Integral quadratic constraints-based robust controller two-mass-spring system

In this paper, we propose the robust controller design for two-mass-spring system based on integral quadratic constraints (IQC's) and give a design example of multipurpose controllers (state-feedback controller case). The controller design need to achieve four major constraints: (i) tracking with zero steady-state error, (ii) guaranteed level of H_∞ performance index γ(L₂ gain) from the exogenous input w to the output z which indicate input-to-output properties of the system, (iii) accordance to IQC's, and (iv) pole placement in a specified region, simultaneously in the presence of physical parameter uncertainties. The simulation results show that our robust controller design for this two-mass-spring system endures the uncertain environment and the setting time is small about 0.1. In particular, we are always able to control required poles in the vertical strip region and to track along any required angle.