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The essential ingredients of any control design procedure include the acquisition of process knowledge (system identification) and its efficient integration into the controller (controller synthesis). Reliable models of industrial plants are often difficult or impossible to obtain due to the high complexity of the plants and/or the excessive cost of modeling. On the other hand, the controllers designed on the basis of reduced-order models might well lead to unsatisfactory performance when applied to real plants due to modeling errors. Recently, the direct synthesis or tuning of controllers from the acquired information from the plant without any mathematical model has been developed in place of model-based controller syntheses. Some tuning methods where the actual response approaches to the desired closed-loop response based on the input/output data acquired from a closed-loop system with a fixed structure controller such as a PID controller are proposed: Iterative Feedback Tuning (IFT), Virtual Reference Feedback Tuning (VRFT), Correlationbased Tuning (CbT), and Fictitious Reference Iterative Tuning (FRIT). These data-driven controller syntheses are effective in comparison with the model-based controller syntheses such as H∞ control synthesis in the cases where a controller structure is fixed and/or a mathematical model can not be obtained. However, These databased controller syntheses have troubles in applying to MIMO systems and in using contaminated data by noise: • IFT requires a lot of data acquisition to perform nonlinear optimization to estimate an unbiased gradient of an evaluation function so as to be minimized at each controller parameter update. • VRFT can be solved within a scope of least-squares method, but it has a restriction on a structure of achievable reference models in MIMO systems. • FRIT requires only one-shop experimental data but it is not applicable for MIMO systems. • CbT might lead to a satisfactory controller even with contaminated data, but needs a lot of data acquisition as well as IFT. The authors have proposed another data-driven controller synthesis named Fictitious Correlation-based Tuning (FCbT) resolving the above mentioned problems. However, FCbT has proposed for the design of a feedback controller, and its effectiveness is confirmed by only numerical simulations. Fig. 1. 2DOF control system

A Direct Design of 2DOF Controller Based on FCbT and an Application to Closed-Loop Identification