A new control design and robustness analysis of a variable speed hydrostatic transmission used to control the velocity o
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A new control design and robustness analysis of a variable speed hydrostatic transmission used to control the velocity of a hydraulic cylinder Hasan H. Ali1
· Ahmed W. Mustafa2 · Fawaz F. Al-Bakri3
Received: 16 July 2020 / Revised: 26 September 2020 / Accepted: 16 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Hydraulic actuator · Velocity control · Variable speed drives · Robustness · Uncertainty · H-infinity
List of symbols A AA AB b GF E Fd Fo Gp C
B
Maximum low frequency (steady state) error Cross sectional area of side A of the actuator Cross sectional area of side B of the actuator Viscous Drag coefficient Transfer function of the disturbance force Error signal Disturbance force Spring preload Transfer function of the plant Transfer function of the controller Hasan H. Ali [email protected]
1
Directorate of Reconstruction and Projects, Ministry of Higher Education and Scientific Research, Baghdad, Iraq
2
Department of Mechanical Engineering, Al-Nahrain University, Baghdad, Iraq
3
Al-Furat Al-Awsat Technical University, Najaf, Iraq
Kp Ki Kd Kl lI M m Pp p Qp S Vo Vr vc w wI wp wu y Z
Gain of the proportional part of the controller gain Gain of the integral part of the controller Gain of the derivative part of the controller gain Leakage coefficient Multiplicative parametric uncertainty Maximum high frequency error Load mass Pump pressure Generalized plant Pump volumetric flow rate Sensitivit
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