Improved Decentralized Controllers for Stable Systems by IMC Method

Abstract

In the present work, the matrix notation is used to derive the Internal Model Control (IMC) decentralized Proportional Integral (PI) controllers. MacLaurin series is applied to the resulting equation to get the controller parameters. For design of the controllers, the diagonal elements of the process are used, whereas for evaluating the performance of the controllers, the full transfer function matrix of the process is used. For a two input–two output (2 × 2) system example, the recently available methods for designing decentralized PI controllers (Equivalent Transfer Function methods, Effective Relative Gain Array method, Direct multi-loop method) are compared with the present method. For a 4 × 4 system, the corresponding recent reported methods are compared. The performance of the present method is better than the above methods. The performances of the control systems are compared in terms of the Integral absolute error and the controller output behaviour is compared in terms of total variation. The robustness of the control system is evaluated by the maximum sensitivity and by the inverse maximum singular value of the input and the output multiplicative uncertainties.

Keywords:

• PI controller
• Stable systems
• MacLaurin series
• Decentralized controller

Disclosure statement

No potential conflict of interest was reported by the authors.