IMC-PID Fractional Order Filter Multi-loop Controller Design for Multivariable Systems Based on Two Degrees of Freedom Control Scheme

An IMC-PID fractional order filter multi-loop controller design method based on two degrees of freedom paradigm is proposed for Multiple Input-Multiple Output systems with time delays. The interactions among the control loops are considered as disturbances. Thus, a two degrees of freedom control scheme, used for monovariable system to ensure the disturbance rejection, is extended to multivariable systems in order to reduce the effect of the coupling among the control loops. The proposed controller design method requires the control pairing selection with the least interactions and a set-point controller is calculated. An interactions reduction effect controller is calculated for each loop by defining a suitable complementary sensitivity function. The proposed controller design method is simple and systematic in relation with the desired closed loop specifications of each loop. The controllers obtained ensure robustness to process variations. Two illustrative examples are presented to show the merits of the proposed method.

[1]  Babatunde A. Ogunnaike,et al.  Advanced multivariable control of a pilot‐plant distillation column , 1983 .

[2]  Antoni Niederlinski.  Two‐variable distillation control: Decouple or not decouple , 1971 .

[3]  Manfred Morari,et al.  Internal Model Control: multiloop design , 1986 .

[4]  Fernando Morilla,et al.  Inverted decoupling internal model control for square stable multivariable time delay systems , 2014 .

[5]  William L. Luyben,et al.  Simple method for tuning SISO controllers in multivariable systems , 1986 .

[6]  Yurong Liu,et al.  Multivariable disturbance observer-based H2 analytical decoupling control design for multivariable systems , 2016, Int. J. Syst. Sci..

[7]  Chih-Hung Chiang,et al.  A direct method for multi-loop PI/PID controller design , 2003 .

[8]  J. A. Tenreiro Machado,et al.  Tuning of PID Controllers Based on Bode’s Ideal Transfer Function , 2004 .

[9]  S. Lakshmanaprabu,et al.  Adaptive multi-loop fractional order PID controller tuning using Bat colony optimization for Quadruple Tank process , 2015, 2015 International Conference on Robotics, Automation, Control and Embedded Systems (RACE).

[10]  Leandro dos Santos Coelho,et al.  Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning , 2012, Comput. Math. Appl..

[11]  Byung Chul Ji,et al.  Computation of multiloop controllers having desired closed-loop responses , 2007 .

[12]  Peng Shi,et al.  A survey on Markovian jump systems: Modeling and design , 2015 .

[13]  Jun Liang,et al.  Multi-loop adaptive internal model control based on a dynamic partial least squares model , 2011 .

[14]  Fei Liu,et al.  Centralized PI control for high dimensional multivariable systems based on equivalent transfer function. , 2014, ISA transactions.

[15]  Moonyong Lee,et al.  Independent design of multi-loop PI/PID controllers for interacting multivariable processes , 2010 .

[16]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

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

[18]  Jianbin Qiu,et al.  A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[19]  Rachid Mansouri,et al.  Fractional IMC-PID-filter controllers design for non integer order systems , 2014 .

[20]  E. Bristol.  On a new measure of interaction for multivariable process control , 1966 .

[21]  Robin De Keyser,et al.  Autotuning method for a fractional order controller for a multivariable 13C isotope separation column , 2016, 2016 European Control Conference (ECC).

[22]  K. S. R. Anjaneyulu,et al.  Control Configuration Selection and Controller Design for Multivariable Processes Using Normalized Gain , 2015 .

[23]  Jianbin Qiu,et al.  Mode-dependent nonrational output feedback control for continuous-time semi-Markovian jump systems with time-varying delay , 2015 .

[24]  Yann Chamaillard,et al.  Development of a fractional order based MIMO controller for high dynamic engine testbeds , 2016 .

[25]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[26]  Abhishek Dutta,et al.  Tuning algorithms for fractional order internal model controllers for time delay processes , 2016, Int. J. Control.

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

[28]  Thomas Hélie,et al.  Simulation of Fractional-Order Low-Pass Filters , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[29]  Fei Liu,et al.  Equivalent transfer function based multi-loop PI control for high dimensional multivariable systems , 2015 .

[30]  Alain Oustaloup,et al.  Robust control design for multivariable plants with time-delays , 2009 .

[31]  Clara M. Ionescu,et al.  Robustness Evaluation of a multivariable fractional order PI controller for Time delay Processes , 2014, Control. Intell. Syst..

[32]  Moonyong Lee,et al.  Design of Multi-loop PID Controllers Based on the Generalized IMC-PID Method with Mp Criterion , 2007 .

[33]  Rachid Mansouri,et al.  Internal Model Control–Proportional Integral Derivative–Fractional-Order Filter Controllers Design for Unstable Delay Systems , 2016 .

[34]  Bing-Gang Cao,et al.  Design of Fractional Order Controller Based on Particle Swarm Optimization , 2006 .

[35]  Y. Chen,et al.  Ideal, Simplified and Inverted Decoupling of Fractional Order TITO Processes , 2014 .

[36]  W. Zhang,et al.  Analytical Design of Decoupling Internal Model Control (IMC) Scheme for Two-Input-Two-Output (TITO) Processes with Time Delays , 2006 .

[37]  B M Patre,et al.  Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes. , 2012, ISA transactions.

[38]  Mansouri Rachid,et al.  IMC-PID-fractional-order-filter controllers design for integer order systems. , 2014, ISA transactions.

[39]  Jianbin Qiu,et al.  Approaches to T–S Fuzzy-Affine-Model-Based Reliable Output Feedback Control for Nonlinear Itô Stochastic Systems , 2017, IEEE Transactions on Fuzzy Systems.

[40]  I. Petras,et al.  The fractional - order controllers: Methods for their synthesis and application , 2000, math/0004064.

[41]  Jianbin Qiu,et al.  Robust and non-fragile static output feedback control for continuous-time semi-Markovian jump systems , 2016 .

[42]  Hamid Reza Karimi,et al.  New results on H∞ dynamic output feedback control for Markovian jump systems with time‐varying delay and defective mode information , 2014 .