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RTD-A Control for General Multivariable Systems

  • Research Article - Chemical Engineering
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Abstract

For general multivariable systems including square ones and fat and thin non-square ones, a unified and analytical optimum control law has been derived for the RTD-A controller. A concise interpretation for the general existence of the control law is provided together with a suggestion for judging this existence in practical applications. Three simulation examples are included to demonstrate the flexibility, friendliness, and excellent robustness, anti-noise performance and dynamic control capability of the RTD-A controller.

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References

  1. Forbes, M.G.; Patwardhan, R.S.; Hamadah, H.; Gopaluni, R.B.: Model predictive control in industry: challenges and opportunities. IFAC-PapersOnLine 48(8), 531–538 (2015)

    Article  Google Scholar 

  2. Cutler, C.R.; Ramaker, B.L.: Dynamic Matrix Control—A Computer Control Algorithm. In: Proceedings of the Joint Automatic Control Conference, San Francisco (1980)

  3. Xi, Y.G.; Li, D.W.; Lin, S.: Model predictive control—status and challenges. Acta Autom. Sin. 39(3), 222–236 (2013)

    Article  MathSciNet  Google Scholar 

  4. Scattolini, R.: Architectures for distributed and hierarchical model predictive control—a review. J. Process Control 19(5), 723–731 (2009)

    Article  Google Scholar 

  5. Rivera, D.E.; Morari, M.; Skogestad, S.: Internal model control: PID controller design. Ind. Eng. Chem. Process Des. Dev. 25(1), 2163–2163 (1986)

    Article  Google Scholar 

  6. Anwar, M.N.; Shamsuzzoha, M.; Pan, S.: A frequency domain PID controller design method using direct synthesis approach. Arab. J. Sci. Eng. 40(4), 995–1004 (2015)

    Article  Google Scholar 

  7. Ogunnaike, B.A.; Mukati, K.: An alternative structure for next generation regulatory controllers: part I: basic theory for design, development and implementation. J. Process Control l6(5), 499–509 (2006)

    Article  Google Scholar 

  8. Mukati, K.; Rasch, M.; Ogunnaike, B.A.: An alternative structure for next generation regulatory controllers. Part II: stability analysis, tuning rules and experimental validation. J. Process Control 19(2), 272–287 (2009)

    Article  Google Scholar 

  9. Anbarasan, K.; Srinivasan, K.: Design of RTDA controller for industrial process using SOPDT model with minimum or non-minimum zero. ISA Trans. 57, 231–244 (2015)

    Article  Google Scholar 

  10. Guan, S.T.; Chu, J.Z.: Research and application of RTD-A controller for multiple input multiple output (MIMO) system. Inf. Control 37(4), 429–434 (2008)

    Google Scholar 

  11. Chu, J.Z.; Du, B.; Chen, J.: Performance analysis and online fuzzy self-tuning of RTD-A controller’s parameters. J. Shanghai Jiaotong Univ. 45(8), 1167–1171 (2011)

    Google Scholar 

  12. Sendjaja, A.Y.; Zhen, F.N.; Si, S.H.; Kariwala, V.: Analysis and tuning of RTD-A controllers. Ind. Eng. Chem. Res. 50(6), 3415–3425 (2011)

    Article  Google Scholar 

  13. Luan, X.L.; Wang, Z.Q.; Liu, F.: Centralized PI control for multivariable non-square systems. Control Decis. 31(5), 811–816 (2016)

    MATH  Google Scholar 

  14. Davison, E.J.: Some properties of minimum phase systems and "squared-down" systems. IEEE Trans. Autom. Control 28(2), 221–222 (1984)

    Article  MathSciNet  Google Scholar 

  15. Treiber, S.: Multivariable control of non-square systems. Ind. Eng. Chem. Process Des. Dev. 23(4), 854–857 (1984)

    Article  Google Scholar 

  16. He, M.J.; Cai, W.J.; Wei, N.; Xie, L.H.: RNGA based control system configuration for multivariable processes. J. Process Control 19(6), 1036–1042 (2009)

    Article  Google Scholar 

  17. Zou, T.; Li, H.Q.; Ding, B.C.; Wang, D.D.: Compatibility and uniqueness analyses of steady state solution for multi-variable predictive control systems. Acta Autom. Sin. 39(5), 519–529 (2013)

    Article  MathSciNet  Google Scholar 

  18. Jin, Q.B.; Hao, F.; Wang, Q.: A multivariable IMC-PID method for non-square large time delay systems using NPSO algorithm. J. Process Control 23(5), 649–663 (2013)

    Article  Google Scholar 

  19. Jin, Q.B.; Liu, Q.: Decoupling proportional-integral-derivative controller design for multivariable processes with time delays. Ind. Eng. Chem. Res. 53(2), 765–777 (2014)

    Article  Google Scholar 

  20. Jin, Q.B.; Du, X.H.; Wang, Q.; Liu, L.Y.: Analytical design 2 DOF IMC control based on inverted decoupling for non square systems with time delay. Can. J. Chem. Eng. 94(7), 1354–1367 (2016)

    Article  Google Scholar 

  21. Yang, S.H.; Wang, X.Z.; Mcgreavy, C.: A multivariable coordinated control system based on predictive control strategy for FCC reactor-regenerator system. Chem. Eng. Sci. 51(11), 2977–2982 (1996)

    Article  Google Scholar 

  22. Zou, T.; Wang, D.; Pan, H.; Yuan, M.; Ji, Z.: From zone model predictive control to double-layered model predictive control. Ciesc J. 64(12), 4474–4483 (2013)

    Google Scholar 

  23. Prett, D.M.; García, C.E.; Ramaker, B.L.: The second shell process control workshop. In: The Shell Process Control Workshop, Butterworths, pp. 325–347 (1987)

  24. Vlachos, C.; Williams, D.; Gomm, J.B.: Solution to the shell standard control problem using genetically tuned PID controllers. Control Eng. Pract. 10(2), 151–163 (2002)

    Article  Google Scholar 

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Acknowledgements

This research work was funded by National Natural Science Foundation of China (Project Number: 21676012) and Fundamental Research Funds for the Central Universities (Project Number: YS1404)

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, China

    Yu Sun, Jizheng Chu & Minghui Chu

Authors
  1. Yu Sun
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  2. Jizheng Chu
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  3. Minghui Chu
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Corresponding author

Correspondence to Jizheng Chu.

Appendix 1: Discretization Method

Appendix 1: Discretization Method

The continuous system model is treated with the equivalent discrete model using the Z-domain discretization method. The zero-order holder is used to obtain the difference equation.

$$\begin{aligned} g_{ij} (s)= & {} \frac{K_{ij} e^{-\alpha _{ij} s}}{\tau _{ij} s+1}\\ g_{ij} (Z)= & {} \mathbf{Z}\left[ {g_h (s)g_{ij} (s)} \right] =\mathbf{Z}\left[ {\frac{1-e^{-Ts}}{s}\cdot \frac{K_{ij} e^{-\alpha _{ij} s}}{\tau _{ij} s+1}} \right] \\&\quad {\mathop {\rightarrow }^{z=e^{Ts}}z^{-\alpha _{ij} /T}(1-z^{-1})\mathbf{Z}\left[ {\frac{1}{s}\cdot \frac{K_{ij} }{\tau _{ij} s+1}} \right] } \\= & {} {z}^{-\alpha _{ij} /T}(1-z^{-1})\mathbf{Z}\left[ {\frac{K_{ij} }{s}-\frac{K_{ij} \tau _{ij} }{\tau _{ij} s+1}} \right] \\= & {} K_{ij} \cdot z^{-\alpha _{ij} /T}(1-z^{-1})\left( {\frac{z}{z-1}-\frac{z}{z-e^{-T/\tau _{ij} }}} \right) \\= & {} K_{ij} \cdot z^{-\alpha _{ij} /T}\cdot \frac{1-e^{-T/\tau _{ij} }}{z-e^{-T/\tau _{ij} }}=\frac{\hat{{y}}_{ij} (z)}{u_j (z)} \\ \end{aligned}$$

difference equation:

$$\begin{aligned} \left( {z-e^{-T/\tau _{ij} }} \right) \cdot \hat{{y}}_{ij} (z)=K_{ij} \cdot z^{-\alpha _{ij} /T}\cdot \left( {1-e^{-T/\tau _{ij} }} \right) \cdot u_j (z) \end{aligned}$$
$$\begin{aligned} \hat{{y}}_{ij} (k+1)=a_{ij} \hat{{y}}_{ij} (k)+b_{ij} u(k-m_{ij} ) \end{aligned}$$
(1)

where \(a_{ij }=e^{-T/\tau ij}, b_{ij}=K_{ij} (1-a_{ij}), m_{ij} = \mathrm{round}({\alpha }_{ij}/T), T\) is the sampling time and k = 0, 1, 2, ... for the current moment.

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Sun, Y., Chu, J. & Chu, M. RTD-A Control for General Multivariable Systems. Arab J Sci Eng 43, 5891–5903 (2018). https://doi.org/10.1007/s13369-017-3008-y

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