A Youla–Kucera formulation of the controller design from data problem

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.