Robust mixed-norm position and vibration control of flexible link mechanisms

This paper introduces a general and practical procedure for the design of high-performance and robust control schemes for the position and vibration control of flexible link mechanisms. The procedure is developed based on a mixed H2/H∞ optimization which allows trading explicitly between nominal performance and robust stability. The controller synthesis, which is iterative, is performed making use of a state-space linear model and initially assuming that the complete state of the system is available. In this phase, only the uncertainty arising from neglecting the unmodeled nonlinear dynamics is considered in order to prevent overly conservative designs. Even if a prototype of the studied mechanism is not available, a truthful definition of the uncertainty model bounds in the frequency domain can obtained by comparing the spectral responses yielded by an accurate nonlinear model, and by the linear one employed in the control design. Appropriate models are briefly described in the paper. Then, the additional uncertainty arising from discarding the spillover dynamics is taken into account by evaluating the effect on the controller robustness of the introduction of a reduced-order state observer. Simulation results prove the effectiveness of the control design method applied to a four-bar linkage with all the links flexible.