Stability Analysis of System with Fixed Structure Controller for Industrial Multi-Stage Separation Process via Vector Lyapunov Function

2009 ◽  
Vol 42 (4) ◽  
pp. 287-291
Author(s):  
A.Yu. Torgashov
2012 ◽  
Vol 9 (2) ◽  
Author(s):  
Rianto. A. Sasongko ◽  
Yazdi. I. Jenie ◽  
Ridanto. E. Poetro

This paper deals with a trajectory analysis of RKN200 multi-stage rocket system. The implementation of a multi-stage configuration means that a separation process has to be taken within the flight phase. The separation process is basically a transition process from a phase with booster as initial/launch propulsion to that with sustainer as the propulsion for the rest of flight time. RKN200 is a multi-stage rocket developed by LAPAN Indonesia for defence applications. In a multi-stage rocket development process, stage separation becomes a critical phase which should be considered carefully, since this phase will significantly affect the entire flight performance of the rocket. In this paper, the trajectory of RKN200 is analyzed in various cases with separation process included. The separation stage is modeled as a discrete process, i.e. by applying a sudden change on the rocket parameters values at the time of separation. In addition to that, impulsive force and moment which occur as a result of the separation ignition will also introduced into the mathematical model of the rocket dynamics, such that their influence to the rocket flight variables can be counted and computed . The modeling, simulation, and analysis of the flight trajectory are conducted using a simulation software already developed for rocket dynamic and performance analysis. Some simulation results are presented and analyzed to evaluate the RKN200 flight trajectory in some flight settings and conditions, and also to observe the effect of stage separation process on the rocket flight. Keywords: Rocket, Flight trajectory, Stage separation


Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.


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