Control relevant identification with steady state gain matching

The prefilter based control relevant identification scheme proposed by Rivera et al.[14], for single input single output(SISO) system gives a model of the system which matches the true system in a range of frequencies that are important for closed loop performance. However, it may also be desirable to have small mismatch at the steady state condition as well. This is specifically true when the desired closed loop speed of response is much higher than the open loop speed of response. Here a method is proposed to estimate a control relevant model that, in addition to having a small mismatch in the control relevant frequencies, also has a good steady state gain match, with that of the true system. With such a control relevant model having steady state gain match, the closed loop internal model control (IMC) based system is shown to give satisfactory response even with higher desired speed of response. Also, a control relevant identification scheme for multi input single output(MISO) system, having steady state gain match is proposed, using uncorrelated inputs. Application of these identified models to a feed forward control scheme has been considered to demonstrate superior performance with these models. Similarly, with combined feed forward/feedback control, the model having steady state gain match gives an improved performance even with higher desired speed of closed loop response.