Synthesis and Optimization of Transient Performances for Underdamped Second-Order Linear System Based on the Switching Control Strategy

2012 ◽  
Author(s):  
Qingyu Su ◽  
Georgi M. Dimirovski ◽  
Jun Zhao
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Optimization Problems ◽  
Switching Control ◽  
Second Order ◽  
Order Linear ◽  
Output Response ◽  
Special Cases ◽  
Switching Control Strategy ◽  
The Given

In this paper, the synthesis and optimization problems of the transient performances, such as overshoot and setting time, of the output response with respect to a step signal for an under-damped second-order linear system are studied. The traditional control strategy and the switching control strategy are used, respectively. Our control objective is twofold: Objective 1 is to ensure that the overshoot of the system output does not violate the given safety bound and objective 2 is to ensure that the settling time is smaller than the given allowable time. The obtained results indicate that the switching control strategy has main two evident advantages: firstly, the switching proportional controllers can take advantages of both the quick response and the small overshoot of the output response. Secondly, the switching controller is always available, while the single proportional controller is available in some special cases. Finally, an example of servomotor is given to demonstrate the effectiveness of the proposed method.

scholarly journals How to Generate Chaos from Switching System: A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Fang Bao ◽  
Simin Yu
Keyword(s):  
Linear System ◽  
Control Strategy ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Autonomous Systems ◽  
Switching Control ◽  
Heteroclinic Loop ◽  
Switching Control Strategy ◽  
Index 2

There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation. Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper. A novel approach for constructing chaotic systems is investigated by applying the switching control strategy and yielding a heteroclinic loop which connects two saddle foci of index 1. A basic 3-D linear system with an arbitrary normal direction of the eigenplane, possessing a saddle focus of index 1 whose corresponding eigenvalues satisfy the Shil'nikov inequality, is first introduced. Then a heteroclinic loop connecting two saddle foci of index 1 will be formed by applying the switching control strategy to the basic 3-D linear system. The heteroclinic loop consists of an unstable manifold, a stable manifold, and a heteroclinic point. Under the necessary conditions for forming the heteroclinic loop, the intended two-segmented piecewise linear system which exhibits the chaotic behavior in the sense of the Smale horseshoe can be finally constructed. An illustrative example is given, confirming the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document