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Performance improvement of PI controller with nonlinear error shaping function: IDA-PBC approach. (English) Zbl 1181.93031

Summary: The general dilemma faced in a conventional linear Proportional-Integral (PI) controller is to achieve the best transient performance (i.e. fast rise time and low overshoot level) at the same time. However, fast response is usually accompanied by high overshoot level. On the other hand, very stable control without overshoot is usually achieved at the expense of a more sluggish response to set point changes and load disturbances. Therefore, compromise between fast response and low overshoot level should be made. In this paper, to overcome these contradictions and limitations, nonlinear Error Shaping Function (ESF) is introduced to amplify gain at low error level but reduce gain at high error level. Firstly, interconnection and damping structure for the closed-loop system composed of PI controller and first-order plant is revealed based on the Port-Controlled Hamiltonian with Dissipation (PCHD) formation. Secondly, passivity analysis is performed by the Interconnection and Damping Assignment (IDA) Passivity-Based Control (PBC) algorithm. In simulation studies, several nonlinear error shaping functions are examined and compared to verify performance improvements.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B35 Sensitivity (robustness)
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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References:

[1] Franklin, G. F.; Powell, J. D.; Workman, M. L., Digital Control of Dynamic Systems (1990), Addison Wesley Publishing Company Inc. · Zbl 0697.93002
[2] Astrom, K. J.; Hagglund, T., PID Controllers (1995), International Society for Measurement and Control
[3] Ho, W. K.; Hang, C. C.; Cao, L. S., Tuning of PID controllers based on gain and phase margin specifications, Automatica, 31, 497-502 (1995) · Zbl 0825.93598
[4] Ho, W. K.; Gan, O. P.; Tay, E. B.; Ang, E. L., Performance and gain and phase margins of well-known PID tuning formulaes, IEEE Transactions on Control Systems Technology, 4, 473-477 (1996)
[5] Kiong, T. K.; Wang, Q. G.; Chieh, H. C., Advances in PID Control (1999), Spring-Verlag
[6] van der Schaft, A. J., \(L_2\) Gain and Passivity Techniques in Nonlinear Control (2000), Springer-Verlag: Springer-Verlag London · Zbl 0937.93020
[7] Maschke, B.; Ortega, R.; van der Schaft, A. J., Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation, IEEE Transactions on Automatic Control, 45, 1498-1502 (2000) · Zbl 0988.93060
[8] Ortega, R.; van der Schaft, A. J.; Mareels, I.; Maschke, B., Putting energy back in control, IEEE Control Systems Magazine, 18-33 (2001)
[9] Astrom, K. J.; Hagglund, T., The future of PID control, Control Engineering Practice, 9, 1163-1175 (2001)
[10] Ortega, R.; van der Schaft, A. J.; Maschke, B.; Escobar, G., Interconnection and damping assignment passivity based control of port-controlled Hamiltonian systems, Automatica, 38, 585-596 (2002) · Zbl 1009.93063
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