Velocity control of single-rod hydrostatic actuators: component sizing and controller design by Moosa Rafiq A Thesis submitted to Faculty of Graduate Studies in partial fulfillment of the requirements for the degree of Master of Science Department of Mechanical Engineering University of Manitoba Winnipeg, Manitoba, Canada Copyright © 2018 by Moosa Rafiq i Abstract Pump-controlled hydraulic actuation of single-rod actuators is more challenging than double-rod actuators due to difference in areas on two sides of single-rod actuators and a need to compensate for differential flow. The performance of a single-rod pump-controlled hydraulic circuit can be significantly affected by variations in load, velocity and circuit design. Designing a simple-to- implement velocity controller for such hydraulic configurations is challenging under these conditions. This thesis presents velocity control of two typical hydraulic circuits; one is commonly used while the other is a novel design. Two issues involved are controller design and component sizing. The design of velocity controllers is based on Quantitative Feedback Theory (QFT) as the design criteria are graphically illustrated for whole range of plant uncertainties in this design procedure. In order to design QFT controllers for closed-loop velocity control of pump- controlled single-rod hydraulic actuators, smooth open loop performance of hydraulic circuit becomes important. Hence component sizing, i.e., choosing optimal hydraulic components and having an optimal hydraulic design becomes necessary. Hence, a methodology to choose hydraulic components and hence improve system performance is proposed. First, a mathematical model of hydraulic circuit is developed, which is later used in simulations. Next, initial values of selected parameters of circuit components (pilot operated check valves and counterbalance valves) to be used in system are chosen based on manufacturer’s specifications, experimental data and conservative judgement. This is followed by choosing few parameters which need to be optimised. Next, an optimisation algorithm is used on the simulation model to optimize parameters chosen based on an optimization criteria. In optimization, particle swarm optimization (PSO) and modified Nelder-Mead (MNM) algorithms are used to obtain smooth, least jerky system performance. Next QFT Controllers are designed based on uncertainties found where families of transfer functions are to be obtained. For this purpose, system identification is used in order to obtain frequency responses from measured data and hence uncertainties. All the development reported ii in this research is experimentally validated. First hydraulic circuit is a commonly used circuit incorporating pilot-operated check valves, while as the second novel circuit uses counterbalance valves. A multistep polynomial input and an alternating step input under different loading conditions is used. In this research a maximum of ten parameter optimization is used. iii Acknowledgments First I would like to thank my advisor, Professor Nariman Sepehri, for his supervision, advice and support. From him, I learnt a lot about problem solving approach and presenting my research. His expertise and knowledge has been a great help in my Master’s program. I would also like to thank the members of dissertation committee: Dr. Q. Peng and Dr. U. Anakkage for their help and support. I would like to thank Ahmed Imam at fluid power and tele-robotics research laboratory U of M for his help, valuable suggestions and friendship. I would like to thank Khurram Butt for his help and support. I would like to thank Ali Maddahi for his support during my research. I would like to thank G.Ren for being a wonderful friend. I would like to thank Y.Cai, George, X.Kaiwen and M.Maziar for always being there for my help. I wish them all the best for their future endeavors. Apart from being colleagues, they have been my best friends throughout my stay at U of M! I would like to thank my family, especially my parents, who have always been there for my support. I would also like to thank my friends who have helped and supported me always. Thanks! iv Table of Contents Abstract…………………………………………………………………………………...…ii Acknowledgments…………………………………………………………………………..iv Table of contents…………………………………………………………………………….v 1 Introduction ............................................................................................................................. 1 1.1. Problem statement ............................................................................................................ 1 1.2. Methodology (Proposed solution) .................................................................................... 1 1.3. Objectives of this thesis.................................................................................................... 2 1.4. Thesis outline ................................................................................................................... 3 2 Single Rod Hydrostatic Actuation: Design, Sizing and Control ............................................. 4 3 Modelling of single-rod hydraulic circuit actuations ............................................................ 10 3.1. Configuration 1 .............................................................................................................. 10 3.2. Configuration 2 .............................................................................................................. 13 4 Description of Test Rig.......................................................................................................... 17 5 Hydraulic component sizing ................................................................................................. 22 5.1. Proposed methodology for selection of components ..................................................... 22 5.2. Initial component selection ............................................................................................ 22 5.3. Objective function and optimization algorithms ............................................................ 27 5.4. Proposed Optimization Criteria ...................................................................................... 31 5.4.1 Configuration 1 ....................................................................................................... 32 5.4.2 Configuration 2 ....................................................................................................... 35 v 5.5. Results ............................................................................................................................ 37 5.5.1 Configuration 1 ....................................................................................................... 38 5.5.2 Configuration 2 ....................................................................................................... 51 5.5.3 Experimental evaluation ......................................................................................... 57 5.6. Summary ........................................................................................................................ 67 6 Controller Design .................................................................................................................. 69 6.1. Concept of Quantitative feedback theory ....................................................................... 69 6.2. Design of QFT Controller for hydraulic circuit with configuration 1............................ 70 6.2.1 System identification for family of linear transfer functions .................................. 72 6.2.2 Verification of results ............................................................................................. 80 6.2.3 Family of transfer functions .................................................................................... 80 6.2.4 Bode plots and step response .................................................................................. 81 6.2.5 Controller Design 1 (Procedure) ............................................................................. 82 6.3. Simulation results ........................................................................................................... 88 6.4. Experimental evaluation ................................................................................................. 90 6.5. Design of QFT Controller for hydraulic circuit with configuration 2............................ 92 6.5.1 System identification for family of linear transfer functions ................................. 93 6.5.2 Verification of results ............................................................................................. 99 6.5.3 Family of transfer functions .................................................................................. 100 6.5.4 Bode plots and step response ................................................................................ 101 6.5.5 Controller Design 2 ............................................................................................... 102 6.6. Simulation results ......................................................................................................... 107 6.7. Experimental evaluation ............................................................................................... 109 6.8. Summary ...................................................................................................................... 113 vi 7 Conclusions ......................................................................................................................... 115 7.1. Contributions made in this thesis ................................................................................. 115 7.2. Future work .................................................................................................................. 117 vii List of figures Figure 2.1 Typical pump-controlled actuation: (a) double rod system; (b) single-rod system. ...... 5 Figure 2.2 Hydraulic circuit configurations: (a) hydraulic circuit using 3-way 2-position shuttle valve; (b) hydraulic circuit using 3-way 3-position shuttle valve with two regulating valves; (c) two pump control of a single-rod actuator shown; (d) hydraulic circuit using pilot check operated valves; (e) hydraulic circuit using counterbalance valves. ............................................................. 7 Figure 3.1 Circuit working with pilot-operated check valves (Configuration 1). ........................ 10 Figure 3.2 Circuit working with counterbalance valves (Configuration 2): 1, 2. Piot operated check valves A and B; 3, 4. Pilot assisted areas of counter balance valves A and B; 5, 6. Check valve areas of counter balance valves A and B............................................................................. 13 Figure 3.3 Areas shown in a counterbalance valve. ...................................................................... 15 Figure 4.1 Experimental test rig: Main components; (1) frame; (2) load; (3) single rod actuator; (4) variable displacement pump; (5) charge pressure unit; (6) pressure transducers; (7) displacement sensors. .................................................................................................................... 18 Figure 4.2 Four quadrants operation for test rig. .......................................................................... 19 Figure 4.3 Flow directions of hydraulic circuit in four quadrants of operation. ........................... 20 Figure 5.1 Pressure drop with flow graph for CBV [reproduced from catalogue www.sunhydraulics.com/model]. ................................................................................................. 24 Figure 5.2 Step response of circuit at high load 368 kg (configuration 2): (a) control signal; (b) pressures at pump ports ‘a’(solid) and ‘b’ (dotted) in the configuration 1; (c) pressures at actuator ports ‘a’(solid) and ‘b’ (dotted) in the configuration 1; (d) pressure difference with time across CBV valves ‘a’ (solid) and ‘b’ side (dotted) of configuration 1; (e) pressures at pump port(solid) and actuator port(dotted) on A side of configuration 1; (f) pressures at pump port(solid) and actuator port(dotted) on B side of configuration 1........................................................................ 26 viii Figure 5.3 Objective function with iterations at various restarts (configuration 1): (a) Zero kg mass attached, low load (𝑝𝑐𝑟1 = 2.38e5 Pa, 𝑝𝑐𝑟2 = 4.89e5 Pa, 𝑝𝑚𝑎𝑥1 = 10.69e5 Pa, 𝑝𝑚𝑎𝑥2 = 6.71e5 Pa, 𝐾𝑝𝑖𝑙𝑜𝑡1= 3.81, 𝐾𝑝𝑖𝑙𝑜𝑡2 = 4.39, 𝐴𝑚𝑎𝑥1 = 0.34e-4 𝑚2, 𝐴𝑚𝑎𝑥2 = 0. 19e-4 𝑚2, 𝑘1= 2.94e-10, 𝑘2= 3.03e-10); (b) 245 kg mass attached, high load (𝑝𝑐𝑟1 = 0.39e5 Pa, 𝑝𝑐𝑟2 = 0.31e5 Pa, 𝑝𝑚𝑎𝑥1 = 9.32e5 Pa, 𝑝𝑚𝑎𝑥2 = 5.69e5 Pa, 𝐾𝑝𝑖𝑙𝑜𝑡1= 4.6, 𝐾𝑝𝑖𝑙𝑜𝑡2 = 4.2, 𝐴𝑚𝑎𝑥1 = 0.31e-4 𝑚2, 𝐴𝑚𝑎𝑥2 = 0. 27e-4 𝑚2, 𝑘1= 3.42e-10, 𝑘2= 3.35e-10 ). ......................................... 34 Figure 5.4 Objective function with iterations at various restarts (configuration 2) for optimized values [2.01, 1.53]. ........................................................................................................................ 37 Figure 5.5 Response of multistep polynomial input (configuration 1) before optimization , mass 245 kg attached (pilot ratio of 3 for both sides): (a) control signal (V); (b) actuator displacement (m); (c) actuator velocity; (d) zoomed in a region of actuator velocity. ....................................... 38 Figure 5.6 Response of multistep polynomial input (configuration 1) after optimization , mass 245 kg attached (pilot ratio 4.99 and 3.65): (a) control signal (V); (b) actuator displacement (m); (c) actuator velocity; (d) zoomed in a region of actuator velocity. ............................................... 40 Figure 5.7 Response of multistep polynomial input (configuration 1) before optimization , mass 41 kg (pilot ratio of 3 for both sides): (a) actuator velocity; (b) actuator acceleration; (c) actuator jerk; (d) pump pressures for side ‘a’(solid) and side ‘b’ (dotted); (e) areas of POCV side ‘a’(solid) and side ‘b’ (dotted). ..................................................................................................... 42 Figure 5.8: Response of multistep polynomial input (configuration 1) after optimization , mass 41 kg attached (pilot ratio 3.42 and 1.52): (a) actuator velocity; (b) actuator acceleration; (c) actuator jerk; (d) pump pressures for side ‘a’ (solid) and side ‘b’ (dotted); (e) areas of POCV side ‘a’(solid) and side ‘b’ (dotted) . .................................................................................................... 43 Figure 5.9: Response of multistep polynomial input (configuration 1) after optimization , mass 245 kg attached (𝑝𝑐𝑟1 = 0.39e5 Pa, 𝑝𝑐𝑟2 = 0.31e5 Pa, 𝑝𝑚𝑎𝑥1 = 9.32e5 Pa, 𝑝𝑚𝑎𝑥2 = 5.69e5 Pa, 𝐾𝑝𝑖𝑙𝑜𝑡1= 4.6, 𝐾𝑝𝑖𝑙𝑜𝑡2 = 4.2, 𝐴𝑚𝑎𝑥1 = 0.31e-4 𝑚2, 𝐴𝑚𝑎𝑥2 = 0. 27e-4 𝑚2, 𝑘1= 3.42e- 10, 𝑘2= 3.35e-10 ): (a) actuator velocity; (b) zoomed in a region of actuator velocity; (c) zoomed in a region of actuator velocity. .................................................................................................... 44 Figure 5.10: Response of multistep polynomial input (configuration 1) after optimization , mass 41 kg attached (𝑝𝑐𝑟1 = 2.38e5 Pa, 𝑝𝑐𝑟2 = 4.89e5 Pa, 𝑝𝑚𝑎𝑥1 = 10.69e5 Pa, 𝑝𝑚𝑎𝑥2 = 6.71e5 ix Pa, 𝐾𝑝𝑖𝑙𝑜𝑡1= 3.81, 𝐾𝑝𝑖𝑙𝑜𝑡2 = 4.39, 𝐴𝑚𝑎𝑥1 = 0.34e-4 𝑚2, 𝐴𝑚𝑎𝑥2 = 0. 19e-4 𝑚2, 𝑘1= 2.94e-10, 𝑘2= 3.03e-10): (a) actuator velocity; (b) actuator acceleration; (c) actuator jerk; (d) pump pressures for side ‘a’(solid) and side ‘b’ (dotted); (e) areas of POCV side ‘a’(solid) and side ‘b’ (dotted); (f) zoomed in a region of Areas of POCV. ....................................................... 46 Figure 5.11 Response of alternating step input (configuration 1) before optimization, mass 245 kg (pilot ratio of 3 for both sides): (a) control signal (V); (b) actuator displacement(m); (c) actuator velocity; (d) zoomed in a region of actuator velocity. .................................................... 47 Figure 5.12 Response of alternating step input (configuration 1) after using optimized parameters, mass 245 kg attached (𝑝𝑐𝑟1 = 0.39e5 Pa, 𝑝𝑐𝑟2 = 0.31e5 Pa, 𝑝𝑚𝑎𝑥1 = 9.32e5 Pa, 𝑝𝑚𝑎𝑥2 = 5.69e5 Pa, 𝐾𝑝𝑖𝑙𝑜𝑡1= 4.6, 𝐾𝑝𝑖𝑙𝑜𝑡2 = 4.2, 𝐴𝑚𝑎𝑥1 = 0.31e-4 𝑚2, 𝐴𝑚𝑎𝑥2 = 0. 27e-4 𝑚2, 𝑘1= 3.42e-10, 𝑘2= 3.35e-10 ): (a) control signal (V); (b)actuator displacement (m) ; (c) actuator velocity; (d) zoomed in a region of actuator velocity. .................................................... 49 Figure 5.13 Response of multistep polynomial input (configuration 2) before optimization, mass 245 kg attached: (a) actuator displacement (m); (b) actuator velocity; (c) zoomed in a region of actuator velocity. ........................................................................................................................... 51 Figure 5.14: Response of multistep polynomial input (configuration 2) after using optimized parameters, mass 245 kg attached (𝑠3 = 2.07, 𝑠4 = 0.99, 𝐾𝑝𝑖𝑙𝑜𝑡3 = 1.04, 𝐾𝑝𝑖𝑙𝑜𝑡4 = 0.80): (a) actuator velocity; (b) zoomed in a region of actuator velocity; (c) actuator acceleration; (d) zoomed in a region of actuator acceleration; (e) actuator jerk; (f) zoomed in a region of actuator jerk. ............................................................................................................................................... 53 Figure 5.15 Response of multistep polynomial input (configuration 2) before optimization, mass 41 kg attached: (a) actuator velocity; (b) zoomed in a region of actuator velocity; (c) zoomed in a region of actuator velocity. ........................................................................................................ 54 Figure 5.16: Response of multistep polynomial input (configuration 2) after optimization, mass 41 kg attached (𝑠3 = 1.5, 𝑠4 = 1.2, 𝐾𝑝𝑖𝑙𝑜𝑡3 = 1.9, 𝐾𝑝𝑖𝑙𝑜𝑡4 = 1.02): (a) actuator velocity; (b) zoomed in a region of actuator velocity; (c) zoomed in a region of actuator velocity......................................................................................................................................... 56 x