IMC based Fractional Order Controller Design for Specific Non-Minimum Phase Systems

Abstract Internal model control (IMC) structure is derived from classical control by introducing the model of plant in the control loop and thereby having significant advantages over classical control such as dual stability, perfect control and zero-steady state offset. The basic one degree of freedom (ODF) IMC provides good compromise between set-point tracking and disturbance rejection and works well for non-minimum phase (NMP) systems. In this work, an IMC based fractional order (FO) controller is designed for NMP system which satisfy desired phase margin (ϕm) at a desired gain-crossover frequency (ωg). The domain of desired ϕm and ωg is provided from which they can be selected. Simulation studies are done for (i) DC-DC boost converter which is a NMP system with one zero in right half of s-plane and (ii) first order plus time delay (FOPTD) system which is also a NMP system because of the delay. Significance of the proposed methodology is verified by comparing with other well-known techniques in IMC based on the performance measures, such as rise time (Tr), settling time (Ts) and overshoot (%Mp) and performance indices such as integral square error (ISE), integral absolute error (IAE) and integral of the time weighted absolute error (ITAE).

[1]  Weng Khuen Ho,et al.  Tuning of PID Controllers based on Gain and Phase Margin Specifications , 1993 .

[2]  Ibrahim Kaya,et al.  Tuning PI controllers for stable processes with specifications on gain and phase margins. , 2004, ISA transactions.

[3]  Vivek Agarwal,et al.  Experimental Evaluation of Internal Model Control Scheme on a DC–DC Boost Converter Exhibiting Nonminimum Phase Behavior , 2017, IEEE Transactions on Power Electronics.

[4]  Wen Tan,et al.  Unified Tuning of PID Load Frequency Controller for Power Systems via IMC , 2010, IEEE Transactions on Power Systems.

[5]  Caifen Fu,et al.  Linear Active Disturbance-Rejection Control: Analysis and Tuning via IMC , 2016, IEEE Transactions on Industrial Electronics.

[6]  Wai-Chuen Gan.  Robust and optimal control of AC machines , 2001 .

[7]  Carlos E. Garcia,et al.  Internal model control. 2. Design procedure for multivariable systems , 1985 .

[8]  Alex Zheng,et al.  Anti-windup design for internal model control , 1994 .

[9]  Daniel E. Rivera,et al.  Internal Model Control , 2010, Encyclopedia of Machine Learning.

[10]  Dazi Li,et al.  Applications of an IMC based PID Controller tuning strategy in atmospheric and vacuum distillation units , 2009 .

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

[12]  Danying Gu,et al.  Algebraic Solution to H~2 Control Problems. I. The Scalar Case , 2006 .

[13]  Gade Pandu Rangaiah,et al.  Adaptive internal model control of nonlinear processes , 1999 .

[14]  Richard D. Braatz,et al.  Improved Filter Design in Internal Model Control , 1996 .

[15]  Weng Khuen Ho,et al.  Self-tuning IMC-PID control with interval gain and phase margins assignment , 2001, IEEE Trans. Control. Syst. Technol..

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

[17]  Yanqing Zhang,et al.  Research on Two-Degree-of-Freedom Internal Model Control Strategy for Induction Motor Based on Immune Algorithm , 2016, IEEE Transactions on Industrial Electronics.

[18]  Brian D. O. Anderson,et al.  I design to generalize internal model control , 2006, Autom..

[19]  Ujjwal Manikya Nath,et al.  Design and implementation of decentralized IMC-PI controllers for real time coupled tank process , 2015 .

[20]  Tao Liu,et al.  New insight into internal model control filter design for load disturbance rejection , 2010 .

[21]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

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

[23]  Aniruddha Datta,et al.  Adaptive internal model control: Design and stability analysis , 1996, Autom..

[24]  Zebin Yang,et al.  Internal Model Control for a Bearingless Permanent Magnet Synchronous Motor Based on Inverse System Method , 2016, IEEE Transactions on Energy Conversion.

[25]  T. Harris,et al.  "Internal model control. 4. PID controller design." Comments , 1987 .