Abstract
The existing theories for closed loop identification with the linear feedback controller are very mature. To apply the existed theories directly in the control field, we propose a new idea about replacing the original unknown and nonlinear feedback controller with one approximated linear controller, while guaranteeing the equivalent property for the obtained closed loop system. Based on some statistical correlation functions, one condition is derived to show the equivalent property between the approximated linear controller and the original nonlinear controller. The detailed explicit form, corresponding to the approximated linear controller, is also constructed. Furthermore, to give a complete analysis for closed loop identification, the cost function is rewritten as one extended expression, being convenient to understand. Then spectral estimation is introduced to identify the unknown plant in the closed loop system. Finally, the proposed theories are verified by one simulation example.
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