On Frequency Domain Loop Shaping for Self-Tuning Control

The self-tuning frequency-domain loop shaping control problem for stable minimum phase systems is considered. The resulting control scheme corresponds to an explicit self-tuning controller, where identification and control is implemented in the frequency domain, thereby taking advantage of the properties afforded by frequency domain identification schemes. The input and output signals to the system are transformed to the frequency domain via discrete Fourier transforms; subsequently the identification part recursively estimates the system's transfer function as a finite impulse response filter. The controller corresponds to a circular convolver, implemented in the frequency domain, and shapes the open loop frequency response by providing the necessary supplement of magnitude and phase in order to match an a priori closed loop frequency response.