Research Article
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Year 2024, Volume: 5 Issue: 2, 16 - 22, 30.12.2024
https://doi.org/10.46572/naturengs.1563008

Abstract

References

  • Anil, C. and Sree, R. P. (2015). Tuning of PID controllers for integrating systems using direct synthesis method. ISA transactions, vol. 57, pp. 211-219.
  • Sarif, B. M., Kumar, D. A. and Rao, M. V. G. (2018). Comparison study of PID controller tuning using classical analytical methods. International Journal of Applied Engineering Research, vol. 13, no. 8; pp. 5618-5625.
  • Ziegler, J. G. and Nichols, N. B. (1942). Optimum settings for automatic controllers. Transactions of the American society of mechanical engineers, vol. 64, no. 8; pp. 759-765.
  • Cohen, G. and Coon, G. (1953). Theoretical consideration of retarded control. Transactions of the American Society of Mechanical Engineers, vol. 75, no. 5; pp. 827-834.
  • Luyben, M. L. and Luyben, W. L. (1997). Essentials of process control. (No Title),
  • Åström, K. J. and Hägglund, T. (1984). Automatic tuning of simple regulators. IFAC Proceedings volumes, vol. 17, no. 2; pp. 1867-1872.
  • Joseph, S. B., Dada, E. G., Abidemi, A., Oyewola, D. O. and Khammas, B. M. (2022). Metaheuristic algorithms for PID controller parameters tuning: Review, approaches and open problems. Heliyon, vol. 8, no. 5;
  • Das, K. R., Das, D. and Das, J. (2015). Optimal tuning of PID controller using GWO algorithm for speed control in DC motor. in 2015 International Conference on Soft Computing Techniques and Implementations (ICSCTI), pp. 108-112: IEEE.
  • Huynh, B.-P., Su, S.-F. and Kuo, Y.-L. (2020). Vision/position hybrid control for a hexa robot using bacterial foraging optimization in real-time pose adjustment. Symmetry, vol. 12, no. 4; p. 564.
  • Mosaad, A. M., Attia, M. A. and Abdelaziz, A. Y. (2019). Whale optimization algorithm to tune PID and PIDA controllers on AVR system. Ain Shams Engineering Journal, vol. 10, no. 4; pp. 755-767.
  • Mosaad, M. I., abed el-Raouf, M. O., Al-Ahmar, M. A. and Banakher, F. A. (2019). Maximum power point tracking of PV system based cuckoo search algorithm; review and comparison. Energy procedia, vol. 162, pp. 117-126.
  • Jung, C. S., Song, H. K. and Hyun, J. C. (1999). A direct synthesis tuning method of unstable first-order-plus-time-delay processes. Journal of process control, vol. 9, no. 3; pp. 265-269.
  • Rao, A. S., Rao, V. and Chidambaram, M. (2009). Direct synthesis-based controller design for integrating processes with time delay. Journal of the Franklin Institute, vol. 346, no. 1; pp. 38-56.
  • Kula, K. S. (2024). Tuning a PI/PID Controller with Direct Synthesis to Obtain a Non-Oscillatory Response of Time-Delayed Systems. Applied Sciences, vol. 14, no. 13; p. 5468.
  • Siddiqui, M. A., Anwar, M. and Laskar, S. (2021). Enhanced control of unstable cascade systems using direct synthesis approach. Chemical Engineering Science, vol. 232, p. 116322.
  • So, G. (2024). DS based 2-DOF PID controller for various integrating processes with time delay. ISA transactions, vol. 153, pp. 276-294.
  • Vilanova Arbós, R., Arrieta Orozco, O. and Ponsa, P. (2018). Robust PI/PID controllers for load disturbance based on direct synthesis. ISA transactions, vol. 81, pp. 177-196.
  • Chen, D. and Seborg, D. E. (2002). PI/PID controller design based on direct synthesis and disturbance rejection. Industrial & engineering chemistry research, vol. 41, no. 19; pp. 4807-4822.
  • Prajapati, A. and Prasad, R. (2022). A new model reduction method for the approximation of large-scale systems. IFAC-PapersOnLine, vol. 55, no. 3; pp. 7-12.
  • Werner, H. and Bandyopadhyay, B. (1997). Suboptimal control for higher order systems via reduced models using periodic output feedback. IFAC Proceedings Volumes, vol. 30, no. 4; pp. 281-285.
  • Davison, E. (1966). A method for simplifying linear dynamic systems. IEEE Transactions on automatic control, vol. 11, no. 1; pp. 93-101.
  • Bosley, M. and Lees, F. (1972). A survey of simple transfer-function derivations from high-order state-variable models. Automatica, vol. 8, no. 6; pp. 765-775.
  • Shamash, Y. (1974). Stable reduced-order models using Padé-type approximations. IEEE transactions on Automatic Control, vol. 19, no. 5; pp. 615-616.
  • Hutton, M. and Friedland, B. (1975). Routh approximations for reducing order of linear, time-invariant systems. IEEE Transactions on Automatic Control, vol. 20, no. 3; pp. 329-337.
  • Krishnamurthy, V. and Seshadri, V. (1978). Model reduction using the Routh stability criterion. IEEE Transactions on Automatic control, vol. 23, no. 4; pp. 729-731.
  • Chen, T., Chang, C. and Han, K. (1979). Reduction of transfer functions by the stability-equation method. Journal of the Franklin Institute, vol. 308, no. 4; pp. 389-404.
  • Mishra, R. and Wilson, D. (1980). A new algorithm for optimal reduction of multivariable systems. International Journal of Control, vol. 31, no. 3; pp. 443-466.
  • Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE transactions on automatic control, vol. 26, no. 1; pp. 17-32.
  • Gutman, P., Mannerfelt, C. and Molander, P. (1982). Contributions to the model reduction problem. IEEE Transactions on Automatic Control, vol. 27, no. 2; pp. 454-455.
  • Sinha, N. K. and Kuszta, B. (1983). Modeling and identification of dynamic systems. (No Title),
  • Glover, K. (1984). All optimal Hankel-norm approximations of linear multivariable systems and their L,∞-error bounds. International journal of control, vol. 39, no. 6; pp. 1115-1193.
  • Lucas, T. N. (1986). Linear system reduction by the modified factor division method. in IEE Proceedings D (Control Theory and Applications), vol. 133, no. 6, pp. 293-296: IET.
  • Sinha, A. and Pal, J. (1990). Simulation based reduced order modelling using a clustering technique. Computers & electrical engineering, vol. 16, no. 3; pp. 159-169.
  • Antoulas, A. (2004). Approximation of large-scale dynamical systems: An overview. IFAC Proceedings Volumes, vol. 37, no. 11; pp. 19-28.
  • Panda, S., Tomar, S., Prasad, R. and Ardil, C. (2009). Model reduction of linear systems by conventional and evolutionary techniques. International Journal of Electrical and Computer Engineering, vol. 3, no. 11; pp. 2144-2150.
  • Kumar, D. and Krishna Nagar, S. (2013). Reducing power system models by Hankel norm approximation technique. International Journal of Modelling and Simulation, vol. 33, no. 3; pp. 139-143.
  • Suman, S. K. and Kumar, A. (2020). Reduction of large-scale dynamical systems by extended balanced singular perturbation approximation. International Journal of Mathematical, Engineering and Management Sciences, vol. 5, no. 5; p. 939.
  • Prajapati, A. K. and Prasad, R. (2019). Reduced order modelling of linear time invariant systems using the factor division method to allow retention of dominant modes. IETE Technical Review, vol. 36, no. 5; pp. 449-462.
  • Suman, S. K. and Kumar, A. (2021). Linear system of order reduction using a modified balanced truncation method. Circuits, Systems, and Signal Processing, vol. 40, pp. 2741-2762.
  • Kumari, A. and Vishwakarma, C. (2021). Order abatement of linear dynamic systems using renovated pole clustering and Cauer second form techniques. Circuits, Systems, and Signal Processing, vol. 40, pp. 4212-4229.
  • Yüce, A. (2024). System Identification Based on Experimental Technique Using Stability Boundary Locus Method for Linear Fractional Order Systems. Arabian Journal for Science and Engineering, pp. 1-13.
  • Das, S., Saha, S., Das, S. and Gupta, A. (2011). On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA transactions, vol. 50, no. 3; pp. 376-388.

Direct Synthesis Method-based PID Controller Design for High Order Systems

Year 2024, Volume: 5 Issue: 2, 16 - 22, 30.12.2024
https://doi.org/10.46572/naturengs.1563008

Abstract

This study presents a PID controller design using the Direct Synthesis (DS) method for high-order systems. The DS method offers an analytical approach to parameter tuning. PID controllers are widely favored due to their simple structure and the easy with which their parameters can be tuned. Classical controller performances may not be sufficient to control unstable, integrator-containing, or high-order systems. To overcome this problem in controlling high-order systems, high-order systems can be reduced to low-order systems using model reduction techniques. PID controller designs can be realized using reduced models. In the study, two high-order systems are taken as an example, and PID controller designs are made using second-order models of these systems. In both examples, time and frequency response analyses are presented with figures, and performance evaluations are interpreted. In the control of high-order systems, very successful results are obtained with the presented method.

References

  • Anil, C. and Sree, R. P. (2015). Tuning of PID controllers for integrating systems using direct synthesis method. ISA transactions, vol. 57, pp. 211-219.
  • Sarif, B. M., Kumar, D. A. and Rao, M. V. G. (2018). Comparison study of PID controller tuning using classical analytical methods. International Journal of Applied Engineering Research, vol. 13, no. 8; pp. 5618-5625.
  • Ziegler, J. G. and Nichols, N. B. (1942). Optimum settings for automatic controllers. Transactions of the American society of mechanical engineers, vol. 64, no. 8; pp. 759-765.
  • Cohen, G. and Coon, G. (1953). Theoretical consideration of retarded control. Transactions of the American Society of Mechanical Engineers, vol. 75, no. 5; pp. 827-834.
  • Luyben, M. L. and Luyben, W. L. (1997). Essentials of process control. (No Title),
  • Åström, K. J. and Hägglund, T. (1984). Automatic tuning of simple regulators. IFAC Proceedings volumes, vol. 17, no. 2; pp. 1867-1872.
  • Joseph, S. B., Dada, E. G., Abidemi, A., Oyewola, D. O. and Khammas, B. M. (2022). Metaheuristic algorithms for PID controller parameters tuning: Review, approaches and open problems. Heliyon, vol. 8, no. 5;
  • Das, K. R., Das, D. and Das, J. (2015). Optimal tuning of PID controller using GWO algorithm for speed control in DC motor. in 2015 International Conference on Soft Computing Techniques and Implementations (ICSCTI), pp. 108-112: IEEE.
  • Huynh, B.-P., Su, S.-F. and Kuo, Y.-L. (2020). Vision/position hybrid control for a hexa robot using bacterial foraging optimization in real-time pose adjustment. Symmetry, vol. 12, no. 4; p. 564.
  • Mosaad, A. M., Attia, M. A. and Abdelaziz, A. Y. (2019). Whale optimization algorithm to tune PID and PIDA controllers on AVR system. Ain Shams Engineering Journal, vol. 10, no. 4; pp. 755-767.
  • Mosaad, M. I., abed el-Raouf, M. O., Al-Ahmar, M. A. and Banakher, F. A. (2019). Maximum power point tracking of PV system based cuckoo search algorithm; review and comparison. Energy procedia, vol. 162, pp. 117-126.
  • Jung, C. S., Song, H. K. and Hyun, J. C. (1999). A direct synthesis tuning method of unstable first-order-plus-time-delay processes. Journal of process control, vol. 9, no. 3; pp. 265-269.
  • Rao, A. S., Rao, V. and Chidambaram, M. (2009). Direct synthesis-based controller design for integrating processes with time delay. Journal of the Franklin Institute, vol. 346, no. 1; pp. 38-56.
  • Kula, K. S. (2024). Tuning a PI/PID Controller with Direct Synthesis to Obtain a Non-Oscillatory Response of Time-Delayed Systems. Applied Sciences, vol. 14, no. 13; p. 5468.
  • Siddiqui, M. A., Anwar, M. and Laskar, S. (2021). Enhanced control of unstable cascade systems using direct synthesis approach. Chemical Engineering Science, vol. 232, p. 116322.
  • So, G. (2024). DS based 2-DOF PID controller for various integrating processes with time delay. ISA transactions, vol. 153, pp. 276-294.
  • Vilanova Arbós, R., Arrieta Orozco, O. and Ponsa, P. (2018). Robust PI/PID controllers for load disturbance based on direct synthesis. ISA transactions, vol. 81, pp. 177-196.
  • Chen, D. and Seborg, D. E. (2002). PI/PID controller design based on direct synthesis and disturbance rejection. Industrial & engineering chemistry research, vol. 41, no. 19; pp. 4807-4822.
  • Prajapati, A. and Prasad, R. (2022). A new model reduction method for the approximation of large-scale systems. IFAC-PapersOnLine, vol. 55, no. 3; pp. 7-12.
  • Werner, H. and Bandyopadhyay, B. (1997). Suboptimal control for higher order systems via reduced models using periodic output feedback. IFAC Proceedings Volumes, vol. 30, no. 4; pp. 281-285.
  • Davison, E. (1966). A method for simplifying linear dynamic systems. IEEE Transactions on automatic control, vol. 11, no. 1; pp. 93-101.
  • Bosley, M. and Lees, F. (1972). A survey of simple transfer-function derivations from high-order state-variable models. Automatica, vol. 8, no. 6; pp. 765-775.
  • Shamash, Y. (1974). Stable reduced-order models using Padé-type approximations. IEEE transactions on Automatic Control, vol. 19, no. 5; pp. 615-616.
  • Hutton, M. and Friedland, B. (1975). Routh approximations for reducing order of linear, time-invariant systems. IEEE Transactions on Automatic Control, vol. 20, no. 3; pp. 329-337.
  • Krishnamurthy, V. and Seshadri, V. (1978). Model reduction using the Routh stability criterion. IEEE Transactions on Automatic control, vol. 23, no. 4; pp. 729-731.
  • Chen, T., Chang, C. and Han, K. (1979). Reduction of transfer functions by the stability-equation method. Journal of the Franklin Institute, vol. 308, no. 4; pp. 389-404.
  • Mishra, R. and Wilson, D. (1980). A new algorithm for optimal reduction of multivariable systems. International Journal of Control, vol. 31, no. 3; pp. 443-466.
  • Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE transactions on automatic control, vol. 26, no. 1; pp. 17-32.
  • Gutman, P., Mannerfelt, C. and Molander, P. (1982). Contributions to the model reduction problem. IEEE Transactions on Automatic Control, vol. 27, no. 2; pp. 454-455.
  • Sinha, N. K. and Kuszta, B. (1983). Modeling and identification of dynamic systems. (No Title),
  • Glover, K. (1984). All optimal Hankel-norm approximations of linear multivariable systems and their L,∞-error bounds. International journal of control, vol. 39, no. 6; pp. 1115-1193.
  • Lucas, T. N. (1986). Linear system reduction by the modified factor division method. in IEE Proceedings D (Control Theory and Applications), vol. 133, no. 6, pp. 293-296: IET.
  • Sinha, A. and Pal, J. (1990). Simulation based reduced order modelling using a clustering technique. Computers & electrical engineering, vol. 16, no. 3; pp. 159-169.
  • Antoulas, A. (2004). Approximation of large-scale dynamical systems: An overview. IFAC Proceedings Volumes, vol. 37, no. 11; pp. 19-28.
  • Panda, S., Tomar, S., Prasad, R. and Ardil, C. (2009). Model reduction of linear systems by conventional and evolutionary techniques. International Journal of Electrical and Computer Engineering, vol. 3, no. 11; pp. 2144-2150.
  • Kumar, D. and Krishna Nagar, S. (2013). Reducing power system models by Hankel norm approximation technique. International Journal of Modelling and Simulation, vol. 33, no. 3; pp. 139-143.
  • Suman, S. K. and Kumar, A. (2020). Reduction of large-scale dynamical systems by extended balanced singular perturbation approximation. International Journal of Mathematical, Engineering and Management Sciences, vol. 5, no. 5; p. 939.
  • Prajapati, A. K. and Prasad, R. (2019). Reduced order modelling of linear time invariant systems using the factor division method to allow retention of dominant modes. IETE Technical Review, vol. 36, no. 5; pp. 449-462.
  • Suman, S. K. and Kumar, A. (2021). Linear system of order reduction using a modified balanced truncation method. Circuits, Systems, and Signal Processing, vol. 40, pp. 2741-2762.
  • Kumari, A. and Vishwakarma, C. (2021). Order abatement of linear dynamic systems using renovated pole clustering and Cauer second form techniques. Circuits, Systems, and Signal Processing, vol. 40, pp. 4212-4229.
  • Yüce, A. (2024). System Identification Based on Experimental Technique Using Stability Boundary Locus Method for Linear Fractional Order Systems. Arabian Journal for Science and Engineering, pp. 1-13.
  • Das, S., Saha, S., Das, S. and Gupta, A. (2011). On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA transactions, vol. 50, no. 3; pp. 376-388.
There are 42 citations in total.

Details

Primary Language English
Subjects Control Theoryand Applications
Journal Section Research Articles
Authors

Mehmet Serhat Can 0000-0003-2356-9921

Tufan Doğruer 0000-0002-0415-3042

Publication Date December 30, 2024
Submission Date October 7, 2024
Acceptance Date November 24, 2024
Published in Issue Year 2024 Volume: 5 Issue: 2

Cite

APA Can, M. S., & Doğruer, T. (2024). Direct Synthesis Method-based PID Controller Design for High Order Systems. NATURENGS, 5(2), 16-22. https://doi.org/10.46572/naturengs.1563008