Disturbance-Observer-Based Control for Multivariable Systems Based on Equivalent Transfer Function

Abstract

Disturbance-observer-based control is a well-known technique for the rejection of unmeasurable disturbances. The application of disturbance-observer-based control is well established for single-input and single-output systems but presents two challenges when applied to multivariable systems with time delays. The first challenge is the calculation of the inverse of the nominal model. The second challenge is the optimal synthesis of the disturbance observer filter to obtain a trade-off between the disturbance rejection and measurement noise attenuation. In this paper, we propose strategies to address these two challenges. To facilitate the design and implementation of the disturbance observer, we propose to approximate the inverse of the nominal model by employing the concept of equivalent transfer function. The equivalent transfer function approximates the inverse of a multivariable model by a matrix whose elements are the inverse of first-order plus time delay transfer functions, that are simpler to deal with. To tackle the second challenge, we propose a synthesis formulation based on a multi-objective optimization problem. Through a multi-objective evolutionary optimization algorithm, it is possible to obtain a set of efficient solutions with different trade-offs between the two objectives. We apply the proposed strategies to two well-known problems in the field of process control to demonstrate its efficiency. We verify that the use of the equivalent transfer function presents the best results in comparison to other methodologies considering the three control objectives: tracking of reference signals, rejection of disturbances, and attenuation of measurement noises.