# Decentralized Control Structures

**Researchers:** Tore Hägglund

There is an unfortunate gap between the centralized computational approaches of multi-variable control theory and the common practice to design local control loops disregarding couplings and interaction. Today it appears that both approaches has reached a point of refinement where the gap can be reduced from both sides. This project aims to revise and improve the basic modules for decentralized control, and to develop new. The ideas to be investigated in this project are relevant not only for process control but is also of interest for general classes of multi-variable systems.

### Low-order Feedforward Controllers

Feedforward is a powerful method to improve the performance of feedback loops. Feedforward can be made both from setpoint and measurable load disturbances. In this project, the goal is to improve both structures and design methods for feeforward control from load disturbances.

The basic idea for design of feedforward compensators is simple. The ideal compensator is formed as the dynamics between the load disturbance and the process output, divided by the dynamics between the control signal and the process output, with reversed sign. However this ideal compensator is seldom realizable. Therefore, there is a need for design methods. There are surprisingly few such methods presented in the literature, and the methods do normally not take the feedback control into account in the design.

In a first phase, new simple tuning rules for feedforward compensators have been derived. The design objective is to minimize IAE without getting any overshoot in step load disturbance responses. This work has been done in collaboration with University of Almeria. This collaboration continues, and University of Brescia has also been involved in the project where e.g. performance indices for feedforward control have been developed.

Using a structure that decouples feedback and feedforward action, optimal design rules that minimizes ISE has been developed. The used structure simplifies tuning of the feedforward controller by allowing the controller to be tuned with respect to the open-loop system while maintaining its properties and performance when used in a closed-loop setting. The structure also enables independent re-tuning of both the feedback and the feedforward controller. Work has also been done concerning characterization of optimal low-order feedforward controllers and practical considerations for implementation.

PID controllers is often implemented with set-point weighting to improve the response to changes in the reference. By using convex optimization techniques the parameters for the set-point weights can be found efficiently, fast as well as be guaranteed to be globally optimal. By solving an optimization problem to find the optimal set-point weights for a large batch of processes, tuning rules have been found that minimizes IAE. The same optimization framework and formulations can also been used to tune feedforward controllers from measurable disturbances.

**Ratio Control**

In ratio control, the control objective is to keep the ratio between two signals, normally flow measurements, at a desired value in spite of variations in the setpoints, load disturbances, and possible control signal saturations. It ils also desirable to keep the ratio also in situations when one of the controllers is switched to local setpoint or manual control.

There are methods available that manage to handle some of these disturbances, but no efficient method exists that handles all disturbances in both loops. The goal of the project is to obtain such a procedure. The project is supported by Vinnova.

### Publications

**José Luis Guzmán, Tore Hägglund, Max Veronesi, Antonio Visioli:**
"Performance indices for feedforward control".
*Journal of Process Control,*
**
26**,
pp. 26–34,2015.

**Carlos Rodríguez, José Luis Guzmán, Manuel Berenguel, Tore Hägglund:**
"Optimal feedforward compensators for systems with right-half plane zeros".
*Journal of Process Control,*
**
24:**4,
pp. 368–374,2014.

**C. Rodríguez, José Luis Guzmán, Manuel Berenguel, Tore Hägglund, J. E. Normey-Rico:**
"Diseño de controladores por Adelanto para Inversión de Retardo no realizable".
In *XXXIV Jornadas de Automática*, Terrassa, Spain,
September 2013.

**Tore Hägglund:**
"A Unified Discussion on Signal Filtering in PID Control".
*Control Engineering Practice,*
**
21:**8,
pp. 994–1006, August 2013.

**C. Rodríguez, José Luis Guzmán, Manuel Berenguel, Tore Hägglund:**
"Generalized feedforward tuning rules for non-realizable delay inversion".
*Journal of Process Control,*
**
23:**9,
pp. 1241–1250,2013.

**Tore Hägglund:**
"Signal Filtering in PID Control".
In *IFAC Conference on Advances in PID Control*, Brescia, Italy,
March 2012.

**Martin Hast, Tore Hägglund:**
"Design of Optimal Low-Order Feedforward Controllers".
In *IFAC Conference on Advances in PID Control*, Brescia, Italy,
March 2012.

**Martin Hast, Tore Hägglund:**
"Design of Optimal Low-Order Feedforward Controllers for Disturbance Rejection".
In *17th Nordic Process Control Workshop*, Kgs Lyngby, Denmark,
January 2012.

**Juan Garrido, Francisco Vázquez, Fernando Morilla, Tore Hägglund:**
"Practical advantages of inverted decoupling".
*Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control,*
**
225:**7,
pp. 977–992, November 2011.

**José Luis Guzmán, Tore Hägglund, Karl Johan Åström, Sebastián Dormido, Manuel Berenguel, Yves Piguet:**
"Feedforward Control Concepts through Interactive Tools".
In *18th IFAC World Congress*, Milano, Italy,
August 2011.

**José Luis Guzmán, Tore Hägglund:**
"Simple tuning rules for feedforward compensators".
*Journal of Process Control,*
**
21:**1,
pp. 92–102, January 2011.

**José Luis Guzmán, Karl Johan Åström, Tore Hägglund, Sebastián Dormido, Manuel Berenguel, Yves Piguet:**
"Interactive Learning Module for Control Interaction Understanding".
In *2009 European Control Conference*, Budapest, Hungary,
August 2009.

**Olof Garpinger, Tore Hägglund:**
"A Software Tool for Robust PID Design".
In *Proc. 17th IFAC World Congress, Seoul, Korea*,
July 2008.

**Alfred Theorin:**
"Implementation of an Autotunable Decoupling TITO Controller".
Master's Thesis
ISRN LUTFD2/TFRT--5800--SE,
Department of Automatic Control, Lund University, Sweden, July 2007.

**Pontus Nordfeldt, Tore Hägglund:**
"Decoupler and PID Controller Design of TITO Systems".
*Journal of Process Control,*
**
16:**9,
pp. 923–936, October 2006.

**Pontus Nordfeldt:**
"PID control of TITO systems".
Licentiate Thesis
ISRN LUTFD2/TFRT--3238--SE,
Department of Automatic Control, Lund University, Sweden, December 2005.

**Pontus Nordfeldt, Tore Hägglund:**
"Design of PID Controllers for Decoupled Multi-Variable Systems".
In *Proc. 16th IFAC World Congress*,
Prague, Czech Republic, July 2005.

2017-02-01