asymptotic method. The stationary oscillations are given by formulae (3.14)-(3.16). The stability of subharmonic is oscillation is studied by Liapunov-Routh-Hurwitz criterium in the fourth paragraph. In general, the stability conditions (4.5) lead to the results which are different from those in second order system. To illustrate the presented method a concrete example has been analysed in the fifth paragraph.

scholarly journals Velocity and acceleration level inverse kinematic calculation alternatives for redundant manipulators

Meccanica ◽  
2021 ◽  
Author(s):  
Dóra Patkó ◽  
Ambrus Zelei
Keyword(s):  
Degrees Of Freedom ◽  
Direct Method ◽  
Tracking Error ◽  
Inverse Kinematic ◽  
Linear Feedback ◽  
Joint Position ◽  
Stability Properties ◽  
Acceleration Level ◽  
Error Elimination ◽  
The Stability

AbstractFor both non-redundant and redundant systems, the inverse kinematics (IK) calculation is a fundamental step in the control algorithm of fully actuated serial manipulators. The tool-center-point (TCP) position is given and the joint coordinates are determined by the IK. Depending on the task, robotic manipulators can be kinematically redundant. That is when the desired task possesses lower dimensions than the degrees-of-freedom of a redundant manipulator. The IK calculation can be implemented numerically in several alternative ways not only in case of the redundant but also in the non-redundant case. We study the stability properties and the feasibility of a tracking error feedback and a direct tracking error elimination approach of the numerical implementation of IK calculation both on velocity and acceleration levels. The feedback approach expresses the joint position increment stepwise based on the local velocity or acceleration of the desired TCP trajectory and linear feedback terms. In the direct error elimination concept, the increment of the joint position is directly given by the approximate error between the desired and the realized TCP position, by assuming constant TCP velocity or acceleration. We investigate the possibility of the implementation of the direct method on acceleration level. The investigated IK methods are unified in a framework that utilizes the idea of the auxiliary input. Our closed form results and numerical case study examples show the stability properties, benefits and disadvantages of the assessed IK implementations.

scholarly journals Local compactness in approach spaces II

2003 ◽  
Vol 2003 (2) ◽  
pp. 109-117
Author(s):  
R. Lowen ◽  
C. Verbeeck
Keyword(s):  
Stability Properties ◽  
Local Compactness ◽  
The Stability ◽  
Approach Spaces

This paper studies the stability properties of the concepts of local compactness introduced by the authors in 1998. We show that all of these concepts are stable for contractive, expansive images and for products.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

Analysis of Acoustic-Structure Interaction Using a High-Order Doubly Asymptotic Approximation

2016 ◽  
Vol 24 (01) ◽  
pp. 1550021 ◽  
Author(s):  
Heekyu Woo ◽  
Young S. Shin
Keyword(s):  
Order Approximation ◽  
Stable Model ◽  
Approximation Model ◽  
Third Order ◽  
Acoustic Structure ◽  
Structure Interaction ◽  
Proposed Model ◽  
The Stability ◽  
Third Order Approximation ◽  
Interaction Problem

In this paper, a new third-order approximation model for an acoustic-structure interaction problem is introduced. The new approximation model is designed to be an accurate and a stable model for predicting the response of a submerged structure. The proposed model is obtained by combining two lower order approximation models instead of using an operator matching method. The stability of this model is checked by a modal analysis. Finally, the approximation model is coupled to the spherical shell structure, and its performance is checked by a shock analysis.

The Correlation between Time and Frequency Dynamic Performance of Control System

2014 ◽  
Vol 628 ◽  
pp. 186-189
Author(s):  
Meng Xiong Zeng ◽  
Jin Feng Zhao ◽  
Wen Ouyang
Keyword(s):  
Control System ◽  
Performance Index ◽  
Dynamic Performance ◽  
Frequency Domain Analysis ◽  
Practical Significance ◽  
Order System ◽  
Time Frequency ◽  
Performance Indexes ◽  
Quantitative Performance ◽  
The Stability

The control system performance requirement was divided into three parts. They were the stability, rapidity and accuracy. The time-frequency domain analysis in the requirements of three performance were measured through quantitative performance index. The mutual restriction of time-frequency performance and system characteristic parameters of normal second order was discussed. The correlation of system time-frequency performance index was established. The relationship between time-frequency performance indexes in standard two order system was extended to higher order system. The mutually constraining and time-frequency correlation between each performance index was obtained by analysis and calculation. The work had been done above had practical significance to reflect the system dynamic performance in different analytical domains.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

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