Optimal Control of Nonlinear Systems Using The New Integral Operational Matrix of Block Pulse Functions

새로운 블럭펄스 적분연산행렬을 이용한 비선형계 최적제어

  • 조영호 (한국항공우주산업(주) 우주개발연구) ;
  • 심재선 (삼척대학교 전기공학과)
  • Published : 2003.04.01

Abstract

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on two steps. The first step transforms nonlinear optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPBCP(two point boundary condition problem) is solved by algebraic equations instead of differential equations using the new integral operational matrix of BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems and is less error value than that by the conventional matrix. In computer simulation, the algorithm was verified through the optimal control design of synchronous machine connected to an infinite bus.

Keywords

References

  1. D. E. Kirk, Optimal Control Theory, Prentice-hall Inc., 1970
  2. A. Isidori, Nonlinear Control Systems, Springer-Verlag, 1985
  3. M. F. Hassan and M. G. Singh, 'Hierarchical Successive Approximation Algorithms for Non-linear Systems. Part I. Generalisation of the Method of Takahara', Large Scale Systems, Vol. 2, pp. 65-79, 1981
  4. M. F. Hassan and M. G. Singh, 'Hierachical Successive Approximation Al-gorithms for Non-linear Systems. Part II. Algorithms Based on Costate C-oordination', Large Scale Systems, Vol. 2, pp. 81-95, 1981
  5. 이한석, 조영호, 이명규, 안두수, '블럭펄스 함수에 의한 비선형계의 2계층 최적제어', 대한전기학회 논문지, 47권 4호, pp. 494-502, 1998
  6. 안두수, WALSH 함수와 시스템 제어, 복두출판사, 2000
  7. N. S. Hsu and B. Cheng, 'Analysis and Optimal Control of time-varying linear systems Via block pulse functions', Int. J. Control, Vol. 33, Vo. 6, pp. 1123-1133, 1981 https://doi.org/10.1080/00207178108922980
  8. Z. H. Jiang and W. Schaufelberger, Block Pulse Functions and Their Applications in Control Systems, Springer-verlag, 1992
  9. A. Deb, G. Sarkar, M. Bhattacharjee and S. K. Sen, 'All-integrator Approach to Linear SISO Control System Analysis using Block Pulse Functions (BPF)', J. Franklin Inst., Vol. 334B, No. 2, pp. 319-335, 1997 https://doi.org/10.1016/S0016-0032(96)00054-3
  10. 조영호, 신승권, 이한석, 안두수, '보간법을 이용한 블럭펄스 함수에 대한 새로운 적분 연산행렬의 유도', 대한전기학회 논문지, 48권 6호, pp. 753-759, 1999
  11. E. Kreyszig, Advanced Engineering Mathematics, 7th Ed., Wiley