What is it about?

Thanks to active power filters, improving the quality at the mains is possible, however, this ability strongly depends on the control strategy. We use Takagi-Sugeno models and the Lyapunov stability criteria as design tools for establishing Linear Matrix Inequalities (LMI) conditions; solving these LMI conditions a parallel-distributed compensation (PDC) control law was obtained. With this control law, the shunt active power filter (SAPF) shows a good performance for reducing the total harmonic distortion (THD) and achieving the power factor (PF) correction during load changes. We could corroborate a satisfactory performance for simulation and experimental tests, even better than several other popular SAPF controllers.

Featured Image

Why is it important?

Since the tasks of SAPF are very challenging, the design of their controllers is of great interest nowadays, so we decided to explore alternatives to traditional SAPF controllers. TS models allow an exact representation of the nonlinear system dynamics, where the result is a model with linear matrices which are useful for establishing LMI conditions. Likewise, the nonlinear character of the original system is encapsulated in nonlinear scalar functions that can be included in the control law. A PDC type control law is obtained once LMI conditions are solved by means of efficient computational algorithms. The independence of the system parameters during the SAPF operation is one of the advantages of this control strategy and allows to obtain a better performance in comparison with other controllers.


Control based on TS models and LMIs is not very popular in power converter applications, thus this article seeks to highlight the benefits of this control strategy within power electronics applications, particularly for the demanding tasks of active power filters.

Raul Teran
Instituto Tecnologico de Sonora

Power quality is an important issue to be addressed since it is necessary to maximize the correct use of electrical energy. The Active Power Filter (APF) helps in this task; however, APF control can be enhanced to allow APF to adapt to different load changes. Using Takagi-Sugeno and Linear Matri Inequalities, better APF performance is achieved.

Javier Perez Ramirez
Instituto Tecnologico de Sonora

Read the Original

This page is a summary of: Takagi‐Sugeno exact model and linear matrix inequalities for an active power filter control, International Transactions on Electrical Energy Systems, November 2021, Hindawi Publishing Corporation,
DOI: 10.1002/2050-7038.13212.
You can read the full text:

Open access logo



The following have contributed to this page