Adaptive Piecewise Linear Controller for Servo Mechanical Control Systems


In this paper, an adaptive piecewise linear control scheme is proposed for improving the performance and response time of servo mechanical control systems. It is a gain stabilized control technique. No large phase lead compensations or pole zero cancellations are needed for performance improvement. Large gain is used for large tracking error to get fast response. Small gain is used between large and small tracking error for good performance. Large gain is used again for small tracking error to cope with disturbance. It gives an almost command independent response. It can speed up the rise time while keeping robustness unchanged. The proposed control scheme is applied to a servo system with large time lag and a complicated electro-hydraulic velocity/position servo system. Time responses show that the proposed method gives significant improvements for response time and performance.

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Tsay, T. (2013) Adaptive Piecewise Linear Controller for Servo Mechanical Control Systems. Journal of Applied Mathematics and Physics, 1, 85-92. doi: 10.4236/jamp.2013.15013.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] B. C. Kuo and F. Golnaraghi, “Automatic Control Systems,” 8th Edition, John Wiley & Sons, Inc., Hoboken, 2003.
[2] R. C. Dorf and R. H. Bisop, “Modern Control Systems,” 7th Edition, Pearson Education Singapore Pte, Ltd., Singapore, 2008.
[3] V. I. Utkin, “Variable Structure Systems with Sliding Modes,” IEEE Transactions on Automatic Control, Vol. 22, No. 2, 1977, pp. 212-222.
[4] G. Bartolini, E. Punta and T. Zolezzi, “Simplex Methods for Nonlinear Uncertain Sliding-Mode Control,” IEEE Transactions on Automatic Control, Vol. 49, No. 6, 2004, pp. 922-933.
[5] J. Y. Hung, W. Gao and J. C. Hung, “Variable Structure Control: A Survey,” IEEE Transactions on Industry Electron, Vol. 40, No. 1, 1993, pp. 2-22.
[6] G. Bartolini, A. Ferrara, E. Usai and V. I. Utkin, “On Multi-Input Chattering-Free Second Order Sliding Mode Control,” IEEE Transactions on Automatic Control, Vol. 45, No. 9, 2000, pp. 1711-1717.
[7] S. R. Vadali, “Variable-Structure Control of Spacecraft Large-Angle Maneuvers,” Journal of Guidance, Control, and Dynamics, Vol. 9, No. 2, 1986, pp. 235-239.
[8] M. Corno, M. Tanelli, S. M. Savaresi and L. Fabbri, “Design and Validation of a Gain-Scheduled Controller for the Electronic Throttle Body in Ride-by-Wire Racing Motorcycles,” IEEE Transactions on Control Systems Technology, Vol. 19, No. 1, 2011, pp. 18-30.
[9] R. A. Nichols, R. T. Reichert and W. J. Rugh, “Gain Scheduling for H-Infinity Controllers: A Flight Control Example,” IEEE Transactions on Control Systems Technology, Vol. 1, No. 2, 1993, pp. 69-79.
[10] T. A. Johansen, I. Petersen, J. Kalkkuhl and J. Ludemann, “Gain-Scheduled Wheel Slip Control in Automotive Brake Systems,” IEEE Transactions on Control Systems Technology, Vol. 11, No. 6, 2003, pp. 799-811.
[11] J. H. Taylor and K. Strobel, “Nonlinear Compensator Synthesis via Sinusoidal-Input Describing Functions,” Proceedings of American Control Conference, Boston, 1985, pp. 1242-1247.
[12] R. D. Colgern and A. Jonckheere, “H Control of a Class of Nonlinear Systems Using Describing Functions and Simplicial Algorithms,” IEEE Transactions on Automatic Control, Vol. 42, No. 5, 1997, pp. 707-712.
[13] A. Nassirharand and H. Karimi, “Controller Synthesis Methodology for Multivariable Nonlinear Systems with Application to Aerospace,” ASME Journal of Dynamic and System Measurement Control, Vol. 126, No. 3, 2004, pp. 595-604.
[14] A. Nassirharand and H. Karimi, “Nonlinear Controller Synthesis Based on Inverse Describing Function Technique in the MATLAB Environment,” Advances in Engineering Software, Vol. 37, No. 6, 2006, pp. 370-374.
[15] W. K. Ho, T. H. Lee, H. P. Han and Y. Hong, “Self-Tuning IMC-PID Controller with Gain and Phase Margins Assignment,” IEEE Transactions on Control System Technology, Vol. 9, No. 3, 2001, pp. 535-541.
[16] T. S. Tsay, “On-Line Computing of PI/Lead Compensators for Industry Processes with Gain and Phase Specifications,” Computers and Chemical Engineering, Vol. 33, No. 9, 2009, pp. 1468-1474.
[17] S. Majhi, “On-Line PI Control of Stable Process,” Journal of Process Control, Vol. 15, No. 8, 2005, pp. 859-867.
[18] J. G. Ziegler and N. B. Nichols, “Optimum Setting for Automatic Controller,” Transactions of ASME, Vol. 65, 1942, pp. 759-768.
[19] K. J. Astrom and T. Hagglund, “Revisting the Ziegler-Nichols Step Responses Method for PID Control,” Journal of Process Control, Vol. 14, No. 6, 2004, pp. 635-650.
[20] K. K. Tan, T. H Lee and X. Jiang, “Robust On-line Relay Automatic Tuning of PID Control System,” ISA Transactions, Vol. 39, 2000, pp. 219-232.
[21] K. K. Tan, T. H. Lee and X. Jiang, “On-Line Relay Identification, Assessment and Tuning of PID Controller,” Journal of Process Control, Vol. 11, No. 5, 2001, pp. 483-486.
[22] H. E. Merritt, “Hydraulic Control System,” John Wiley, New York, 1967.

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