Multivariable PID control by decoupling

Abstract

This paper presents a new methodology to design multivariable proportional-integral-derivative (PID) controllers based on decoupling control. The method is presented for general n × n processes. In the design procedure, an ideal decoupling control with integral action is designed to minimise interactions. It depends on the desired open-loop processes that are specified according to realisability conditions and desired closed-loop performance specifications. These realisability conditions are stated and three common cases to define the open-loop processes are studied and proposed. Then, controller elements are approximated to PID structure. From a practical point of view, the wind-up problem is also considered and a new anti-wind-up scheme for multivariable PID controller is proposed. Comparisons with other works demonstrate the effectiveness of the methodology through the use of several simulation examples and an experimental lab process.

Keywords:

• decoupling control
• PID control
• multivariable control
• centralised control

Additional information

Funding

This work was supported by the Autonomous Government of Andalusia (Spain) under the Excellence Project P10-TEP-6056; the Spanish Ministry of Economy and Competitiveness [grant number DPI2012-37580-C02-01].

Notes on contributors

Juan Garrido

Juan Garrido received the degree in electronics engineering in 2006 from the University of Cordoba (Spain) and the PhD in automatic control from the National Distance Education University (UNED) of Spain, in 2012. Currently, he is an assistant professor at the Computer Science Department of the University of Cordoba. He is interested in control systems, multivariable control, PID controllers, and modelling and simulation.

Francisco Vázquez

Francisco Vazquez received the Physical Sciences degree in 1995 and the PhD degree in automatic control from UNED, Madrid, Spain, in 2001. He is currently working with Department of Computer Sciences at University of Cordoba as a full professor. Nowadays he is the director of the School of Polytechnics Sciences at University of Cordoba and belongs to Spanish Committee of Automatic Control of IFAC. He is interested in control systems, multivariable control and advanced methodologies of simulation and modelling.

Fernando Morilla

Fernando Morilla received the degree from Seville University (Spain) in 1979 and the PhD from the National Distance Education University (UNED), Madrid (Spain), in 1987, both in physics. In 1983, he joined the Department of Computer Sciences and Automatic Control of UNED, where he has been a full professor of control engineering since 1998. Dr Morilla is a member of the Spanish Committee of Automatic Control of IFAC. He is interested in process modelling, simulation and control, PID control, multivariable control, control education and system dynamics applications.