Cascade multi-resonant disturbance observer design. Application to a distillation column

Abstract

In this work, we present a novel approach for input disturbance estimation design and implementation for dynamical processes under the influence of unknown disturbances that present a clear periodical behaviour of a known frequency. Both the design and the implementation are focused on simplicity. The observer consists of a set of transfer functions fed by the process manipulated variable and the sensor measurement that are implemented through a mixture of cascade and series connections. For the synthesis of the disturbance observer, we just need an input–output model of the process and one tuning parameter in each of the transfer functions. We present simple rules for the design considering the trade-off between the transient time needed to estimate changes in the behaviour of the disturbance and the robustness against measurement noise effects. We show the benefits in using this disturbance estimation as a feed-forward signal in both open loop and closed loop control applications, and we quantify the robustness modification when used together with a closed loop controller. The transfer functions of the observer include both a low pass filter and a set of resonant terms. We quantify the effect of the different terms and their parameter tuning. Our implementation method uses standard tools available in industrial control systems and we have applied it to a real distillation column under ambient temperature disturbances. The main contribution of this work is the simplicity of the design and implementation of the disturbance observer, making it suitable for the process industry and to be managed by non-experts in control systems. Another contribution is the a priori design based in intuitive engineering performance indices.