Minimax design of robust controllers for flexible systems

The focus of this paper is on the design of robust controllers based on the range of expected variation of uncertain parameters from their nominal values. A minimax optimization problem is formulated with the objective of minimizing the maximum value of the cost function over the range of the uncertain parameter. To expedite the optimization process, equations are derived for the gradient of the cost and constraint functions with respect to the parameters of the controller. The proposed technique is illustrated on two examples. The first is a spring-mass-dashpot and the second is a two-mass-spring benchmark problem.

[1]  Warren P. Seering,et al.  Preshaping Command Inputs to Reduce System Vibration , 1990 .

[2]  Tarunraj Singh,et al.  Robust time-optimal control - Frequency domain approach , 1994 .

[3]  Tarunraj Singh,et al.  Robust Time-Delay Control , 1993 .

[4]  Warren P. Seering,et al.  On-off control of flexible spacecraft with specified fuel usage , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Otto J. M. Smith.  Posicast Control of Damped Oscillatory Systems , 1957, Proceedings of the IRE.

[6]  John L. Junkins,et al.  Near-minimum-time maneuvers of flexible vehicles - A Liapunov control law design method , 1990 .

[7]  Yasuo Tokita,et al.  On the Vibration Reduction , 1978 .

[8]  Qiang Liu,et al.  Robust Time-Optimal Control of Uncertain Flexible Spacecraft , 1992 .

[9]  Tarunraj Singh,et al.  Robust Time-Optimal Control of Flexible Structures With Parametric Uncertainty , 1997 .

[10]  Tarunraj Singh,et al.  Fuel/Time Optimal Control of the Benchmark Problem , 1995 .

[11]  William Singhose,et al.  On-Off Control With Specified Fuel Usage , 1999 .

[12]  C. Loan.  Computing integrals involving the matrix exponential , 1978 .

[13]  Lucy Y. Pao,et al.  Input shaper designs for minimizing the expected level of residual vibration in flexible structures , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[14]  Lisa J. Porter,et al.  Vibration Reduction Using Multi-Hump Extra-Insensitive Input Shapers , 1995 .

[15]  Arthur E. Bryson,et al.  Linear-Quadratic-Gaussian Controllers with Specified Parameter Robustness , 1998 .

[16]  Chen-Chien Hsu,et al.  Design of optimal controller for interval plant from signal energy point of view via evolutionary approaches , 2004, IEEE Trans. Syst. Man Cybern. Part B.