A universal map of three-dominant-pole assignment for PID controller tuning

ABSTRACT A novel dimensionless parameterisation of the three-pole assignment for control plants with delay is presented. A second-order model with input delay is chosen as an approximation of the plant properties. The prescribed trio of poles is considered in form of one pair of complex conjugates and a real pole and it is shown that this option is not a matter of choice but necessary constraint for control design with delay in the loop. The prescribed poles are determined by the damping and root ratios with a natural frequency derived from the ultimate frequency of the plant. The three-pole assignments are determined by two similarity numbers considered as coordinates of the map. The limitation of admissible damping ratio due to the dominance condition is one of the original results presented in the paper. Furthermore, the influence of the root ratio is evaluated and final design recommendations are presented.

[1]  Saurabh Srivastava,et al.  An optimal PID controller via LQR for standard second order plus time delay systems. , 2016, ISA transactions.

[2]  Karl Johan Åström,et al.  DOMINANT POLE DESIGN - A UNIFIED VIEW OF PID CONTROLLER TUNING , 1993 .

[3]  Hsueh-Chia Chang,et al.  A theoretical examination of closed-loop properties and tuning methods of single-loop PI controllers , 1987 .

[4]  Sabine Mondié,et al.  An Analytical Approach to Tuning of Delay-Based Controllers for LTI-SISO Systems , 2017, SIAM J. Control. Optim..

[5]  T. Vyhlídal,et al.  Magnitude Optimum Design of PID Control Loop with Delay , 2015 .

[6]  Tomás Vyhlídal,et al.  Dynamic similarity approach to control system design: delayed PID control loop , 2019, Int. J. Control.

[7]  Pavel Zítek,et al.  IAE optimization of delayed PID control loops using dimensional analysis approach , 2014, 2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP).

[8]  Karl Johan Åström,et al.  Self-Tuning Controllers Based on Pole-Zero Placement , 1980 .

[9]  Pavel Zítek,et al.  Dimensional analysis approach to dominant three-pole placement in delayed PID control loops , 2013 .

[10]  Tomás Vyhlídal,et al.  Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros , 2009, IEEE Transactions on Automatic Control.

[11]  Karl Johan Åström,et al.  Guaranteed dominant pole placement with PID controllers , 2009 .

[12]  Shankar P. Bhattacharyya,et al.  Controller Synthesis Free of Analytical Models: Three Term Controllers , 2008, IEEE Transactions on Automatic Control.

[13]  Saptarshi Das,et al.  Performance Analysis of Robust Stable PID Controllers Using Dominant Pole Placement for SOPTD Process Models , 2018, Knowl. Based Syst..

[14]  P. Balaguer.  Application of Dimensional Analysis in Systems Modeling and Control Design , 2013 .

[15]  Pavel Zítek,et al.  Dominant Trio of Poles Assignment in Delayed PID Control Loop , 2014 .

[16]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[17]  Saptarshi Das,et al.  A Conformal Mapping Based Fractional Order Approach for Sub-optimal Tuning of PID Controllers with Guaranteed Dominant Pole Placement , 2012, 1202.5662.