Unbiased MIMO VRFT with application to process control

• Common framework for SISO and MIMO VRFT.
• Achievement of the ideal controller for different performance requirements.
• Filter proposal for bias reduction in non-optimal case.
• Application to level control of a pilot plant.

Continuous process industries usually have hundreds to thousands of control loops, most of which are coupled, i.e. one control loop affects the behavior of another control loop. In order to properly design the controllers and reduce the interactions between loops it is necessary to consider the multivariable structure of the process. Usually MIMO (multiple-input, multiple-output) controllers are designed using MIMO models of the process, but obtaining these models is a task very demanding and time consuming. Virtual Reference Feedback Tuning (VRFT) is a data-driven technique to design controllers which do not use a model of the process; all the needed information is collected from input/output data from an experiment. The method is well established for SISO (single-input, single-output) systems and there are some extensions to MIMO process which assume that all the outputs should have the same closed-loop performance. In this paper we develop a complete framework to MIMO VRFT which provides unbiased estimates to the optimal MIMO controller (when it is possible) even when the closed-loop performances are distinct to each loop. When it is not possible to obtain the optimal controller because the controller class is too restrictive (for example PID controllers) then we propose the use of a filter to reduce the bias on the estimates. Also, when the data is corrupted by noise, the use of instrumental variables to eliminate the bias on the estimate should be considered. The article presents simulation examples and a practical experiment on a tree tank system where the goal is to control the level of two tanks.