Performance measures, performance limits and optimal PI control for the IPDT plant

Abstract This paper considers PI controller tuning for the Integral Plus Dead Time (IPDT) plant subject to constraints on tolerable deviations from ideal shapes and guaranteeing minimal combined IAE (Integral of Absolute Error) measure composed of weighted IAE values of the setpoint and disturbance step responses. As the ideal responses at the plant output, monotonic (MO) transients are chosen. This implies one-pulse (1P) responses consisting of two monotonic intervals at the plant input. Optimal nominal tunings for the most important situations regarding the servo/regulation trade-off are determined by the newly developed Matlab/Simulink tool based on the performance portrait (PP) method. Generated results confirm Pareto-like limits of performance achievable under PI control and are used in classifying traditional tuning approaches into the setpoint and disturbance oriented ones. Principles of robust PP based tuning are briefly illustrated and conditions of invariance of the closed loop performance against the dead time uncertainty are formulated and checked by simulation.

[1]  J. Ackermann,et al.  Robust Control: The Parameter Space Approach , 2012 .

[2]  Sigurd Skogestad,et al.  Optimal PI-Control and Verification of the SIMC Tuning Rule , 2012 .

[3]  Mikuláš Huba,et al.  Setpoint Versus Disturbance Responses of the IPDT Plant , 2012 .

[4]  K. Åström,et al.  Revisiting The Ziegler‐Nichols Tuning Rules For Pi Control , 2002 .

[5]  Yoichi Hori,et al.  Robust speed control of DC servomotors using modern two degrees-of-freedom controller design , 1991 .

[6]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[7]  Stanko Strmcnik,et al.  Design of 2-DOF PI controller for integrating processes , 2011, 2011 8th Asian Control Conference (ASCC).

[8]  M. Morari,et al.  Internal model control: PID controller design , 1986 .

[9]  Tore Hägglund,et al.  Advanced PID Control , 2005 .

[10]  Mikulás Huba,et al.  Comparing Approaches to Constrained Design of Integrating Controllers , 2012, ACE.

[11]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[12]  A. O'Dwyer.  School of Electrical and Electronic Engineering 2006-0101 PI and PID controller tuning rules : an overview and personal perspective , 2017 .

[13]  Francesco Amato,et al.  Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters , 2006 .

[14]  Raymond Gorez,et al.  Discussion on: 'Balanced Tuning of PI Controllers' by P. Klàn and R. Gorez , 2000, Eur. J. Control.

[15]  Sigurd Skogestad,et al.  Simple analytic rules for model reduction and PID controller tuning , 2003 .

[16]  J. Doyle,et al.  Essentials of Robust Control , 1997 .

[17]  Ramon Vilanova,et al.  IMC-like analytical H∞ design with S/SP mixed sensitivity consideration: Utility in PID tuning guidance , 2011 .

[18]  Ramon Vilanova,et al.  A look into robustness/performance and servo/regulation issues in PI tuning , 2012 .

[19]  Miroslav R. Mataušek,et al.  PID controller frequency-domain tuning for stable, integrating and unstable processes, including dead-time , 2011 .

[20]  K. Åström,et al.  Revisiting the Ziegler-Nichols step response method for PID control , 2004 .

[21]  Aidan O'Dwyer,et al.  Handbook of PI and PID controller tuning rules , 2003 .

[22]  M. Huba,et al.  NUMERICAL ISSUES IN DESIGNING PI CONTROLLER FOR IPDT PLANT , 2009 .

[23]  Miroslav R. Mataušek,et al.  Revisiting the Ziegler–Nichols process dynamics characterization , 2010 .

[24]  Mikulás Huba.  Modular disturbance observer based constrained PI-controller design , 2012, 2012 12th IEEE International Workshop on Advanced Motion Control (AMC).

[25]  A. Isidori.  Nonlinear Control Systems , 1985 .

[26]  Ramon Vilanova,et al.  Simple PID tuning rules with guaranteed Ms robustness achievement , 2011 .

[27]  Sigurd Skogestad,et al.  Tuning for Smooth PID Control with Acceptable Disturbance Rejection , 2006 .

[28]  Raymond Gorez,et al.  Balanced Tuning of PI Controllers , 2000, Eur. J. Control.

[29]  K.J. ÅSTRÖM,et al.  Design of PI Controllers based on Non-Convex Optimization , 1998, Autom..