The problem of robust pole assignment (RPA) in high-order descriptor linear system is considered. By using the result of eigenstructure assignment via proportional plus derivative state feedback and the perturbation theory of generalised pole problem proposed by Stewart, the RPA problem in high-order descriptor linear system is converted into a minimisation problem, and a simple algorithm is derived for solution to this RPA problem. An example of third-order is worked out with multiple solutions, both the indices and the numerical robustness test demonstrate the effect of the proposed approach.
Inspec keywords: PD control; pole assignment; eigenstructure assignment; state feedback; robust control; linear systems
Other keywords:
Subjects: Stability in control theory; Control system analysis and synthesis methods
References
-
-
1)
- Duan, G.R., Yu, H.H.: `Eigenstructure assignment in high-order descriptor linear systems via proportional plus derivative state feedback', Proc. 6th Word Congress on Control and Automation, 2006, Dalian, China, p. 500–505.
-
2)
- T.J. Owens , J. O'reilly . Parametric state-feedback control for arbitrary eigenvalue assignment with minimun sensitivity. IEE Proc., Control Theory Appl. , 6 , 307 - 313
-
3)
- W.C. Ho Daniel , J. Lam , J.H. Xu . Robust approximate pole assignment for second-order systems; Neural network computation. J. Guid. Control Dyn. , 6 , 923 - 929
-
4)
- G.R. Duan , N.K. Nichols , G.P. Liu . Robust pole assignment in descriptor linear systems via state feedback. Eur. J. Control , 136 - 149
-
5)
- J. Lam , W.Y. Yan . A gradient flow approach to the robust pole-placement problem. Int. J. Robust Nonlinear Control , 175 - 185
-
6)
- G.R. Duan , R.J. Patton . Robust pole assignment in descriptor systems via proportional plus partial derivative state feedback. Int. J. Control , 13 , 1193 - 1203
-
7)
- G.R. Duan . Robust eigenstructure assignment via dynamical compensators. Automatica , 469 - 474
-
8)
- J. Kautsky , N.K. Nichols . Robust pole assignment in systems subject to structured perturbations. Sys. Control. Lett. , 373 - 380
-
9)
- E.K. Chu , B.N. Datta . Numerically robust pole assignment for second-order systems. Int. J. Control , 6 , 1113 - 1127
-
10)
- Wang, G.S., Duan, G.R.: `Robust pole assignment via P-D feedback in a class of second-order dynamic systems', 8thInt. Conf. Control, Automation, Robotics and Vision, 2004, Kunming, China, 2, p. 1152–1156.
-
11)
- Kautsky, J., Nichols, N.K.: `Algorithm for robust pole assignment in singular systems', Proc. American Control Conf, 1986, Seattle, WA, USA, p. 433–436.
-
12)
- Duan, G.R., Zhang, X.: `Dynamical order assignment in linear descriptor systems via state derivative feedback', Proc. 41th IEEE Conf. Decision and Control, 2006, Las Vegas, Nevada, USA, 4, p. 4533–4538.
-
13)
- V.L. Syrmos , F.L. Lewis . Robust eigenvalue assignment for generalised systems. Automatica , 1223 - 1228
-
14)
- J. Kautsky , N.K. Nichols , E.K.W. Chu . Robust pole assignment in singular control systems. Linear Algebr. Appl. , 9 - 37
-
15)
- G.R. Duan , Y.L. Wu . Robust pole assignment in matrix descriptor second-order linear systems. Trans. Inst. Meas. Control , 4 , 279 - 295
-
16)
- A. Varga . A numerically reliable approach to robust pole assignment for descriptor systems. Future Gener. Comput. Syst. , 7 , 1221 - 1230
-
17)
- G.W. Stewart . Gerschgorin theory for the generalised eigenvalue problem Ax=λBx. Math. Comp. , 600 - 606
-
18)
- A.G. Wu , G.R. Duan . Separation principle for robust pole assignment in descriptor linear systems. Syst. Eng. Electr. (China) , 10 , 1785 - 1787
-
19)
- Chan, H.C., Lam, J., Ho Daniel, W.C.: `Gradient flow approach to robust pole assignment in second-order systems', Proc. Conf. Decision and Control, 1996, Kobe, Japan, 4, p. 4589–4590.
-
20)
- N. Biswa , W.W. Lin , J.N. Wang . Robust partial pole assignment for vibrating systems with aerodynamic effects. IEEE Trans. Autom. Control , 12 , 1979 - 1984
-
21)
- V. Sundarapandian . A separation theorem for robust pole placement of discrete-time linear control systems with full-order observers. Math. Comput. Model. , 42 - 48
-
22)
- J. Kautsky , N.K. Nichols , P. Van Dooren . Robust pole assignment in linear state feedback. Int. J. Control , 1129 - 1155
-
23)
- G.R. Duan . Simple algorithm for robust eigenvalue assignment in linear output feedback. IEE Proc., Control Theory Appl. , 465 - 469
-
1)
Related content