Direct iterative tuning via spectral analysis

Iterative minimization of H2 control performance criteria

“…On the other hand, the particular parametrizationC (z) used to represent this class can often be manipulated. It has been proven in this paper, and also noted elsewhere (Kammer et al, 2000), that this parametrization must represent the class C with the minimal number of parameters but it can otherwise be freely chosen. Though this choice does play a role in the properties of the cost function, and thus might be useful for cost function shaping, we do not explore it in this paper.…”

“…Data-based design, on the other hand, addresses the minimization of the criterion (4) directly from data collected from the system, without the intermediate step of deriving a process model from these data. Such methods as IFT (Hjalmarsson et al, 1998) and FDT (Kammer et al, 2000) rely on iterative optimization procedures, mostly gradient descent algorithms. The quantities required in the optimization procedure are the cost function's gradient and possibly its Hessian, which are estimated pointwise directly from batches of input-output data collected from the closed-loop system.…”

“…The minimization of J e (ρ) for a free-form controller with known process model is a classical problem known as minimum variance control, whose solution is well known (Åström, 1970;Åström & Wittenmark, 1973;Kammer et al, 2000). The minimization of J y (ρ) has also been widely studied in the literature, particularly in the context of model reference adaptive control (Åström & Wittenmark, 1995;Goodwin & Sin, 1984).…”

“…In Kammer, Bitmead, and Bartlett (2000) an iterative procedure based on spectral analysis, named Frequency Domain Tuning (FDT), has been proposed for the minimization of an H 2 performance criterion for a system with zero reference; hence, no tracking objective is pursued. The Virtual Reference Feedback Tuning (VRFT) method Campi & Savaresi, 2006) is based on a clever manipulation of variables which transforms an H 2 performance criterion into one which is quadratic in the design parameters.…”

Frequency domain iterative feedforward/feedback tuning for MIMO ANVC

“…Its advantage is that it does not need modelling, given a stable and reasonably functioning controller to start with is available. Recent efforts were aimed at improving gradient estimation (Jansson et al, 2002;Jansson and Hjalmarsson, 2004) of the control performance criterion, improving stability robustness without modelling (Veres and Hjalmarsson, 2002) and through spectrum analysis (Kammer et al, 2000).…”