Non-linear feedback control for improved peak response reduction

The linear quadratic regulator has been used extensively in many control systems designed for structural control applications due to its stability and robustness. Recent results obtained from simulation, model experiments, and full-scale structural applications, however, show that it is difficult to employ linear feedback control laws to produce a significant peak response reduction when the peak response occurs during the first few cycles of the time history. In this paper, based on the fact that minimizing the maximum response can be approximated by minimizing a higher-order performance index, a higher-order performance criterion is introduced and an optimal nonlinear feedback control law is derived based upon this criterion. It is shown that this nonlinear control law can significantly improve peak response reduction under the same constraints imposed on the control resources as in the linear quadratic regulator case.