A Youla–Kucera formulation of the controller design from data problem. (January 2022) - Valderrama, Freddy; Ruiz, Fredy
Abstract: The Youla–Kucera parametrization is a fundamental result in system theory, very useful when designing model-based controllers. In this paper, this formulation is employed to solve the controller design from data problem, without requiring a process model. It is shown that, given a set of input–output data generated by the plant and a desired closed-loop reference model, it is possible to estimate an stable filter that parametrizes the controller that minimizes the norm between the closed-loop dynamics and the requested behavior. The employed parametrization gives more degrees of freedom in the controller design than previous works in literature, allowing to achieve more stringent closed-loop performances. The proposed design methodology does not imply a plant identification step and it provides an estimate of the model-matching error between the requested and the resulting model as indicator of stability and performance of the derived control loop. The proposed solution is evaluated in regulation problems for non-minimum phase systems through Monte Carlo simulations and in experimental conditions for the regulation of temperature in an ohmic assisted hydrodistillation process. Highlights: Data-driven controller tuning approach based on the Youla–Kucera parametrization. The method allows to reach more stringent reference models than existing solutions. Open and closed loop data handled by instrumental variables and convex optimization. Stability and feasibility certificates are provided a posteriori. Simulations and experimental results confirm the validity of the methodology.