  Many techniques have been developed for the loop-shaping method in control
design. While most loop-shaping methods apply a model of the open-loop
controlled plant, the resulting performance depends on the accuracy of the
dynamical model. This paper aims to develop a model-free loop-shaping
technique. The core idea is to convert the model matching problem to a
trajectory tracking problem. To achieve the desired loop gain, we need to
determine the control input such that the system output tracks the impulse
response of the loop gain function. In this paper, a model-free iterative
learning control (ILC) algorithm is applied to solve this tracking problem.
Once the ILC converges, the feedback controller that meets the desired loop
gain can then be constructed. This method does not require the model of the
controlled plant; hence it provides better performance of loop-shaping control
design. The proposed method is validated through numerical simulation on a
third order plant.
