Tensor product-based real-time control of the liquid levels in a three tank system

This paper presents an original application of the Tensor Product-based model transformation to the real-time control of the liquid levels in an experimental three tank system. A parallel distributed compensation technique is used for the design of the inner control loop resulting in a new equivalent state feedback matrix. A frequency domain design is then used for the design of PI controllers in the outer control loop.

I. Introduction

THE tensor product (TP)-based model transformation allows transforming a dynamic system model defined over a bounded domain into a polytopic or Takagi-Sugeno fuzzy model [1]–[6]. It provides a convenient way to transform linear parameter-varying (LPV) dynamic models into parameter-varying weighted combination of parameter independent (constant) models expressed as linear time-invariant (LTI) systems. The LPV model transformation is uniform from both theoretical and algorithmic point of view and takes in consideration the optimization constraints.