Skip to main content

A new control design and robustness analysis of a variable speed hydrostatic transmission used to control the velocity of a hydraulic cylinder

International Journal of Dynamics and Control volume 9, pages 1078–1091 (2021)Cite this article

Abstract

Controlling the velocity of a hydraulic cylinder is a common objective in fluid power industry. This objective is achieved by controlling the hydraulic fluid quantity that enters the cylinder. In this work, a control system that is used to control the velocity of a hydraulic cylinder was designed considering uncertainty in some of the design parameters. A fixed displacement pump was used to reduce the cost and complexity of the system. Furthermore, using variable speed drive eliminates the energy losses associated with valve controlled systems since no throttling or flow recirculation is needed. First, the system dynamics was modelled. Then, the stability and performance of the open loop system was studied using MATLAB/SIMULINK®. Next, controllers (PID and H-infinity) were designed and the stability and the performance of the closed loop system were studied and compared with those of the open loop system. Finally, the robustness of the system was studied considering multiplicative parametric uncertainty. Three parameters were considered as uncertain parameters which are the fluid bulk modulus, the viscous friction coefficient, and the leakage coefficient with a variation of ± 5% of their nominal values. The results showed that the open loop system is stable with a poor response in terms of input tracking and disturbance rejection. Using PID controller improved the system response. The system with the PID controller does not meet the robustness requirements. The system with H-infinity controller has better performance and satisfies the robustness requirements.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Abbreviations

A :

Maximum low frequency (steady state) error

A A :

Cross sectional area of side A of the actuator

A B :

Cross sectional area of side B of the actuator

b :

Viscous Drag coefficient

G F :

Transfer function of the disturbance force

E :

Error signal

F d :

Disturbance force

F o :

Spring preload

G p :

Transfer function of the plant

C :

Transfer function of the controller

K p :

Gain of the proportional part of the controller gain

K i :

Gain of the integral part of the controller

K d :

Gain of the derivative part of the controller gain

K l :

Leakage coefficient

l I :

Multiplicative parametric uncertainty

M :

Maximum high frequency error

m :

Load mass

P p :

Pump pressure

p :

Generalized plant

Q p :

Pump volumetric flow rate

S :

Sensitivity transfer function

V o :

Actuator internal volume

V r :

Reference input velocity

v c :

Velocity of the cylinder

w :

Exogenous input

w I :

Transfer function of the uncertainty rational weight

w p :

Performance weight

w u :

Effort weight of the controller

y :

Cylinder displacement

Z :

Exogenous output

β :

Bulk modulus of the hydraulic fluid

η c :

Efficiency of the hydraulic cylinder

\(\varnothing_{1,2,3,4}\) :

Nondimensional groups

τ:

Time constant

ω b :

Bandwidth frequency

\(\widehat{{\,}}\) :

Dimensionless quantity

References

  1. Tomlinson SP, Burrows CR (1992) Achieving a variable flow supply by controlled unloading of a fixed-displacement pump. ASME J Dyn Syst Meas Control 114(1):166–171

    Article  Google Scholar 

  2. Zhang Q (1999) Hydraulic linear actuator velocity control using a feedforward-plus-PID control. In: Ninth international flexible automation and intelligent manufacturing conference, Tilburg, The Netherlands, June 1, pp 277–292

  3. Yuan C, Pan M, Plummer A (2018) A review of switched inertance hydraulic converter technology. In: Proceedings of the BATH/ASME 2018 symposium on fluid power and motion control. Bath, UK. September 12–14, 2018. V001T01A013. ASME. https://doi.org/10.1115/FPMC2018-8829

  4. Pan M, Robertson J, Johnston N, Plummer A, Hillis A (2014) Experimental investigation of a switched inertance hydraulic system. ASME Paper No. FPMC2014-7829

  5. Ali HH, Wisch JK, Fales RC, Manring ND (2019) Efficiency of a fixed displacement pump with flow control using an inlet metering valve. J Dyn Syst Meas Control 141:1–14. https://doi.org/10.1115/1.4041606

    Article  Google Scholar 

  6. Ali HH, Fales RC, Manring ND (2017) Design of a velocity control system using an inlet metered pump. In: Bath/ASME symposium on fluid power and motion control (FPMC 2017). Sarasota, FL. October 16–19, 2017

  7. Zimmerman JD, Hippalgaonkar R, Ivantysynova M (2011) Optimal control for the series–parallel displacement controlled hydraulic hybrid excavator.In: Proceedings of the ASME 2011 dynamic systems and control conference DSCC2011, October 31–November 2, 2011, Arlington, VA, USA

  8. Bakman I, Gevorkov L (2015) Speed control strategy selection for multi-pump systems. In: 2015 56th international scientific conference on power and electrical engineering of Riga Technical University (RTUCON), Riga, 2015, pp 1–4. https://doi.org/10.1109/RTUCON.2015.7343174

  9. Wilson WE (1950) Positive displacement pumps and fluid motors. Pitman Publishing Corporation, New York

    Google Scholar 

  10. Thoma J (1969) Mathematical models and effective performance of hydrostatic machines and transmissions. Hydraul Pneum Power 23:642–651

    Google Scholar 

  11. Zeiger G, Aker A (1985) Torque on the swashplate of an axial piston pump. ASME J Dyn Syst Meas Control 107(3):220–226

    Article  Google Scholar 

  12. Rahmfeld R, Ivantysynova M (1998) Energy saving hydraulic actuators for mobile machines. In: 1rst Bratislavian fluid power symposium, Casta Pila, Slovakia, pp 47–57

  13. Gao Y, Cheng J, Huang J, Quan L (2017) Applied sciences simulation analysis and experiment of variable–displacement asymmetric axial piston pump, pp 1–16. https://doi.org/10.3390/app7040328

  14. Manring ND, Mehta VS, Kuehn JL, Nelson BE (2015) Sensitivity analysis for the operating efficiency of an axial piston pump. In: Proceedings of the ASME/BATH 2015 symposium on fluid power and motion control, Chicago, Illinois, USA, October 12–14, 2015. V001T01A017. ASME. https://doi.org/10.1115/FPMC2015-9524

  15. Manring ND (2016) Mapping the efficiency for a hydrostatic transmission. J Dyn Syst Meas Control 138:1–8. https://doi.org/10.1115/1.4032289

    Article  Google Scholar 

  16. Brogan A, Sturtevant K (2016) Improving variable-speed pumping control to maximize savings, vol 122

  17. Hu D, Ding S, Zhu H, Xu B, Yang H (1995) Velocity-tracking control of the variable-speed controlled hydraulic system: using compound algorithm of PD & feedforward-feedback control, pp 1109–1115. https://doi.org/10.1109/ICMTMA.2011.846

  18. Calıskan H, Balkan T, Platin BE (2009) Hydraulic position control system with variable speed pump, ASME Paper No. DSCC2009-2693

  19. Manring ND, Fales RC (2019) Hydraulic control systems. Wiley, Hoboken

    Book  Google Scholar 

  20. Ali HH, Fales RC, Manring ND (2019) Modeling and control design for an inlet metering valve-controlled pump used to control actuator velocity via H-infinity and two-degrees-of- freedom methods. https://doi.org/10.1115/1.4044182

  21. Franklin GF, David Powell J, Emami-Naeini A (2014) Feedback control of dynamic systems. Pearson, New York

    MATH  Google Scholar 

  22. Matušů R, Şenol B, Yeroğlu C (2017) Linear systems with unstructured multiplicative uncertainty: modeling and robust stability analysis. PLoS ONE 12(7):e0181078

    Article  Google Scholar 

  23. Carpenter R, Fales R (2012) Mixed sensitivity H-infinity control design with frequency domain uncertainty modeling for a pilot operated proportional control valve. ASME Paper No. DSCC2012-MOVIC2012-8845

  24. Fales R (2010) Uncertainty modeling and predicting the probability of stability and performance in the manufacture of dynamic systems. ISA Trans 49(4):528–534. https://doi.org/10.1016/j.isatra.2010.02.003

    Article  Google Scholar 

  25. Ali H, Fales R (2020) Robust control design for an inlet metering velocity control system of a linear hydraulic actuator. Int J Fluid Power. https://doi.org/10.13052/ijfp1439-9776.2113

    Article  Google Scholar 

  26. Skogestad S, Postlethwaite I (2005) Multivariable feedback control: analysis and design, 2nd edn. Wiley, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Directorate of Reconstruction and Projects, Ministry of Higher Education and Scientific Research, Baghdad, Iraq

    Hasan H. Ali

  2. Department of Mechanical Engineering, Al-Nahrain University, Baghdad, Iraq

    Ahmed W. Mustafa

  3. Al-Furat Al-Awsat Technical University, Najaf, Iraq

    Fawaz F. Al-Bakri

Authors
  1. Hasan H. Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed W. Mustafa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fawaz F. Al-Bakri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hasan H. Ali.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ali, H.H., Mustafa, A.W. & Al-Bakri, F.F. A new control design and robustness analysis of a variable speed hydrostatic transmission used to control the velocity of a hydraulic cylinder. Int. J. Dynam. Control 9, 1078–1091 (2021). https://doi.org/10.1007/s40435-020-00716-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-020-00716-w

Keywords

  • Hydraulic actuator
  • Velocity control
  • Variable speed drives
  • Robustness
  • Uncertainty
  • H-infinity