Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


A Time-Frequency PID Controller Design for Improved Anti-Interference Performance of a Solenoid Valve Applicable to Hydraulic Cylinder Actuation

Journal of Vibration Testing and System Dynamics 1(4) (2017) 281--294 | DOI:10.5890/JVTSD.2017.12.001

Xiu-Heng Wu$^{1}$, Zheng-He Song$^{1}$, Yue-Feng Du$^{1}$, En-Rong Mao$^{1}$, C. Steve Suh$^{2}$

$^{1}$ Beijing Key Laboratory of Optimized Design for Modern Agricultural Equipment, China Agricultural University, Beijing 100083, China

$^{2}$ Nonlinear Engineering and Control Lab, Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3123, USA

Download Full Text PDF



PID control is widely used in electro-hydraulic systems. However, enhancing PID control performance in response to system nonlinearity, fluctuations of external load, and noise inevitably renders the chattering of the system that are also telltale indications of poor efficiency and dynamic instability. On the other hand, tuning down PID parameters would alleviate chatter at the expenses of reduced performance and inefficient use of resources. To address the particular issue, a novel controller concept termed as the time-frequency PID (TFPID) is developed. Firstly, a nonlinear electro-hydraulic dynamic model to be controlled is built for numerical and physical studies. Next, the working principle of the TFPID control is elaborated where the discrete wavelet transform is employed to decompose the error signal into high frequency error and low frequency error. Two unique PID controllers incorporating proportion, differential, and integral control are designed to mitigate the two error signals. The TFPID controller and system model are developed in MATLAB/Simulink to optimize the parameters and a hardware-in-the-loop test bench is employed to establish the performance of the system subject to interferences. Physical test results show that TFPID performs significantly better in anti-interference, stability, and dynamic response.


  1. [1]  Chiang, M.H., Lee, L.W., and Liu, H.H. (2014), Adaptive Fuzzy Controller with Self-Tuning Fuzzy Sliding- Mode Compensation for Position Control of An Electro-Hydraulic Displacement-Controlled System, Journal of Intelligent & Fuzzy Systems, 26(2): 815-830.
  2. [2]  Guo, Q., Sun, P., Yin, J.M., Yu, T., and Jiang, D. (2016), Parametric Adaptive Estimation and Back-Stepping Control of Electro-Hydraulic Actuator with Decayed Memory Filter, ISA Transactions, 62, 202-214.
  3. [3]  Yao, J., Jiao, Z., Ma, D., and Yan, L. (2014), High-Accuracy Tracking Control of Hydraulic Rotary Actuators with Modeling Uncertainties, IEEE/ASME Transactions on Mechatronics, 19(2), 633-641.
  4. [4]  Liem, D.T., Truong, D.Q., Park, H.G., and Ahn, K.K. (2016), A Feedforward Neural Network Fuzzy Grey Predictor-Based Controller for Force Control of An Electro-Hydraulic Actuator, International Journal of Precision Engineering and Manufacturing, 17(1), 309-321.
  5. [5]  Wang, Y., Luo, G., Gu, L., and Li, X. (2016), Fractional-Order Nonsingular Terminal Sliding Mode Control of Hydraulic Manipulators Using Time Delay Estimation, Journal of Vibration and Control, 22(19), 3998-4011.
  6. [6]  Guan, C. and Pan, S. (2008), Adaptive Sliding Mode Control of Electro-Hydraulic System with Nonlinear Unknown Parameters, Control Engineering Practice, 16(11), 1275-1284.
  7. [7]  Dotoli, M., Fay, A., Miśowicz, M., and Seatzu, C. (2017), Advanced Control in Factory Automation: A Survey, International Journal of Production Research, 55(5), 1243-1259.
  8. [8]  Vilanova, R. and Visioli, A. (2012), PID Control in The Third Millennium, London: Springer.
  9. [9]  Hägglund, T. (2013), A Unified Discussion on Signal Filtering in PID Control, Control Engineering Practice, 21(8), 994-1006.
  10. [10]  Yang, S., Yang K., Wu, B., and Xiong, L. (2002), Control Principle of Mechanical Engineering, Wuhans: Huazhong University of Science & Technology Press. (in Chinese)
  11. [11]  Shin, H.B. and Park, J.G. (2012), Anti-Windup PID Controller With Integral State Predictor for Variable- Speed Motor Drives, IEEE Transactions on Industrial Electronics, 59(3), 1509-1516.
  12. [12]  Sun, W., Chen, Z., and Yuan, Z. (2000), Adaptive PID Controller Based on Band-Wise Design Using Wavelet, Acta Scientiarum Naturallum Universitatis Nankalensls, 33(2): 48-52. (in Chinese)
  13. [13]  Parvez, S. and Gao, Z. (2005), A Wavelet-Based Multiresolution PID Controller, IEEE Transactions on Industry Applications, 41(2), 537-543.
  14. [14]  Khan, M.A.S.K. and Rahman, M.A. (2008), Implementation of A New Wavelet Controller for Interior Permanent-Magnet Motor Drives, IEEE Transactions on Industry Applications, 44(6), 1957-1965.
  15. [15]  Tolentino, J.A.C., Silva, A.J., Velasco, L.E.R., and Ramírez, O.A.D. (2012), Wavelet PID And Wavenet PID: Theory And Applications, InTech Open Access Publisher.
  16. [16]  Liu, M.K. and Suh, C.S. (2012), Simultaneous Time–Frequency Control of Bifurcation And Chaos, Communications in Nonlinear Science and Numerical Simulation, 17(6), 2539-2550.
  17. [17]  Liu, M.K. and Suh, C.S. (2013), Synchronization of Chaos in Simultaneous Time-Frequency Domain, Applied Mathematical Modelling, 37(23), 9524-9537.
  18. [18]  Wang, X. and Suh, C.S. (2016), Nonlinear Time-Frequency Control of PM Synchronous Motor Instability Applicable to Electric Vehicle Application, International Journal of Dynamics and Control, 4(4), 400-412.
  19. [19]  Ayalew, B. (2007), Robustness to Friction Estimation for Nonlinear Position Control of An Electrohydraulic Actuator, In American Control Conference, 2007. ACC’07 (pp. 100-105). IEEE.
  20. [20]  Ayalew, B. and Kulakowski, B.T. (2005), Modeling Supply And Return Line Dynamics for An Electrohydraulic Actuation System, ISA Transactions, 44(3), 329-343.
  21. [21]  Alleyne, A. and Liu, R. (2000), A Simplified Approach to Force Control for Electro-hydraulic Systems, Control Engineering Practice, 8(12), 1347-1356.
  22. [22]  Sohl, G.A. and Bobrow, J.E. (1999), Experiments And Simulations on The Nonlinear Control of A Hydraulic Servosystem, IEEE Transactions on Control Systems Technology, 7(2), 238-247.
  23. [23]  De Wit, C.C., Olsson, H., Astrom, K.J., and Lischinsky, P. (1995), A New Model for Control of Systems with Friction, IEEE Transactions on Automatic Control, 40(3), 419-425.
  24. [24]  Owen, W.S. and Croft, E.A. (2003). The Reduction of Stick-Slip Friction in Hydraulic Actuators. IEEE/ASME Transactions on Mechatronics, 8(3), 362-371.
  25. [25]  Kalyoncu, M. and Haydim, M. (2009), Mathematical Modelling And Fuzzy Logic Based Position Control of An Electrohydraulic Servosystem with Internal Leakage, Mechatronics, 19(6), 847-858.
  26. [26]  Haessig, D. and Friedland, B. (1991), On The Modeling And Simulation of Friction, Journal of Dynamic Systems, Measurement, And Control, 113(3), 354-362.
  27. [27]  Merritt, H.E. (1967), Hydraulic Control Systems, John Wiley & Sons.
  28. [28]  Milić, V.,Šitum,Ž., and Essert, M. (2010), Robust Hꝏ Position Control Synthesis of An Electro-Hydraulic Servo System, ISA Transactions, 49(4), 535-542.
  29. [29]  Tafazoli, S., de Silva, C.W., and Lawrence, P.D. (1998), Tracking Control of An ElectrohydraulicManipulator in The Presence of Friction, IEEE Transactions on Control Systems Technology, 6(3), 401-411.
  30. [30]  Jelali, M., and Kroll, A. (2012), Hydraulic Servo-systems: Modelling, Identification and Control, Springer Science & Business Media.
  31. [31]  Kilic, E., Dolen, M., Caliskan, H., Koku, A.B., and Balkan, T. (2014), Pressure Prediction on A Variable- Speed Pump Controlled Hydraulic System Using Structured Recurrent Neural Networks, Control Engineering Practice, 26, 51-71.
  32. [32]  Nakkarat, P. and Kuntanapreeda, S. (2009), Observer-Based Backstepping Force Control of An Electrohydraulic Actuator, Control Engineering Practice, 17(8), 895-902.
  33. [33]  Kim, W., Won, D., Shin, D., and Chung, C.C. (2012), Output Feedback Nonlinear Control for Electro- Hydraulic Systems, Mechatronics, 22(6), 766-777.
  34. [34]  Daubechies, I. (1992), Ten Lectures on Wavelets, Philadelphia: Society for industrial and applied mathematics.
  35. [35]  Boggess, A. and Narcowich, F.J. (2015), A First Course in Wavelets with Fourier Analysis, John Wiley & Sons.
  36. [36]  Mallat, S. and Hwang, W.L. (1992), Singularity Detection and Processing with Wavelets, IEEE Transactions on Information Theory, 38(2), 617-643.
  37. [37]  Gomes, J. and Velho, L. (2015), From Fourier Analysis to Wavelets, Springer International Publishing.
  38. [38]  Liu, M.K. and Suh, C.S. (2012), On Controlling Milling Instability And Chatter at High Speed, Journal of Applied Nonlinear Dynamics, 1(1), 59-72.