Discrete-time filter proportional-integral-derivative controller design for linear time-invariant systems

This paper introduces a new discrete-time filter proportional–integral–derivative (FPID) controller framework for linear time-invariant (LTI) systems. The discrete-time FPID controller plays an important role in both determining the dynamic response of the system and further improving the performance of the controller in itself. However, the introduction of the filter parameter brings more challenge for the design of discrete-time FPID controllers than that of discrete-time PID controllers. A novel result on the co-design of such a controller via dominant eigenvalue assignment is first provided, which enables us to tune the controller directly in accordance with the desired system performance indexes. Then, a further result on the discrete-time FPID controller design to improve the dynamic response of the closed-loop system is derived by placing the non-dominant eigenvalues in some assigned region. Compared with the discrete-time PID controller, on the one hand, the discrete-time FPID controller plays a significant role in improving the output of the controller in addition to guaranteeing the desired dynamic performance of the closed-loop system. On the other hand, a discrete-time FPID controller makes it possible to expand the effective parameter region and give a set of parameters which makes the controller achieve the objective of dominant eigenvalue assignment for the closed-loop system when a traditional discrete-time PID controller cannot do. Numerical examples have illustrated the effectiveness of the proposed results.

[1]  Katsuhiko Ogata,et al.  Discrete-time control systems , 1987 .

[2]  Shankar P. Bhattacharyya,et al.  Generalizations of the Hermite–Biehler theorem , 1999 .

[3]  Shankar P. Bhattacharyya,et al.  A new approach to digital PID controller design , 2003, IEEE Trans. Autom. Control..

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

[5]  W. Michiels,et al.  Control design for time-delay systems based on quasi-direct pole placement , 2010 .

[6]  Yu Zhang,et al.  New result on PID controller design of LTI systems via dominant eigenvalue assignment , 2015, Autom..

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

[8]  Pavel Zítek,et al.  Dominant four-pole placement in filtered PID control loop with delay , 2017 .

[9]  Sigurd Skogestad,et al.  Optimal PI and PID control of first-order plus delay processes and evaluation of the original and improved SIMC rules , 2018, Journal of Process Control.

[10]  Tore Hägglund,et al.  Measurement noise filtering for PID controllers , 2014 .

[11]  Nam Nguyen,et al.  Overshoot and settling time assignment with PID for first‐order and second‐order systems , 2018, IET Control Theory & Applications.

[12]  Honghai Wang,et al.  New Results on PID Controller Design of Discrete-time Systems via Pole Placement , 2017 .

[13]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[14]  S. Bhattacharyya,et al.  Root counting, phase unwrapping, stability and stabilization of discrete time systems , 2002 .

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

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

[17]  Marko Č. Bošković,et al.  Dominant pole placement with fractional order PID controllers: D-decomposition approach. , 2017, ISA transactions.

[18]  Tore Hägglund,et al.  Measurement noise filtering for common PID tuning rules , 2014 .

[19]  Pavol Bistak,et al.  Filtered PI and PID control of an Arduino based thermal plant , 2016 .

[20]  Jianchang Liu,et al.  New Results on Eigenvalue Distribution and Controller Design for Time Delay Systems , 2017, IEEE Transactions on Automatic Control.

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

[22]  Shyh Hong Hwang,et al.  CLOSED-LOOP TUNING METHOD BASED ON DOMINANT POLE PLACEMENT , 1995 .

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