A predictor for square multivariable dead-time systems with multiple delays based on the Kalman filter. (April 2023) - Lima, Daniel Martins; Lima, Bruno Martins; Normey-Rico, Julio Elias
Abstract: Dead-time is a phenomena that is present in many industrial processes and it presents a challenge for feedback control, especially for multivariable processes. To attenuate the dead-time effects, a common method is the use of predictor structures, which use input/output information of the process to predict the output (or states) of the system after the dead-time. In this paper, the Modified Kalman Predictor (MKP) is proposed, which is a novel predictor for linear multivariable square systems with multiple dead-time (or delays) based on the Kalman Filter that has disturbance estimation and can cope with systems of any order or dynamics, including unstable ones. It uses a specific state-space representation of the process which makes its implementation more straight-forward when compared to other methods. The MKP affects the disturbance rejection but not the closed-loop stability in the nominal case, and it can help to improve closed-loop robustness in the uncertain case. The impacts of the MKP tuning in the closed-loop response considering disturbance rejection and robustness are analyzed using standard frequency domain tools. To illustrate the benefits of the MKP, two examples are used that highlight the tuning guidelines for disturbance rejection and robustness improvements. Highlights: A predictor based on the Kalman Filter is proposed for MIMO processes with delays. It implicitly defines a Filtered Smith Predictor and has the same properties. Can be applied to MIMO square process with multiple delays. Can cope with systems of any order or dynamics (non-minimum phase, unstable, etc.). Tuning rules are simple and independent of system order or dynamics.