IJMNTA  Vol.3 No.2 , June 2014
On the Generalization of Integrator and Integral Control Action
Author(s) Baishun Liu*
ABSTRACT

This paper provides a solution to generalize the integrator and the integral control action. It is achieved by defining two function sets to generalize the integrator and the integral control action, respectively, resorting to a stabilizing controller and adopting Lyapunov method to analyze the stability of the closed-loop system. By originating a powerful Lyapunov function, a universal theorem to ensure regionally as well as semi-globally asymptotic stability is established by some bounded information. Consequently, the justification of two propositions on the generalization of integrator and integral control action is verified. Moreover, the conditions used to define the function sets can be viewed as a class of sufficient conditions to design the integrator and the integral control action, respectively.


Cite this paper
Liu, B. (2014) On the Generalization of Integrator and Integral Control Action. International Journal of Modern Nonlinear Theory and Application, 3, 44-52. doi: 10.4236/ijmnta.2014.32007.
References
[1]   Khalil, H.K. (2000) Universal Integral Controllers for Minimum-Phase Nonlinear Systems. IEEE Transactions on Automatic Control, 45, 490-494. http://dx.doi.org/10.1109/9.847730

[2]   Krikelis, N.J. and Barkas, S.K. (1984) Design of Tracking Systems Subject to Actuator Saturation and Integrator Windup. International Journal of Control, 39, 667-682.
http://dx.doi.org/10.1080/00207178408933196

[3]   Hanus, R., Kinnaert, M. and Henrotte, J.L. (1987) Conditioning Technique, a General Anti-Windup and Bumpless Transfer Method. Automatica, 23, 729-739. http://dx.doi.org/10.1016/0005-1098(87)90029-X

[4]   Peng, Y., Varanceic, D. and Hanus, R. (1996) Anti-Windup, Bumpless, and Conditioned Transfer Techniques for PID Controllers. IEEE Control Systems Magazine, 16, 48-57. http://dx.doi.org/10.1109/37.526915

[5]   Cao, Y.Y., Lin, Z.L. and David, G.W. (2004) Anti-Windup Design of Output Tracking Systems Subject to Actuator Saturation and Constant Disturbances. Automatica, 40, 1221-1228.
http://dx.doi.org/10.1016/j.automatica.2004.02.012

[6]   Marchand, N. and Hably, A. (2005) Global Stabilization of Multiple Integrators with Bounded Controls. Automatica, 41, 2147-2152. http://dx.doi.org/10.1016/j.automatica.2005.07.004

[7]   Seshagiri, S. and Khalil, H.K. (2005) Robust Output Feedback Regulation of Minimum-Phase Nonlinear Systems Using Conditional Integrators. Automatica, 41, 43-54.

[8]   Astrom, K.J. and Rundquist, L. (1989) Integrator Windup and How to Avoid It. Proceedings of the 1989 American Control Conference, Pittsburgh, 21-23 June 1989, 1693-1698.

[9]   Shahruz, S.M. and Schwartz, A.L. (1994) Design and Optimal Tuning of Nonlinear PI Compensators. Journal of Optimization Theory and Applications, 83, 181-198. http://dx.doi.org/10.1007/BF02191768

[10]   Hodel, A.S. and Hall, C.E. (2001) Variable-Structure PID Control to Prevent Integrator Windup. IEEE Transactions on Industrial Electronics, 48, 442-451. http://dx.doi.org/10.1109/41.915424

[11]   Matsuda, Y. and Ohse, N. (2006) An Approach to Synthesis of Low Order Dynamic Anti-Windup Compensations for Multivariable PID Control Systems with Input Saturation. Proceedings of the 2006 Joint SICE-ICASE Conference, Busan, 18-21 October 2006, 988-993.
http://dx.doi.org/10.1109/SICE.2006.315736

[12]   Shahruz, S.M. and Schwartz, A.L. (1997) Nonlinear PI Compensators That Achieve High Performance. Journal of Dynamic Systems, Measurement and Control, 11, 105-110.
http://dx.doi.org/10.1115/1.2801198

[13]   Kelly, R. (1998) Global Positioning of Robotic Manipulators via PD Control plus a Class of Nonlinear Integral Actions. IEEE Transactions on Automatic Control, 43, 934-938. http://dx.doi.org/10.1109/9.701091

[14]   Tarbouriech, S., Pittet, C. and Burgat, C. (2000) Output Tracking Problem for Systems with Input Saturations via Nonlinear Integrating Actions. International Journal of Robust and Nonlinear Control, 10, 489-512.
http://dx.doi.org/10.1002/(SICI)1099-1239(200005)10:6<489::AID-RNC489>3.0.CO;2-D

[15]   Hu, B.G. (2006) A Study on Nnonlinear PID Controllers—Proportional Component Approach. Acta Automatica Sinica, 32, 219-227.

[16]   Huang, C.Q., Peng, X.F. and Wang, J.P. (2008) Robust Nonlinear PID Controllers for Anti-Windup Design of Robot Manipulators with an Uncertain Jacobian Matrix. Acta Automatica Sinica, 34, 1113-1121.
http://dx.doi.org/10.3724/SP.J.1004.2008.01113

[17]   Liu, B.S. and Tian, B.L. (2009) General Integral Control. Proceedings of the International Conference on Advanced Computer Control, Singapore, 22-24 January 2009, 136-143.

[18]   Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Linear System Theory. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3174-3177.

[19]   Liu, B.S. and Tian, B.L. (2012) General Integral Control Design Based on Sliding Mode Technique. Proceedings of the 3rd International Conference on Mechanic Automation and Control Engineering, 5, 3178-3181.

[20]   Liu, B.S., Li, J.H. and Luo, X.Q. (2014) General Integral Control Design via Feedback Linearization. Intelligent Control and Automation, 5, 19-23. http://dx.doi.org/10.4236/ica.2014.51003

[21]   Liu, B.S., Luo, X.Q. and Li, J.H. (2013) General Concave Integral Control. Intelligent Control and Automation, 4, 356-361. http://dx.doi.org/10.4236/ica.2013.44042

[22]   Liu, B.S., Luo, X.Q. and Li, J.H. (2014) General Convex Integral Control. International Journal of Automation and Computing, Accepted.

[23]   Khalil, H.K. (2007) Nonlinear Systems. 3rd Edition, Electronics Industry Publishing, Beijing, 126-128, 482-484.

 
 
Top