A New Tuning Method for Two-Degree-of-Freedom Internal Model Control under Parametric Uncertainty

Abstract Internal model control (IMC) yields very good performance for set point tracking, but gives sluggish response for disturbance rejection problem. A two-degree-of-freedom IMC (2DOF-IMC) has been developed to overcome the weakness. However, the setting of parameter becomes a complicated matter if there is an uncertainty model. The present study proposes a new tuning method for the controller. The proposed tuning method consists of three steps. Firstly, the worst case of the model uncertainty is determined. Secondly, the parameter of set point controller using maximum peak (Mp) criteria is specified, and finally, the parameter of the disturbance rejection controller using gain margin (GM) criteria is obtained. The proposed method is denoted as Mp-GM tuning method. The effectiveness of Mp-GM tuning method has evaluated and compared with IMC-controller tuning program (IMCTUNE) as bench mark. The evaluation and comparison have been done through the simulation on a number of first order plus dead time (FOPDT) and higher order processes. The FOPDT process tested includes processes with controllability ratio in the range 0.7 to 2.5. The higher processes include second order with underdamped and third order with nonminimum phase processes. Although the two of higher order processes are considered as difficult processes, the proposed Mp-GM tuning method are able to obtain the good controller parameter even under process uncertainties.

[1]  O. J. M. Smith,et al.  A controller to overcome dead time , 1959 .

[2]  Coleman B. Brosilow,et al.  Tuning and design of single‐input, single‐output control systems for parametric uncertainty , 2000 .

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

[4]  Bin Hu,et al.  Multi-loop Internal Model Controller Design Based on a Dynamic PLS Framework , 2010 .

[5]  Manfred Morari,et al.  Internal model control and process uncertainty: mapping uncertainty regions for SISO controller design , 1986 .

[6]  Wen Tan.  Analysis and design of a double two-degree-of-freedom control scheme. , 2010, ISA transactions.

[7]  Min-Sen Chiu,et al.  Data-based internal model controller design for a class of nonlinear systems , 2005, 2005 International Conference on Control and Automation.

[8]  Akira Ohkawa,et al.  New tuning method for IMC controller , 1998 .

[9]  Ramon Vilanova,et al.  IMC based Robust PID design: Tuning guidelines and automatic tuning , 2008 .

[10]  Min-Sen Chiu,et al.  Adaptive IMC Controller Design for Nonlinear Process Control , 2007 .

[11]  Irving Lefkowitz,et al.  Internal model-based control for integrating processes. , 2010, ISA transactions.

[12]  Hannu T. Toivonen,et al.  Internal model control of nonlinear systems described by velocity-based linearizations , 2003 .

[13]  Yu Zhang,et al.  PID tuning with exact gain and phase margins , 1999 .

[14]  Wen Tan,et al.  IMC design for unstable processes with time delays , 2003 .

[15]  Tao Liu,et al.  Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics. , 2011, ISA transactions.

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

[17]  Cheng-Ching Yu,et al.  Coordinated control of blending systems , 1998, IEEE Trans. Control. Syst. Technol..

[18]  Weng Khuen Ho,et al.  A comparison of two design methods for PID controllers , 1994 .

[19]  Weng Khuen Ho,et al.  Optimal Gain and Phase Margin Tuning for PID Controllers , 1998, Autom..

[20]  Babu Joseph,et al.  Techniques of Model-Based Control , 2002 .

[21]  Mark L. Nagurka,et al.  Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants , 2004, Autom..

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

[23]  Cheng-Ching Yu,et al.  PID tuning rules for SOPDT systems: review and some new results. , 2004, ISA transactions.

[24]  Carlos E. Garcia,et al.  Internal model control. A unifying review and some new results , 1982 .

[25]  Rui Wang,et al.  Three-degree-of-freedom internal model control for unstable process , 2007, SICE Annual Conference 2007.