DESIGN, ANALYSIS AND EXPERIMENTAL VERIFICATION OF A NOVEL NONLINEAR PI CONTROLLER
Year 2017,
Volume: 18 Issue: 4, 876 - 896, 31.10.2017
Ali Fuat Ergenc
,
Handan Nak
,
Şirin Akkaya
Abstract
In this study, a novel variable gain PI controller
structure is introduced. The proposed controller structure consists of a
sector-bounded nonlinear function of the relative error value in cascade with a
linear fixed-gain PI controller. The stability analysis of the closed loop
system is examined through Popov stability criterion, Routh-Hurwitz stability
method and stability boundary locus method for both second-order and higher-order
systems. In addition, the performance of the controller against parameter
variations and disturbances is investigated through some simulations for second
order systems. An experimental study, an
active suspension system, is conducted to examine the performance of the
controller for higher order systems. In the literature, there are
similar controllers, but the proposed one is superb in terms of effectiveness
and stability. The new controller prevents the saturation of the controller
signal. Simulation results and experimental studies reveal that proposed
controller structure is quite effective for both lower and higher order
systems.
References
- [1] Ang K, Chong G, Li Y. PID control system analysis, design, and technology, IEEE Trans. Control Syst. Technol., vol. 13, no. 4, pp. 559–576, Jul. 2005.
- [2] Lau K, Middleton R. Switched integrator control schemes for integrating plants, in Proc. Eur. Control Conf., 2003.
- [3] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Performance optimization of piecewise affine variable-gain controllers for linear motion systems, Mechatronics, vol. 24, no. 6, pp. 648–660, Sep. 2014.
- [4] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Contr. Syst. Technol., vol. 9, pp. 399–406, Mar. 2001.
- [5] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Synthesis of variable gain integral controllers for linear motion systems, IEEE Trans. on Contr. Syst. Technology, 23(1), pp. 139-149, 2015.
- [6] Armstrong B., McPherson J., and Li Y. Stability of nonlinear PD control, Appl. Math. Comput. Sci., vol. 7, no. 2, pp. 101–120, 1997.
- [7] Armstrong B., Neevel D., and Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, in Proc. 1999 Int. Conf. Robot. Automat., 1999,
pp. 837–842.
- [8] Armstrong B. and Wade B. Nonlinear PID control with partial state knowledge: Damping without derivatives, Int. J. Robot. Res., vol. 18, no. 8, pp. 715–731, 2000.
- [9] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Control Syst. Technol., vol. 9, no. 2, pp. 399–406, Mar. 2001.
- [10] Heertjes M, Schuurbiers X, Nijmeijer H. Performance-improved design of N-PID controlled motion systems with application to wafer stages, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1347–1355, May 2009.
- [11] Wouw N, Pastink H, Heertjes M, Pavlov A, Nijmeijer H. Performance of convergence-based variable-gain control of optical storage drives, Automatica, vol. 44, no. 1, pp. 15–27, 2008.
- [12] Sun D, Hu S, Shao X, Liu C. Global stability of a saturated nonlinear PID controller for robot manipulators, IEEE Trans. Ind. Electron., vol. 17, no. 4, pp. 892–899, Jul. 2009.
- [13] Salim S N S, Rahmat M F, Faudzi A A, Athif M, Ismail Z H, Sunar N. Position Control of Pneumatic Actuator Using Self-Regulation Nonlinear PID, Mathematical Problems in Engineering, vol. 2014, p. 12, 2014
- [14] Seraji H. A new class of nonlinear PID controllers with robotic applications, J. Robot. Syst., vol. 15, no. 3, pp. 161–173, 1998.
- [15] Su Y X, Sun D, Duan B Y. Design of an enhanced nonlinear PID controller, Mechatronics, vol. 15, no. 8, pp. 1005–1024, Oct. 2005.
- [16] Salim S N S, Rahmat M F, Faudzi A, Z. Ismail Z H, Sunar N. Robust Control Strategy for Pneumatic Drive System via Enhanced Nonlinear PID Controller, International Journal of Electrical and Computer Engineering (IJECE), vol. 4, pp. 658-667, 2014.
- [17] Armstrong B, McPherson J, Li YG. A Lyapunov stability proof for nonlinear stiffness PD control, Proceedings of the IEEE international conference on robot. autom., Minneapolis, p. 945–50, 1996.
- [18] Xu Y, Ma D, Hollerbach J. M. Nonlinear Proportional and Derivative Control for High Disturbance Rejection and High Gain Force Control, Proc. IEEE Intern. Conf. on Robotics and Automation, Vol. 1, pp. 752-759, Atlanta, 1993.
- [19] Tan, N, Kaya, I, Yeroglu C, Atherton, D. P. Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47(18), 3045-3058.
- [20] Yeroglu C, Tan N. Design of robust PI controller for vehicle suspension system. Journal of Electrical Engineering and Technology, 3(1), 135-142.
- [21] Khalil H K, Grizzle J. Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002.
- [22] Active suspension system - Laboratory Guide, Active Suspension Experiment for Matlab/Simulink Users, 2013.
Year 2017,
Volume: 18 Issue: 4, 876 - 896, 31.10.2017
Ali Fuat Ergenc
,
Handan Nak
,
Şirin Akkaya
References
- [1] Ang K, Chong G, Li Y. PID control system analysis, design, and technology, IEEE Trans. Control Syst. Technol., vol. 13, no. 4, pp. 559–576, Jul. 2005.
- [2] Lau K, Middleton R. Switched integrator control schemes for integrating plants, in Proc. Eur. Control Conf., 2003.
- [3] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Performance optimization of piecewise affine variable-gain controllers for linear motion systems, Mechatronics, vol. 24, no. 6, pp. 648–660, Sep. 2014.
- [4] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Contr. Syst. Technol., vol. 9, pp. 399–406, Mar. 2001.
- [5] Hunnekens B G B, Heertjes M, van de Wouw N, Nijmeijer H. Synthesis of variable gain integral controllers for linear motion systems, IEEE Trans. on Contr. Syst. Technology, 23(1), pp. 139-149, 2015.
- [6] Armstrong B., McPherson J., and Li Y. Stability of nonlinear PD control, Appl. Math. Comput. Sci., vol. 7, no. 2, pp. 101–120, 1997.
- [7] Armstrong B., Neevel D., and Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, in Proc. 1999 Int. Conf. Robot. Automat., 1999,
pp. 837–842.
- [8] Armstrong B. and Wade B. Nonlinear PID control with partial state knowledge: Damping without derivatives, Int. J. Robot. Res., vol. 18, no. 8, pp. 715–731, 2000.
- [9] Armstrong B, Neevel D, Kusik T. New results in NPID control: Tracking, integral control, friction compensation and experimental results, IEEE Trans. Control Syst. Technol., vol. 9, no. 2, pp. 399–406, Mar. 2001.
- [10] Heertjes M, Schuurbiers X, Nijmeijer H. Performance-improved design of N-PID controlled motion systems with application to wafer stages, IEEE Trans. Ind. Electron., vol. 56, no. 5, pp. 1347–1355, May 2009.
- [11] Wouw N, Pastink H, Heertjes M, Pavlov A, Nijmeijer H. Performance of convergence-based variable-gain control of optical storage drives, Automatica, vol. 44, no. 1, pp. 15–27, 2008.
- [12] Sun D, Hu S, Shao X, Liu C. Global stability of a saturated nonlinear PID controller for robot manipulators, IEEE Trans. Ind. Electron., vol. 17, no. 4, pp. 892–899, Jul. 2009.
- [13] Salim S N S, Rahmat M F, Faudzi A A, Athif M, Ismail Z H, Sunar N. Position Control of Pneumatic Actuator Using Self-Regulation Nonlinear PID, Mathematical Problems in Engineering, vol. 2014, p. 12, 2014
- [14] Seraji H. A new class of nonlinear PID controllers with robotic applications, J. Robot. Syst., vol. 15, no. 3, pp. 161–173, 1998.
- [15] Su Y X, Sun D, Duan B Y. Design of an enhanced nonlinear PID controller, Mechatronics, vol. 15, no. 8, pp. 1005–1024, Oct. 2005.
- [16] Salim S N S, Rahmat M F, Faudzi A, Z. Ismail Z H, Sunar N. Robust Control Strategy for Pneumatic Drive System via Enhanced Nonlinear PID Controller, International Journal of Electrical and Computer Engineering (IJECE), vol. 4, pp. 658-667, 2014.
- [17] Armstrong B, McPherson J, Li YG. A Lyapunov stability proof for nonlinear stiffness PD control, Proceedings of the IEEE international conference on robot. autom., Minneapolis, p. 945–50, 1996.
- [18] Xu Y, Ma D, Hollerbach J. M. Nonlinear Proportional and Derivative Control for High Disturbance Rejection and High Gain Force Control, Proc. IEEE Intern. Conf. on Robotics and Automation, Vol. 1, pp. 752-759, Atlanta, 1993.
- [19] Tan, N, Kaya, I, Yeroglu C, Atherton, D. P. Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47(18), 3045-3058.
- [20] Yeroglu C, Tan N. Design of robust PI controller for vehicle suspension system. Journal of Electrical Engineering and Technology, 3(1), 135-142.
- [21] Khalil H K, Grizzle J. Nonlinear Systems, 3rd ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2002.
- [22] Active suspension system - Laboratory Guide, Active Suspension Experiment for Matlab/Simulink Users, 2013.