Identification of Transfer Function Models in Closed-Loop

The identification and estimation of transfer function models in a closed-loop situation has received a lot of attention in the control systems literature: see e.g. Ljung (1999); Soderstrom and Stoica (1989); Verhaegen (1993); Van den Hof (1998); Gilson and Van den Hof (2005). Provided there is an external command input signal, simple, sub-optimal transfer function estimation within a closed automatic control loop has always been straightforward when using Instrumental Variable (IV) estimation methodology (Young, 1970b). However, the more recent RIV and RIVC algorithms discussed in previous chapters of this book provide a new stimulus to the development of statistically optimal methods of closed-loop estimation and a number of possible solutions are discussed by Gilson et al (2008, 2009), within a continuous-time setting.