Design and Modeling of Anti Wind Up PID Controllers

In this chapter several anti windup control strategies for SISO and MIMO systems are proposed to diminish or eliminate the unwanted effects produced by this phenomena, when it occurs in PI or PID controllers. Windup is a phenomena found in PI and PID controllers due to the increase in the integral action when the input of the system is saturated according to the actuator limits. As it is known, the actuators have physical limits, for this reason, the input of the controller must be saturated in order to avoid damages. When a PI or PID controller saturates, the integral part of the controller increases its magnitude producing performance deterioration or even instability. In this chapter several anti windup controllers are proposed to eliminate the effects yielded by this phenomena. The first part of the chapter is devoted to explain classical anti windup architectures implemented in SISO and MIMO systems. Then in the second part of the chapter, the development of an anti windup controller for SISO systems is shown based on the approximation of the saturation model. The derivation of PID SISO (single input single output) anti windup controllers for continuous and discrete time systems is implemented adding an anti windup compensator in the feedback loop, so the unwanted effects are eliminated and the system performance is improved. Some illustrative examples are shown to test and compare the performance of the proposed techniques. In the third part of this chapter, the derivation of a suitable anti windup PID control architecture is shown for MIMO (multiple input multiple output) continuous and discrete time systems. These strategies consist in finding the controller parameters by static output feedback (SOF) solving the necessary linear matrix inequalities (LMI’s) by an appropriate anti windup control scheme. In order to obtain the control gains and parameters, the saturation is modeled with describing functions for the continuous time case and a suitable model to deal with this nonlinearity in the discrete time case. Finally a discussion and conclusions sections are shown in this chapter to analyze the advantages and other characteristics of the proposed control algorithms explained in this work.

[1]  Moonyong Lee,et al.  IMC−PID Controller Design for Improved Disturbance Rejection of Time-Delayed Processes , 2007 .

[2]  Zongli Lin,et al.  An analysis and design method for discrete-time linear systems under nested saturation , 2002, IEEE Trans. Autom. Control..

[3]  Zongli Lin,et al.  Output feedback stabilization of linear systems with actuator saturation , 2005, Proceedings of the 2005, American Control Conference, 2005..

[4]  Bernd Tibken,et al.  Controller synthesis of multi dimensional, discrete LTI systems based on numerical solutions of linear matrix inequalities , 2013, 2013 American Control Conference.

[5]  Radhakisan Sohanlal Baheti.  Simple Anti-Windup Controllers , 1989, 1989 American Control Conference.

[6]  Y S Chen,et al.  Digital redesign of anti-wind-up controller for cascaded analog system. , 2003, ISA transactions.

[7]  A. T. Neto,et al.  Stabilization via static output feedback , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[8]  Evanghelos Zafiriou,et al.  Robust process control , 1987 .

[9]  Shuping Ma,et al.  Stability and H∞ control for discrete-time singular systems subject to actuator saturation , 2009, 2009 American Control Conference.

[10]  Biao Huang,et al.  Robust digital model predictive control for linear uncertain systems with saturations , 2004, IEEE Trans. Autom. Control..

[11]  David G. Ward,et al.  An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation , 2002, IEEE Trans. Autom. Control..

[12]  N. Ohse,et al.  An Approach to Synthesis of Low Order Dynamic Anti-windup Compensators for Multivariable PID Control Systems with Input Saturation , 2006, 2006 SICE-ICASE International Joint Conference.

[13]  Bjorn Wittenmark.  Integrators, Nonlinearities, and Anti-reset Windup for Different Control Structures , 1989, 1989 American Control Conference.

[14]  R. Ocampo-Pérez,et al.  Adsorption of Fluoride from Water Solution on Bone Char , 2007 .

[15]  James H. Taylor,et al.  Synthesis of Nonlinear Controllers with Rate Feedback via Sinusoidal-Input Describing Function Methods , 1990, 1990 American Control Conference.

[16]  Young Il Lee,et al.  Design of discrete-time multivariable PID controllers via LMI approach , 2008, 2008 International Conference on Control, Automation and Systems.

[17]  Muhammad Abid,et al.  Anti-windup-based dynamic controller synthesis for nonlinear systems under input saturation , 2013, Appl. Math. Comput..

[18]  Sunwon Park,et al.  PID controller tuning for desired closed‐loop responses for SI/SO systems , 1998 .

[19]  Ming-Tzu Ho,et al.  Synthesis of low-order anti-windup compensators for PID control , 2011, 2011 8th Asian Control Conference (ASCC).

[20]  D. P. Atherton,et al.  An analysis package comparing PID anti-windup strategies , 1995 .

[21]  Sophie Tarbouriech,et al.  Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach , 1999, IEEE Trans. Autom. Control..

[22]  J. C. Cockbum,et al.  Loop Gain-Phase Shaping Design of SISO Robust Controllers Having Mixed Uncertainty , 1991, 1991 American Control Conference.

[23]  Wook Hyun Kwon,et al.  Sufficient LMI conditions for the H/sub /spl infin// output feedback stabilization of linear discrete-time systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[24]  Qing-Guo Wang,et al.  An Improved ILMI Method for Static Output Feedback Control With Application to Multivariable PID Control , 2006, IEEE Transactions on Automatic Control.

[25]  Zongli Lin,et al.  Set Invariance Conditions for Singular Linear Systems Subject to Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[26]  Masami Saeki,et al.  Design of anti-windup controller based on matrix inequalities , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[27]  Francis J. Doyle,et al.  An anti-windup input–output linearization scheme for SISO systems , 1999 .

[28]  R. M. Morales,et al.  Robust anti-windup against LTI uncertainty using frequency dependent IQCs , 2009, 2009 ICCAS-SICE.

[29]  Atsushi Fujimori.  Optimization of static output feedback using substitutive LMI formulation , 2004, IEEE Transactions on Automatic Control.

[30]  Jian Zhang,et al.  Design and applications of an optimal anti-windup digital controller using scalar sign function approach , 2011, 2011 IEEE International Conference on Control Applications (CCA).

[31]  O. Sawodny,et al.  Design of anti-windup-extensions for digital control loops , 2004, Proceedings of the 2004 American Control Conference.