Minimax linear quadratic gaussian control of longitudinal vibration for cable transporter systems with multiplicative nonparametric uncertainties

This paper demonstrates a new application of robust control to the longitudinal vibration suppression of cable transporter systems with multiplicative nonparametric uncertainties. Both the infinite-dimensional theoretical model for the system and the robust controller are presented. Experimental results have verified the effectiveness of the proposed robust controller. The infinite-dimensional model of the transporter system is truncated to obtain a finite-dimensional model for robust controller design. A minimax Linear Quadratic Gaussian (LQG) controller is designed for multiplicative nonparametric uncertainties. The minimax controller design involves the solution of two simultaneous Riccati equations. The robust controller is implemented on a laboratory cable connected linear transporter system using dSPACE 1103 systems. System identification theory is applied to obtain a state-space representation in the 5-20 Hz frequency range for the experiment. The experimental results show reductions of 9 dB in the fundamental resonant peak of the cable transporter system.