Robust Fractional-Order PI Controller with Ziegler-Nichols Rules
In process control applications, above 90% of the
controllers are of PID type. This paper proposed a robust PI
controller with fractional-order integrator. The PI parameters were
obtained using classical Ziegler-Nichols rules but enhanced with the
application of error filter cascaded to the fractional-order PI. The
controller was applied on steam temperature process that was
described by FOPDT transfer function. The process can be classified
as lag dominating process with very small relative dead-time. The
proposed control scheme was compared with other PI controller
tuned using Ziegler-Nichols and AMIGO rules. Other PI controller
with fractional-order integrator known as F-MIGO was also
considered. All the controllers were subjected to set point change and
load disturbance tests. The performance was measured using Integral
of Squared Error (ISE) and Integral of Control Signal (ICO). The
proposed controller produced best performance for all the tests with
the least ISE index.
<p>[1] K. J. Åström and T. Hägglund, “The future of PID control,” Control
Engineering Practice, vol. 9, no. 11, pp. 1163–1175, Nov. 2001.
[2] K. J. Astrom, “Toward Intelligent Control,” in American Control
Conference, 1988.
[3] K. Astrom and T. Hagglund, “Revisiting the Ziegler-Nichols step
response method for PID control,” Journal of Process Control, vol. 14,
no. 6, pp. 635–650, Sep. 2004.
[4] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation,
Systems, and Automation Society (ISA), 2006, p. 158.
[5] K. J. Åström and T. Hägglund, “Revisiting the Ziegler–Nichols step
response method for PID control,” Journal of Process Control, vol. 14,
no. 6, pp. 635–650, Sep. 2004.
[6] A. O. Dwyer, “A summary of PI and PID controller tuning rules for
processes with time delay . Part 1: PI controller tuning rules,” pp. 175–
180, 2000.
[7] I. Podlubny, “Fractional-order Systems and PIλDD,” IEEE Transaction
on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
[8] A. Ruszewski and A. Sobolewski, “Comparative studies of control
systems with fractional controllers,” Electrical Review, vol. 88, no. 4b,
pp. 204–208, 2012.
[9] Y. Q. Chen and K. L. Moore, “Discretization schemes for fractionalorder
differentiators and integrators,” IEEE Transactions on Circuits
and Systems- I: Fundamental Theory and Applications, vol. 49, no. 3,
pp. 363–367, Mar. 2002.
[10] C. Ma and Y. Hori, “Fractional Order Control: Theory and Applications
in Motion Control,” Industrial Electronics Magazine, IEEE, no. 1, pp.
6–16, 2007.
[11] S. Manabe, “The non-integer Integral and its Application to Control
Systems,” vol. 6, no. 3, pp. 84–87, 1961.
[12] M. Axtell and M. E. Bise, “Fractional Calculus Applications in Control
Systems,” in IEEE 1990 Nat. Aerospace and Electronics Conference,
1990, pp. 563–566.
[13] A. Oustaloup, X. Moreau, and M. Nouillant, “The crone suspension,”
Control Engineering Practice, vol. 4, no. 8, pp. 1101–1108, 1996.
[14] A. Oustaloup, J. Sabatier, and P. Lanusse, “From fractal robustness to
the CRONE,” 2000.
[15] Y. Chen, H. Dou, B. M. Vinagre, and C. A. Monje, “A Robust Tuning
Method For Fractional Order PI Controllers,” in Proceedings of the 2nd
IFAC Workshop on Fractional Differentiation and its Applications,
2006.
[16] J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of
fractional calculus,” Communications in Nonlinear Science and
Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, Mar. 2011.
[17] B. M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, “Some
Approximations of Fractional Order Operators Used in Control Theory
and Applications,” Fractional calculus and applied analysis, vol. 3, no.
3, pp. 231–248, 2000.
[18] C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and autotuning
of fractional order controllers for industry applications,” Control
Engineering Practice, vol. 16, no. 7, pp. 798–812, Jul. 2008.
[19] C. A. Monje, B. M. Vinagre, Y. Q. Chen, V. Feliu, P. Lanusse, and J.
Sabatier, “Proposals for Fractional PID Tuning,” 2005, vol. 024, pp. 2–
7.
[20] A. Narang, S. L. Shah, and T. Chen, “Tuning of fractional PI controllers
for fractional order system models with and without time delays,” in
American Control Conference, 2010, pp. 6674–6679.
[21] V. Feliu-Batlle, R. R. Pérez, and L. S. Rodríguez, “Fractional robust
control of main irrigation canals with variable dynamic parameters,”
Control Engineering Practice, vol. 15, no. 6, pp. 673–686, Jun. 2007.
[22] C. Wang and Y. Chen, “Fractional order proportional integral (FOPI)
and [proportional integral] (FO[PI]) controller designs for first order
plus time delay (FOPTD) systems,” 2009 Chinese Control and Decision
Conference, vol. 2, no. 3, pp. 329–334, Jun. 2009.
[23] R. Barbosa, J. A. T. Machado, and I. S. Jesus, “On the Fractional PID
Control of a Laboratory Servo System,” in Proceedings of the 17th
World Congress The International Federation of Automatic Control
(IFAC), 2008, pp. 15273–15279.
[24] J. J. Gude and E. Kahoraho, “Modified Ziegler-Nichols method for
fractional PI controllers,” in Conference on Emerging Technologies &
Factory Automation, 2010, no. 2, pp. 1–5.
[25] Y. Chen, T. Bhaskaran, and D. Xue, “Practical Tuning Rule
Development for Fractional Order Proportional and Integral
Controllers,” Journal of Computational and Nonlinear Dynamics, vol.
3, no. 2, p. 021403, 2008.
[26] F. Merrikh-Bayat, “Rules for selecting the parameters of Oustaloup
recursive approximation for the simulation of linear feedback systems
containing PIλDμ controller,” Communications in Nonlinear Science
and Numerical Simulation, vol. 17, no. 4, pp. 1852–1861, Apr. 2012.
[27] D. Valério and J. S. da Costa, “Tuning of fractional PID controllers with
Ziegler–Nichols-type rules,” Signal Processing, vol. 86, no. 10, pp.
2771–2784, Oct. 2006.
[28] I. Podlubny, L. Dorcak, and I. Kostial, “On Fractional Derivatives,
Fractional-Orlder Dynamic Systems and PIλ Dμ Controllers,” in
Proceedings of the 36th Conference on Decision & Control, 1997, no.
December, pp. 4985–4990.
[29] F. Merrikh-Bayat, “Efficient method for time-domain simulation of the
linear feedback systems containing fractional order controllers.” ISA
transactions, vol. 50, no. 2, pp. 170–6, Apr. 2011.
[30] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation,
Systems, and Automation Society (ISA), 2006, p. 158.
[31] T. Hagglund and K. J. Astrom, “Revisiting the Ziegler-Nichols Tuning
Rules for PI Control,” Asian Journal of Control, vol. 4, no. 4, pp. 364–
380, 2002.</p>
<p>[1] K. J. Åström and T. Hägglund, “The future of PID control,” Control
Engineering Practice, vol. 9, no. 11, pp. 1163–1175, Nov. 2001.
[2] K. J. Astrom, “Toward Intelligent Control,” in American Control
Conference, 1988.
[3] K. Astrom and T. Hagglund, “Revisiting the Ziegler-Nichols step
response method for PID control,” Journal of Process Control, vol. 14,
no. 6, pp. 635–650, Sep. 2004.
[4] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation,
Systems, and Automation Society (ISA), 2006, p. 158.
[5] K. J. Åström and T. Hägglund, “Revisiting the Ziegler–Nichols step
response method for PID control,” Journal of Process Control, vol. 14,
no. 6, pp. 635–650, Sep. 2004.
[6] A. O. Dwyer, “A summary of PI and PID controller tuning rules for
processes with time delay . Part 1: PI controller tuning rules,” pp. 175–
180, 2000.
[7] I. Podlubny, “Fractional-order Systems and PIλDD,” IEEE Transaction
on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
[8] A. Ruszewski and A. Sobolewski, “Comparative studies of control
systems with fractional controllers,” Electrical Review, vol. 88, no. 4b,
pp. 204–208, 2012.
[9] Y. Q. Chen and K. L. Moore, “Discretization schemes for fractionalorder
differentiators and integrators,” IEEE Transactions on Circuits
and Systems- I: Fundamental Theory and Applications, vol. 49, no. 3,
pp. 363–367, Mar. 2002.
[10] C. Ma and Y. Hori, “Fractional Order Control: Theory and Applications
in Motion Control,” Industrial Electronics Magazine, IEEE, no. 1, pp.
6–16, 2007.
[11] S. Manabe, “The non-integer Integral and its Application to Control
Systems,” vol. 6, no. 3, pp. 84–87, 1961.
[12] M. Axtell and M. E. Bise, “Fractional Calculus Applications in Control
Systems,” in IEEE 1990 Nat. Aerospace and Electronics Conference,
1990, pp. 563–566.
[13] A. Oustaloup, X. Moreau, and M. Nouillant, “The crone suspension,”
Control Engineering Practice, vol. 4, no. 8, pp. 1101–1108, 1996.
[14] A. Oustaloup, J. Sabatier, and P. Lanusse, “From fractal robustness to
the CRONE,” 2000.
[15] Y. Chen, H. Dou, B. M. Vinagre, and C. A. Monje, “A Robust Tuning
Method For Fractional Order PI Controllers,” in Proceedings of the 2nd
IFAC Workshop on Fractional Differentiation and its Applications,
2006.
[16] J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of
fractional calculus,” Communications in Nonlinear Science and
Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, Mar. 2011.
[17] B. M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, “Some
Approximations of Fractional Order Operators Used in Control Theory
and Applications,” Fractional calculus and applied analysis, vol. 3, no.
3, pp. 231–248, 2000.
[18] C. A. Monje, B. M. Vinagre, V. Feliu, and Y. Chen, “Tuning and autotuning
of fractional order controllers for industry applications,” Control
Engineering Practice, vol. 16, no. 7, pp. 798–812, Jul. 2008.
[19] C. A. Monje, B. M. Vinagre, Y. Q. Chen, V. Feliu, P. Lanusse, and J.
Sabatier, “Proposals for Fractional PID Tuning,” 2005, vol. 024, pp. 2–
7.
[20] A. Narang, S. L. Shah, and T. Chen, “Tuning of fractional PI controllers
for fractional order system models with and without time delays,” in
American Control Conference, 2010, pp. 6674–6679.
[21] V. Feliu-Batlle, R. R. Pérez, and L. S. Rodríguez, “Fractional robust
control of main irrigation canals with variable dynamic parameters,”
Control Engineering Practice, vol. 15, no. 6, pp. 673–686, Jun. 2007.
[22] C. Wang and Y. Chen, “Fractional order proportional integral (FOPI)
and [proportional integral] (FO[PI]) controller designs for first order
plus time delay (FOPTD) systems,” 2009 Chinese Control and Decision
Conference, vol. 2, no. 3, pp. 329–334, Jun. 2009.
[23] R. Barbosa, J. A. T. Machado, and I. S. Jesus, “On the Fractional PID
Control of a Laboratory Servo System,” in Proceedings of the 17th
World Congress The International Federation of Automatic Control
(IFAC), 2008, pp. 15273–15279.
[24] J. J. Gude and E. Kahoraho, “Modified Ziegler-Nichols method for
fractional PI controllers,” in Conference on Emerging Technologies &
Factory Automation, 2010, no. 2, pp. 1–5.
[25] Y. Chen, T. Bhaskaran, and D. Xue, “Practical Tuning Rule
Development for Fractional Order Proportional and Integral
Controllers,” Journal of Computational and Nonlinear Dynamics, vol.
3, no. 2, p. 021403, 2008.
[26] F. Merrikh-Bayat, “Rules for selecting the parameters of Oustaloup
recursive approximation for the simulation of linear feedback systems
containing PIλDμ controller,” Communications in Nonlinear Science
and Numerical Simulation, vol. 17, no. 4, pp. 1852–1861, Apr. 2012.
[27] D. Valério and J. S. da Costa, “Tuning of fractional PID controllers with
Ziegler–Nichols-type rules,” Signal Processing, vol. 86, no. 10, pp.
2771–2784, Oct. 2006.
[28] I. Podlubny, L. Dorcak, and I. Kostial, “On Fractional Derivatives,
Fractional-Orlder Dynamic Systems and PIλ Dμ Controllers,” in
Proceedings of the 36th Conference on Decision & Control, 1997, no.
December, pp. 4985–4990.
[29] F. Merrikh-Bayat, “Efficient method for time-domain simulation of the
linear feedback systems containing fractional order controllers.” ISA
transactions, vol. 50, no. 2, pp. 170–6, Apr. 2011.
[30] K. J. Astrom and T. Hagglund, Advanced PID Control. Instrumentation,
Systems, and Automation Society (ISA), 2006, p. 158.
[31] T. Hagglund and K. J. Astrom, “Revisiting the Ziegler-Nichols Tuning
Rules for PI Control,” Asian Journal of Control, vol. 4, no. 4, pp. 364–
380, 2002.</p>
@article{"International Journal of Information, Control and Computer Sciences:58840", author = "Mazidah Tajjudin and Mohd Hezri Fazalul Rahiman and Norhashim Mohd Arshad and Ramli Adnan", title = "Robust Fractional-Order PI Controller with Ziegler-Nichols Rules", abstract = "In process control applications, above 90% of the
controllers are of PID type. This paper proposed a robust PI
controller with fractional-order integrator. The PI parameters were
obtained using classical Ziegler-Nichols rules but enhanced with the
application of error filter cascaded to the fractional-order PI. The
controller was applied on steam temperature process that was
described by FOPDT transfer function. The process can be classified
as lag dominating process with very small relative dead-time. The
proposed control scheme was compared with other PI controller
tuned using Ziegler-Nichols and AMIGO rules. Other PI controller
with fractional-order integrator known as F-MIGO was also
considered. All the controllers were subjected to set point change and
load disturbance tests. The performance was measured using Integral
of Squared Error (ISE) and Integral of Control Signal (ICO). The
proposed controller produced best performance for all the tests with
the least ISE index.
", keywords = "PID controller, fractional-order PID controller, PI
control tuning, steam temperature control, Ziegler-Nichols tuning.", volume = "7", number = "7", pages = "1006-8", }
