A DIRECT SYNTHESIS CONTROL STRATEGY FOR SINGLE-INPUT, SINGLE-OUTPUT NONLINEAR SYSTEM

Abstract

This paper describes the strategy to design and modify a conventional controller by direct synthesis and the internal model control (IMC) methods for a single-input, single-output (SISO) process system. Both of these methods are the most widely used approaches, both in their simplicity and in their generality. The design of a direct synthesis controller based on a linear inversion of the non-linear process model about a steady-state was first considered. The particular linear design technique adopted resulted in a Proportional – Integral (PI) controller whose parameters are easily computed as a function of the parameters of the linear invertible model and the controller tuning parameter. The internal model control (IMC) methods were also considered to determine the fault from external disturbance. From this study, it was observed that under certain conditions both direct synthesis and internal model control methods are equal. Their use in the design of analog and digital controllers is presented by the method of the required model.

Keywords

• PID
• direct-synthesis
• IMC
• required-medel
• controller design

References

1. [1] Åström, K.J., Hägglund, T., PID controllers: theory, design, and tuning. ISA-The Instrumentation, Systems, and Automation Society Research Triangle Park, NC, 1995.
2. [2] Åström, K.J., Hägglund, T., Astrom, K.J., Advanced PID control. ISA-The Instrumentation, Systems, and Automation Society Research Triangle Park, NC, 2006.
3. [3] Olufemi, A.S., Ogbeide, S.E. (2017). Dynamics and Control System Design for Biodiesel Transesterification Reactor. International Robotics & Automation Journal, 2(6), 1-6.
4. [4] O'Dwyer, A., Handbook of PI and PID controller tuning rules. Imperial College Press, 2009.
5. [5] do Val, J.B., Souto, R.F., (2017). Modeling and control of stochastic systems with poorly known dynamics. IEEE Transactions on Automatic Control, 62(9), 4467-4482.
6. [6] Ogunnaike, B., Ray, W., Process Modeling, Dynamics and Control. ed: Oxford Univ Press, New York, USA, 1994.
7. [7] Chen, D., Seborg, D.E., (2002). PI/PID controller design based on direct synthesis and disturbance rejection. Industrial & engineering chemistry research. 41(19), 4807-4822.
8. [8] Jung, C.S., Song, H.K., Hyun, J.C., (1999b). A new direct‐synthesis tuning method for pi‐controllers. The Canadian Journal of Chemical Engineering, 77(1), 180-185.

9. [9] Rivera, D.E., Morari, M., Skogestad, S., (1986). Internal model control: PID controller design," Industrial Engineering Chemistry Process Design Development, 25(1), 252-265, 1986.
10. [10] Wang, Q.G., Hang, C.C., Yang, X.P., (2001). Single-loop controller design via IMC principles. Automatica, 37(12), 2041-2048.
11. [11] Wang, Y.C., Sheu, D., Lin, C.E., (2015). A unified approach to nonlinear dynamic inversion control with parameter determination by eigenvalue assignment. Mathematical Problems in Engineering, 2015.
12. [12] Tan, W., Marquez, H.J., Chen, T., (2003). IMC design for unstable processes with time delays. Journal of Process Control, 13(3), 203-213.
13. [13] Rivera, D.E., Internal model control: a comprehensive view," A. S. University, Ed., ed. Arizona, 19, 1999.
14. [14] Rao, A.S., Rao, V., Chidambaram, M., (2009). Direct synthesis-based controller design for integrating processes with time delay. Journal of the Franklin Institute, 346(1), 38-56.
15. [15] Adams, R.J., Banda, S.S., (1993). Robust flight control design using dynamic inversion and structured singular value synthesis. IEEE Transactions on Control Systems Technology, 1(2), 80-92.
16. [16] Dighe, Y.N., Kadu, C.B., Parvat, B.J., (2014). Direct Synthesis Approach for Design of PID Controller. International Journal of Application or Innovation in Engineering & Management, 3(5), 161-167.
17. [17] Ajmeri, M., Ali, A., (2015). Direct synthesis based tuning of the parallel control structure for integrating processes. International Journal of Systems Science, 46(13), 2461-2473.