ii ACKNOWLEDGMENTS The project is supported in part by the National Science Foundation under the CAREER grant CMS The fund from the Purdue El

Transcription

1 ENERGY-SAVING CONTROL OF ELECTROHYDRAULIC SYSTEMS WITH OVER-REDUNDANT PROGRAMMABLE VALVES A Thesis Submitted to the Faculty of Purdue University by Christopher C. DeBoer In Partial Fulfillment ofthe Requirements for the Degree of Master of Science in Mechanical Engineering August 21

2 ii ACKNOWLEDGMENTS The project is supported in part by the National Science Foundation under the CAREER grant CMS The fund from the Purdue Electro-Hydraulic Research Center supported by the Caterpillar Inc. and the donation of cartridge valves by Vickers Inc. for setting up the programmable valves used in the experiments is gracefully acknowledged. Much gratitude is due to my advisor, Dr. Bin Yao, for his help and continued support as well as to many friends and family for their encouragement and support. Many thanks go to my patient and loving wife, Kara, and gratitude to God for the strength and ability tocomplete this work.

3 iii TABLE OF CONTENTS Page LIST OF TABLES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vi LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vii ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xi 1 INTRODUCTION : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 EXPERIMENTAL SETUP : : : : : : : : : : : : : : : : : : : : : : : : : : : Experimental Systems : : : : : : : : : : : : : : : : : : : : : : : : : : Mechanical Linkages : : : : : : : : : : : : : : : : : : : : : : : Pump : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Electro-Hydraulic Valves : : : : : : : : : : : : : : : : : : : : : Servo and Proportional Valves : : : : : : : : : : : : : Programmable Valves : : : : : : : : : : : : : : : : : Instrumentation : : : : : : : : : : : : : : : : : : : : : : : : : : Control and Data Acquisition Hardware and Software : : : : : Dynamic Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Robot Manipulator Model : : : : : : : : : : : : : : : : : : : : Hydraulic Cylinder Model : : : : : : : : : : : : : : : : : : : : Valve Models : : : : : : : : : : : : : : : : : : : : : : : : : : : System Identification : : : : : : : : : : : : : : : : : : : : : : : : : : : Model Validation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 23 3 PRESSURE FEEDBACK CONTROLLER : : : : : : : : : : : : : : : : : : Pressure Feedback Control Development Model : : : : : : : : : : : : Controller Design : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Cylinder Level Controller : : : : : : : : : : : : : : : : : : : : : 32

4 iv Valve Level Controller : : : : : : : : : : : : : : : : : : : : : : Simulation Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : Experimental Results : : : : : : : : : : : : : : : : : : : : : : : : : : : Conclusions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 4 ENERGY SAVING ADAPTIVE ROBUST CONTROL : : : : : : : : : : : Problem Formulation and Dynamic Model : : : : : : : : : : : : : : : Energy Efficient Adaptive Robust Controller Design : : : : : : : : : : Task Level: Valve Utilization : : : : : : : : : : : : : : : : : : Valve Level: Pressure Controller Design : : : : : : : : : : : : Valve Level: Adaptive Robust Controller Design : : : : : : : : Design Model and Issues to be Addressed : : : : : : ARC Controller Design : : : : : : : : : : : : : : : : Simulation Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : Experimental Results : : : : : : : : : : : : : : : : : : : : : : : : : : : Conclusions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 69 5 CONCLUSIONS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Results : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Contributions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Future Work : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 73 LIST OF REFERENCES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 74 APPENDICES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 76 Appendix A: Experimental Setup : : : : : : : : : : : : : : : : : : : : : : : 76 A.1 Dynamic Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 77 A.2 Joint Angles : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 A.3 System Identification : : : : : : : : : : : : : : : : : : : : : : : : : : : 83 A.4 Model Validation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 83 Appendix B: Pressure Feedback Controller : : : : : : : : : : : : : : : : : : 88 B.1 Pressure Feedback Control Development Model : : : : : : : : : : : : 89 B.2 Pressure Feedback Control Design : : : : : : : : : : : : : : : : : : : : 92

5 v B.2..3 Trajectory Modification : : : : : : : : : : : : : : : : 92 B.2.1 Inverse Valve Mappings : : : : : : : : : : : : : : : : : : : : : 94 B.2.2 Valve Level Controller Design : : : : : : : : : : : : : : : : : : 96 B.2.3 Controller Tuning : : : : : : : : : : : : : : : : : : : : : : : : : 97 B.3 Pressure Feedback Simulation Results : : : : : : : : : : : : : : : : : : 1 B.4 Experimental Results : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 Appendix C: Adaptive Robust Controller : : : : : : : : : : : : : : : : : : : 18 C.1 Adaptive Robust Controller Simulation Gains : : : : : : : : : : : : : 19 C.2 Adaptive Robust Controller Simulation Results : : : : : : : : : : : : 11 C.3 Adaptive Robust Controller Experiment Gains : : : : : : : : : : : : : 114 C.4 Adaptive Robust Controller Experimental Results : : : : : : : : : : : 115

6 vi LIST OF TABLES Table Page 2.1 Cylinder Physical Parameters : : : : : : : : : : : : : : : : : : : : : : : : Function Selection : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Cylinder Functions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 34 B.1 Operating Points : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 B.2 Trajectory Generation Parameters : : : : : : : : : : : : : : : : : : : : : : 93 B.3 Controller Parameters : : : : : : : : : : : : : : : : : : : : : : : : : : : : 97 B.4 Pressure Feedback Simulations : : : : : : : : : : : : : : : : : : : : : : : : 1 B.5 Pressure Feedback Experiments : : : : : : : : : : : : : : : : : : : : : : : 14 C.1 Adaptive Robust Controller Gains : : : : : : : : : : : : : : : : : : : : : : 19 C.2 Adaptive Robust Controller Simulations : : : : : : : : : : : : : : : : : : 11 C.3 Adaptive Robust Controller Experiment Gains : : : : : : : : : : : : : : : 114 C.4 Adaptive Robust Controller Experiments : : : : : : : : : : : : : : : : : : 115

7 vii LIST OF FIGURES Figure Page 1.1 Dual Valve Meter-In Meter-Out : : : : : : : : : : : : : : : : : : : : : : : Four Valve Meter-In Meter-Out : : : : : : : : : : : : : : : : : : : : : : : Regeneration Flow : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Programmable Valve Layout : : : : : : : : : : : : : : : : : : : : : : : : : Experimental Setup : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Hydraulic Pump : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Programmable Valve Layout : : : : : : : : : : : : : : : : : : : : : : : : : Programmable Valves : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Electro-hydraulic Robot Arm : : : : : : : : : : : : : : : : : : : : : : : : Flowmeter Test Stand : : : : : : : : : : : : : : : : : : : : : : : : : : : : Schematic of Sensors, Data and Control Hardware : : : : : : : : : : : : : Control and Data Acquisition Hardware : : : : : : : : : : : : : : : : : : Coordinate Systems, Joints and Physical Parameters : : : : : : : : : : : Programmable Valve Layout : : : : : : : : : : : : : : : : : : : : : : : : : Valve 1:HECT Flow Mapping f v1 ( P v1 ;x v1 ) : : : : : : : : : : : : : : : : Boom -No Load : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Cylinder Model : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Controls Development Model : : : : : : : : : : : : : : : : : : : : : : : : Valve 1:HECT Inverse Mapping : : : : : : : : : : : : : : : : : : : : : : : Boom Extend-Resistive Root Locus : : : : : : : : : : : : : : : : : : : : : Boom Extend-Resistive Step Response : : : : : : : : : : : : : : : : : : : Boom Sim: No Load 1% Step Open Loop and Pres Fbk : : : : : : : : Boom Sim: Loaded 1% Step Open Loop and Pres Fbk : : : : : : : : : 4

8 viii 3.8 Boom Exp: No Load 1% Step Open Loop and Pres Fbk : : : : : : : : Boom Exp: Loaded 1% Step Open Loop and Pres Fbk : : : : : : : : : Extend Resistive : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Extend Overrunning : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Extend Overrunning Regeneration : : : : : : : : : : : : : : : : : : : : : Retract Resistive : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Retract Overrunning : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Retract Overrunning Regeneration : : : : : : : : : : : : : : : : : : : : : Point to Point Trajectories : : : : : : : : : : : : : : : : : : : : : : : : : : Boom ARC Sim: Slow Traj. No Load : : : : : : : : : : : : : : : : : : : : Boom ARC Sim: Slow Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : Standard Boom ARC Sim: Slow Traj. No Load : : : : : : : : : : : : : : Standard Boom ARC Sim: Slow Traj. 5 lb. Load : : : : : : : : : : : : Boom ARC Exp: Slow Traj. No Load : : : : : : : : : : : : : : : : : : : Boom ARC Exp: Slow Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : 69 A.1 Swing Joint Configuration : : : : : : : : : : : : : : : : : : : : : : : : : : 8 A.2 Boom Joint Configuration : : : : : : : : : : : : : : : : : : : : : : : : : : 81 A.3 Stick Joint Configuration : : : : : : : : : : : : : : : : : : : : : : : : : : : 82 A.4 Valve 1:HECT Flow Mapping f v1 ( P v1 ;x v1 ) : : : : : : : : : : : : : : : : 83 A.5 Valve 2:HEPC Flow Mapping f v2 ( P v2 ;x v2 ) : : : : : : : : : : : : : : : : 83 A.6 Valve 3:REGENPC Flow Mapping f v3 ( P v3 ;x v3 ) : : : : : : : : : : : : : 83 A.7 Valve 3:REGENCT Flow Mapping f v3 ( P v3 ;x v3 ) : : : : : : : : : : : : : 83 A.8 Valve 4:REPC Flow Mapping f v4 ( P v4 ;x v4 ) : : : : : : : : : : : : : : : : 84 A.9 Valve 5:RECT Flow Mapping f v5 ( P v5 ;x v5 ) : : : : : : : : : : : : : : : : 84 A.1 Swing No Load : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 84 A.11 Swing Loaded : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 85 A.12 Boom No Load : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 85 A.13 Boom Loaded : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 86 A.14 Stick No Load : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 87

9 ix A.15 Stick Loaded : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 87 B.1 Boom Equivalent Mass-No Load : : : : : : : : : : : : : : : : : : : : : : : 89 B.2 Boom Equivalent Mass-Loaded : : : : : : : : : : : : : : : : : : : : : : : 89 B.3 Boom Equivalent Gravity-No Load : : : : : : : : : : : : : : : : : : : : : 91 B.4 Boom Equivalent Gravity-Loaded : : : : : : : : : : : : : : : : : : : : : : 91 B.5 Valve 1:HECT Inverse Mapping : : : : : : : : : : : : : : : : : : : : : : : 94 B.6 Valve 2:HECT Inverse Mapping : : : : : : : : : : : : : : : : : : : : : : : 94 B.7 Valve 3:REGENPC Inverse Mapping : : : : : : : : : : : : : : : : : : : : 94 B.8 Valve 3:REGENCT Inverse Mapping : : : : : : : : : : : : : : : : : : : : 94 B.9 Valve 4:REPC Inverse Mapping : : : : : : : : : : : : : : : : : : : : : : : 95 B.1 Valve 5:RECT Inverse Mapping : : : : : : : : : : : : : : : : : : : : : : : 95 B.11 Boom Extend-Resistive Root Locus : : : : : : : : : : : : : : : : : : : : : 97 B.12 Boom Extend-Resistive Step Response : : : : : : : : : : : : : : : : : : : 98 B.13 Boom Retract-Resistive Root Locus : : : : : : : : : : : : : : : : : : : : : 98 B.14 Boom Retract-Resistive Step Response : : : : : : : : : : : : : : : : : : : 99 B.15 Boom Sim: No Load 3% Step Open Loop and Pres Fbk : : : : : : : : : 11 B.16 Boom Sim: Loaded 3% Step Open Loop and Pres Fbk : : : : : : : : : : 11 B.17 Boom Sim: No Load 7% Step Open Loop and Pres Fbk : : : : : : : : : 12 B.18 Boom Sim: Loaded 7% Step Open Loop and Pres Fbk : : : : : : : : : : 12 B.19 Boom Sim: No Load 1% Step Open Loop and Pres Fbk : : : : : : : : 13 B.2 Boom Sim: Loaded 1% Step Open Loop and Pres Fbk : : : : : : : : : 13 B.21 Boom Exp: No Load 3% Step Open Loop and Pres Fbk : : : : : : : : : 15 B.22 Boom Exp: Loaded 3% Step Open Loop and Pres Fbk : : : : : : : : : : 15 B.23 Boom Exp: No Load 7% Step Open Loop and Pres Fbk : : : : : : : : : 16 B.24 Boom Exp: Loaded 7% Step Open Loop and Pres Fbk : : : : : : : : : : 16 B.25 Boom Exp: No Load 1% Step Open Loop and Pres Fbk : : : : : : : : 17 B.26 Boom Exp: Loaded 1% Step Open Loop and Pres Fbk : : : : : : : : : 17 C.1 Boom ARC Sim: Slow Traj. No Load : : : : : : : : : : : : : : : : : : : : 111 C.2 Boom ARC Sim: Slow Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : 111

10 x C.3 Boom ARC Sim: Fast Traj. No Load : : : : : : : : : : : : : : : : : : : : 112 C.4 Boom ARC Sim: Fast Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : 112 C.5 Standard Boom ARC Sim: Slow Traj. No Load : : : : : : : : : : : : : : 113 C.6 Standard Boom ARC Sim: Slow Traj. 5 lb. Load : : : : : : : : : : : : 113 C.7 Boom ARC Exp: Slow Traj. No Load : : : : : : : : : : : : : : : : : : : 115 C.8 Boom ARC Exp: Slow Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : 116 C.9 Boom ARC Exp: Fast Traj. No Load : : : : : : : : : : : : : : : : : : : : 116 C.1 Boom ARC Exp: Fast Traj. 5 lb. Load : : : : : : : : : : : : : : : : : : 117

11 xi ABSTRACT DeBoer, Christopher C., M.S.M.E., Purdue University, August, 21. Energy-Saving Control of Electrohydraulic Systems with Over-Redundant Programmable Valves. Major Professor: Dr. Bin Yao, School of Mechanical Engineering. An investigation into the potential use of a programmable electro-hydraulic valve for high performance tracking and high energy efficiency is conducted in this study. The energy-saving utilization of the programmable valve is investigated as well as the control methods with both limited and full state feedback availability. A three degrees-of-freedom electrohydraulic robot arm is used as a case study. The programmable valve used in this study is a unique combination of five proportional cartridge valves connected in such a way that the meter-in and meter-out flows of a hydraulic cylinder can be independently controlled by four of the valves as well as a true cross port flow controlled by the fifth valve. The programmable valve decouples the meter-in and meter-out flows, which in turn allows tremendous control flexibility. The flexibility can be used to increase the energy efficiency in a number of motion and loading conditions by utilizing the potential and kinetic energy of the load at the cost of coordinating the control of five individual valves. A simple control scheme using pressure feedback only is first designed to control the hydraulic cylinder velocities. The design mimics the situation on many industrial backhoes and excavators that lack cylinder velocity feedback. The effectiveness of this controller is verified through simulation and experimental results. The results show that velocity tracking and energy efficiency can be improved through the use of pressure feedback only. A complex control algorithm is then developed to control the boom motion when full state feedback isavailable. The controller utilizes an adaptive robust controller for

12 xii motion tracking and a pressure controller to provide energy efficiency. Simulation and experimental results are used to demonstrate that high performance motion tracking and energy efficiency can be obtained with the use of a programmable valve. The use of a programmable valve has been shown to be very effective in obtaining significant gains in tracking control and energy efficiency in operations typically seen in industrial hydraulic equipment. These gains have been attained with the availability of both limited feedback as well as full state feedback.

13 1 1. INTRODUCTION The use of hydraulic systems is widespread throughout industry due to the large power to size ratio. Hydraulic systems are used very heavily in the construction and agricultural industries. Hydraulics are well suited for these applications. Traditionally the hydraulics on most equipment was controlled by a lever mechanically connected to some sort of spool valve, resulting in crude open loop control. In recent years, the trend is to replace the mechanical valve with an electrically controlled valve. The result is that the valve can be located remotely from the operator, improving safety and comfort as well as increasing mechanical design flexibility [1]. The use of electrohydraulic valves means that sophisticated electronic control can be applied to control the system. The control of a hydraulic system is far from trivial, due to the highly nonlinear hydraulic dynamics [2]. In addition, parameters such as the bulk modulus change drastically with changing oil temperature and component wear. In the case of construction and agricultural machinery, the mechanical system driven by the hydraulic cylinder may be highly nonlinear itself. Typically, the parameters of the mechanical linkages may vary drastically and are usually unknown, such as the external payload. In addition, significant uncertain nonlinearities such as external disturbances, leakages and friction are unknown and cannot be modeled accurately [3]. These factors result in significant difficulties in controlling a hydraulic system. In the past, much of the control work has been done using linear control techniques and feedback linearization [3]. Linear controllers are inherently limited in their ability to handle nonlinear systems and as a result the performance can be improved but not to the level of a nonlinear controller. One nonlinear control method used effectively is a nonlinear model-based adaptive robust controller as developed by Yao and Bu

14 2 [3, 4, 5, 6, 7, 8]. This type of controller has been proven to have a guaranteed output tracking transient performance and final tracking accuracy and also, asymptotic output tracking in the case of parametric uncertainties only. The advent of electrohydraulic valves and the incorporation of complex digital control has significantly improved the performance of hydraulic system. However, with a typical four-way directional control valve only one of the two cylinder states, (pressures), is completely controllable and there is a one-dimensional internal dynamics. Although the one-dimensional dynamics is shown to be stable [3], it cannot be modified by any control strategy. The result is that while high performance tracking can be attained, simultaneous high levels of energy efficiency cannot. The uncontrollable state is due to the fact that the meter-in and meter-out orifices are mechanically linked together in a typical directional control valve. This is a fundamental drawback of typical four-way directional control valves. If this link were to be broken the flexibility of the valve could be drastically increased, making the way for significant improvements in hydraulic efficiency [9]. The technique of breaking the mechanical linkage between the meter-in and meterout orifices is well known and has been used in heavy industrial applications for several years. Typically, the spool valve is replaced by four poppet type valves [9]. There are anumber of slight variations on this theme throughout the mobile hydraulics industry. Patents by Deere & Company, Moline, IL as well as Caterpillar Inc., Joliet, IL. and Moog Inc., East Aurora, NY attest to the potential of this technique [1, 11, 12]. One variation of independent meter-in meter-out control is proposed by Aardema [13] and makes use of two directional control valves. One valve controls the head end chamber flows and the other controls the rod end chamber flows. The meter-in and meter-out linkage is now broken. The essence of this configuration is depicted in Fig One drawback to this approach is that now two directional control valves are needed at an increased cost. The other drawback is that the control of the meter-in and meter-out flows are not completely independent. A more widely used variation is the use of four independent poppet type valves,

15 3 Cylinder Load Figure 1.1. Dual Valve Meter-In Meter-Out allowing truly independent meter-in and meter-out control. This is used in a number of studies [1, 1, 11]. Fig. 1.2 shows a typical schematic diagram. The advantage of this approach is that each metering valve is completely independent and permits a wide range of potential usages of the valve. Another advantage of poppet type valves is that the cost of each poppet valve is relatively small. The disadvantages of four independent valves is that they are much more difficult to control and coordinate. The four valve version allows a tremendous amount of flexibility of usage and control. The use of this "Smart Valve" [1] or "Independent Metering Valve" [11] provides independent control of each meter-in and meter-out ports resulting in the ability to completely control both cylinder states. This authority can be used to achieve the dual objective of tracking control and high energy efficiency. Energy efficiency can also be improved by taking advantage of regeneration flow. Regeneration flow is fluid pumped from one chamber to the other chamber using the energy of the external load. Regeneration is a highly efficient process in which little pump energy is needed. Ideally, regeneration should be used whenever the external force is in the same direction as the desired motion for attaining maximum efficiency. The four valve metering

16 4 Load Cylinder Figure 1.2. Four Valve Meter-In Meter-Out unit enables the use of regeneration flow but not to the fullest extent possible [11]. A true cross port flow is not available. The work done by Garnjost [12] introduced a number of possible methods for taking advantage of available regeneration flow. Garnjost puts forth a number of possible ways to make use of regenerative flow using one and two valves with a double acting cylinder. One such example is seen in Fig It shows a standard directional control valve with a two-way valve allowing flow from one chamber to another. This configuration takes full advantage of regeneration flow with the use of the additional valve dedicated to cross port flow. If the full potential for energy efficiency is to be realized a hydraulic system must incorporate cross port flow. The valve configuration used in this study takes the benfits of using four valve poppet type valve [11] and makes the addition of an additional valve to enable true cross port flow [12]. The result is a valve capable of fully independent meter-in, meter-out control in addition to the availability ofcross port regenerative flow. The result is a programmable valve capable of controlling each cylinder state as well as providing regeneration flow for maximum energy efficiency. The programmable valve configuration used in this study is seen in Fig. 1.4.

17 5 P S P T Figure 1.3. Regeneration Flow X L Load Q 2 P 2 Cylinder Q 1 P 1 Valve #3 Q V3 Q V1 Q V5 Valve #1 Valve #5 Q V2 Q V4 Valve #2 Valve #4 P S P T Figure 1.4. Programmable Valve Layout

18 6 This study investigates the most effective and efficient use of the programmable valve in achieving the dual objectives of high performance motion tracking and high energy efficiency. The programmable valve is implemented on an robot arm modeled after an industrial backhoe emulating a typical hydraulic system. The thesis is organized as follows. Chapter 1 provides background information on the programmable valve. The literature review looks at previous implementations of a programmable valve as well as utilization of regenerative flow. Chapter 1 outlines the motivation and direction of the thesis. Chapter 2 serves as an introduction to the mechanical system. The components of the system are discussed. Chapter 2 also develops a complex nonlinear model of the system for use in later chapters. Chapter 3 investigates the problem of improving motion control and energy efficiency with limited feedback. The pressure feedback controller design and testing is given here. Chapter 4 details the design and testing of a full state feedback controller that incorporates a pressure controller and adaptive robust controller to provide high performance motion control and high energy efficiency. Chapter 5 outlines the major contributions of the work as well as possible future investigations.

19 7 2. EXPERIMENTAL SETUP The experimental set up is an electrohydraulic robot arm located in the Ray W. Herrick Laboratories at Purdue University. The robot arm is designed to emulate a scaled-down version of an industrial excavator. This chapter describes the details of the experimental setup seen in Fig. 2.1, as well as the analytical model of the setup. The techniques used to validate the analytical model are also reported Experimental Systems Mechanical Linkages The experimental setup is built around a three degrees-of-freedom electrohydraulic robot arm as seen in Fig The configuration is very similar to an industrial hydraulic backhoe loader arm with the three degrees-of-freedom corresponding to the three main linkages of a backhoe, those linkages being the swing, boom and stick. The linkages are connected to a rigid base with a 16 lb. counterweight for stability. The linkages are driven by Parker DB 2. HXT23A electrohydraulic actuators with a 2 inch bore and strokes of 11, 1 and 12 inches for the swing, boom and stick respectively. An end effector is located at the end of the stick. The end effector allows the arm to pick updumbell-type weights as a means of loading the arm. The weights are used to simulate an excavator with a bucket loaded with material. The weight used varies from -1 pounds.

20 8 Figure 2.1. Experimental Setup Pump The electrohydraulic arm is powered by Racine constant pressure pump driven by a Baldor 1 horsepower electric motor as shown in Fig The pump is set at a maximum pump pressure of 1 psi and the maximum flow is approximately 8 gpm before the pressure begins to fall off. The pump stand also provides cooling to the hydraulic fluid via cooling water and a heat exchanger located within the tank. The oil temperature is maintained below 14 ffi Fahrenheit Electro-Hydraulic Valves The robot arm utilizes three different types of electro-hydraulic valves, a servo valve, a proportional directional control valve and a programmable valve. The valves and hoses are fitted with quick-disconnects so that any valve can be easily used on any circuit or allow connection to a stand-alone flowmeter.

21 9 Figure 2.2. Hydraulic Pump Servo and Proportional Valves The proportional valve is a Parker D3FXE1HCNBJ1 proportional directional control valve with a maximum flow of 5.5 gpm. The servo valve isaparker BD76AAAN1 servo valve with a maximum flow of 1 gpm. These two valves are used for the swing and stick circuits, which are not investigated in this work but are included for completeness and used to generate disturbances to the boom circuit Programmable Valves The programmable valve used on the boom circuit is the valve that is utilized in this work. The programmable valve is intended to replace a standard four-way valve with a number of independent two-way valves, in this case five. The use of a programmable valve allows the head-end and rod-end flows to be decoupled and independently controlled. The result is a very flexible valve with the ability to have

22 1 flow curves programmed in software instead of built into the hardware. The result is a standard valve that can be incorporated into nearly any piece of equipment and programmed specifically for the machine as well as providing a number of unique and efficient flow configurations. The valves utilized are Vickers EPV 1-A-8H-12D-U-1 2-way proportional flow control valves with Vickers C-1-2 SAE8 manifolds. The valve is a solenoid-actuated cartridge-type valve with pressure compensation. The maximum rated flow of the valve is 8 gpm and the rated bandwidth of the valve at -3 db is approximately 32 Hz with a phase lag of 67:5 ffi. The valves are driven by a pulse width modulated signal produced by the Vickers EHH-AMP-72-J-2 power plugs. The PWM frequency is 12 Hz with a dither frequency of 12 Hz. The power plugs have adjustable gain, deadband and dither currents. The configuration of the cartridge valves is the key to the functionality of the programmable valve. Fig. 2.3 shows the configuration of the five cartridge valves. Fig. 2.4 shows the implemented hardware Instrumentation The robot arm is fully instrumented to provide full state feedback for the entire system. The pump, tank and cylinder pressures are fitted with dynamic pressure sensors to provide pressure information at any point in the hydraulic system. The pump, tank and cylinders driven by the proportional directional valve and the servo valve make use of Entran EPXH-X1-2.5KP pressure transducers with an external amplifier. The Entran pressure transducers are responsive to pressure changes up to 3 KHz. The programmable valve makes use of two Omega PX63 pressure transducers with internal amplifiers. The Omega pressure transducers have a response time of 1 ms. The robot arm is equipped with LDT position transducers on each cylinder as well as joint encoders at each joint. The Parkers cylinders are fitted with LDT transducers

23 11 X L Load Q 2 P 2 Cylinder Q 1 P 1 Valve #3 Q V3 Q V1 Q V5 Valve #1 Valve #5 Q V2 Q V4 Valve #2 Valve #4 P S P T Figure 2.3. Programmable Valve Layout Figure 2.4. Programmable Valves

24 12 Figure 2.5. Electro-hydraulic Robot Arm with a -1 Volt output with a rated infinite resolution. Practically, the resolution is limited by the resolution of the ADC of the data acquisition system and any noise that corrupts the signal, which leads to a.5 mm resolution for the current set-up. Also available is an RS422 Digital Personality Module that translates the analog output into an quadrature signal. The resolution provided by the quadrature signal is.1 inch per count. Practically, this gives a better resolution. Each joint is equipped with a BEI HS35 Incremental Optical Encoder. The encoder has a resolution of 496 counts per turn or approximately :9 ffi. Fig. 2.5 shows the locations of the LDT position sensors and the optical encoders. In addition, a stand alone Omega FTB-12 turbine flowmeter calibrated at 4 ffi C for Texaco Rando HD hydraulic fluid with a viscosity of 94 centistrokes at 4 ffi C is used to obtain the valve mapping of various valves, as shown in Fig The flowmeter incorporates an Omega FLSC-35B Signal Conditioner. The flowmeter is mounted on a movable stand providing the correct pipe lengths for flow straightening and incorporates a check valve to protect the flowmeter and a manually adjustable needle valve to enable pressure drop adjustments.

25 13 Figure 2.6. Flowmeter Test Stand Control and Data Acquisition Hardware and Software The control and data acquisition hardware is centered around a dspace expansion box and breakout boxes with a DT 13 processor board and additional boards to support ADC, DAC, Encoders, and digital I/O. The dspace system is connected to a 233 MHz Pentium II host PC running Control Desk, Matlab and Simulink. This system provides the capability to generate, compile and run controller code as well as data acquisition and processing. The controller code and data acquisition run at 1 Hz sample frequency, well above the natural dynamics of the system which is approximately around 3-11 Hz. Two joysticks are available to provide input signals to the systems as a means of manual operator control. The equipment and the schematic diagram of the sensors, control and data acquisition hardware are shown in Fig. 2.7 and Fig. 2.8 respectively Dynamic Model The system is modeled as a robot manipulator with the hydraulic dynamics of

26 Pressure Sensors LDT Position Sensors Incremental Encoders Programmable Valve Hydraulic Lines Position Sensor Lines Encoder Lines Valve Control Lines Pressure Sensor Lines dspace Controller Host PC Joystick Inputs Figure 2.7. Schematic of Sensors, Data and Control Hardware 14

27 15 Figure 2.8. Control and Data Acquisition Hardware the valves and cylinders included. The model is derived from first principles and then validated by comparing simulation results and experimental test data in order to guarantee that the model is an accurate representation of the system Robot Manipulator Model The three linkages of the hydraulic arm can be modeled by the robot manipulator equation. This dynamic model accounts for the inertial, gravitational, coriolis, centrifugal and external forces on the robot arm dynamics. The model is written in terms of joint angles and joint torques. The robot manipulator equations describing the electro-hydraulic robot arm are taken from Fu [14]. The coordinate systems, joints and physical parameters used in the model are defined as in Fig The joint angles, q 1, q 2 and q 3, correspond to the swing, boom and stick joints respectively. The base coordinate system, x y z,is defined with the x y plane as the ground and the z axis as the axis about which joint angle q 1 rotates. Joint angle q 1 is defined as the angle from the x axis to the x 1 axis

28 16 z y 1 y 2 x 2 -q 3 y 3 a 1 z 2 q 2 x 1 z 1 y α 1 =9 deg. z 3 x 3 d 1 q 1 x Figure 2.9. Coordinate Systems, Joints and Physical Parameters about the z axis. The positive direction is defined as in a right-handed coordinate system. Coordinate system x 1 y 1 z 1 is fixed at the end of the swing arm, with the z 1 axis the axis about which the boom joint q 2 rotates. The boom joint angle q 2 is defined as the angle from the x 1 axis to the x 2 boom axis about the z 1 axis with the positive direction defined as in a right handed coordinate system. The coordinates system x 2 y 2 z 2 is fixed at the end of the boom link with the z 2 axis the axis of rotation for joint angle q 3. The stick joint angle q 3 is defined as the angle from the x 2 axis to the stick axis x 3 about the z 2 axis. Once again, the positive direction is as defined as in a right handed coordinate system. Coordinate system x 3 y 3 z 3 is fixed at the end of the stick arm and the direction of the z 3 axis is parallel to the z 2 axis. Using the coordinate systems and joint angles defined above, the dynamic equation of the robot arm can be described by, D (q(t)) q(t)+h (q(t); _q(t)) + c (q(t)) + B _q(t)+d(t) =fi(t) (2.1) where fi(t) is the joint torques generated by the hydraulic cylinders, D (q(t)) is an

29 17 n n symmetric inertial matrix, h (q(t); _q(t)) is an n 1 nonlinear coriolis and centrifugal force vector, c (q(t)) is an n 1 gravity force vector, B is a diagonal damping matrix, and d(t) is the lumped external disturbances including the unmodeled joint friction torques. A more thorough discussion of each of these terms is given in appendix A.1. The joint torques, fi(t), generated by the hydraulic cylinders, are in terms of the joint angles q i (t), while the hydraulic cylinder forces, P load, acting on the joints are in terms of the linear cylinder displacements x Li (t). The angular joint torques are related to the linear cylinder forces by, fi = JP load (2.2) where J is the Jacobian matrix given by, J = (2.3) 2 (A.21) respectively. 3 are defined appendix A.2 in equations (A.17),(A.19) and Hydraulic Cylinder Model The hydraulic cylinder force, P load, is generated by the hydraulic cylinders. Once the hydraulic cylinder dynamics as well as the flows into and out of the cylinder are known, the P load matrix can be calculated. The hydraulic dynamics of each cylinder are described by [2, 3], V 1 fi e V 2 fi e P_ 1 = A 1 _x C tm (P 1 P 2 ) C em1 (P 1 P r )+Q 1 (2.4) P_ 2 = A 2 _x + C tm (P 1 P 2 ) C em2 (P 2 P r ) Q 2 (2.5) where x L is the displacement ofthecylinder, V 1 = V h1 + A 1 x L is the total volume of the head end of the cylinder including the hose volume from the valve to the cylinder,

30 18 V h1 is the volume when x L =,V 2 = V h2 A 2 x L is the total volume of the rod end of the cylinder including the hose volume from the valve to the cylinder, V h2 is the volume when x L =, fi e is the effective bulk modulus, P 1 and P 2 are the pressures of the head-end and rod-end of the cylinder respectively, A 1 and A 2 are the cylinder areas respectively, C tm is the coefficient ofinternal leakage of the cylinder, C em1 is the coefficient of external leakage for the head-end chamber, C em2 is the similar coefficient for the rod-end chamber and Q 1 and Q 2 are defined as the flows in and out of the head-end and rod-end of the cylinder respectively. The cylinder dynamic equations when given flow inputs Q 1 and Q 2 generate both head-end and rod-end cylinder pressures. Using these pressures the P load matrix in (2.2) is calculated by P load = P loadsw P loadbm P loadst (2.6) (2.7) P loadsw = P 1sw Λ A 1sw P 2sw Λ A 2sw P loadbm = P 1bm Λ A 1bm P 2bm Λ A 2bm (2.8) P loadbm = P 1st Λ A 1st P 2st Λ A 2st (2.9) where the subscripts sw, bm and st, denote the swing, boom or stick cylinders, respectively. The cylinder flows Q 1 and Q 2 are regulated by the electro-hydraulic valves described in the next section Valve Models The valve models used for the swing and stick circuits are servo valve models. This is a simplification from the actual machine due to the more complex nature of

31 19 X L Load Q 2 P 2 Cylinder Q 1 P 1 Valve #3 Q V3 Q V1 Q V5 Valve #1 Valve #5 Q V2 Q V4 Valve #2 Valve #4 P S P T Figure 2.1. Programmable Valve Layout the proportional directional control valves. The focus of the research is on the programmable valve and this assumption is justified for the sake of simplicity. The servo valves are modeled by a standard orifice equation and a transfer function describing the dynamic response of the valves. The swing and stick circuits are only used to generate external disturbances to the boom circuit. The programmable valve model is much more complex. The model consists of five individual cartridge valve models combined together through the specific piping configuration as shown in Fig With the positive directions of all orifice flows defined in Fig. 2.1, Q 1 and Q 2 are defined as, Q 1 = Q v2 Q v1 Q v3 Q 2 = Q v3 Q v4 + Q v5 (2.1)

32 2 where the orifice flows Q vi can be described by Q v1 = f v1 ( P v1 ;x v1 ) P v1 = P 1 P t Q v2 = f v2 ( P v2 ;x v2 ) P v2 = P s P 1 Q v3 = f v3 ( P v3 ;x v3 ) P v3 = P 1 P 2 (2.11) Q v4 = f v4 ( P v4 ;x v4 ) P v4 = P s P 2 Q v5 = f v5 ( P v5 ;x v5 ) P v5 = P 2 P t in which f vi ( P vi ;x vi ) is the nonlinear orifice flow mapping as a function of the pressure drop, P vi, and the orifice opening, x vi, of the ith cartridge valve. In the s-domain, x vi is related to the command voltage by the transfer function given in the manufacturers data as described below. x vi (s) v i (s) = 1 8: s 2 + :581s +1 (2.12) Each valve model is made up of a transfer function representing the dynamic response of the valve and a non-linear valve mapping giving the flow through the valve for various combinations of command voltage and pressure drop across the valve System Identification The process of system identification incorporates a number of techniques in determining the various physical parameters. These included looking up physical dimensions or measurements, off-line testing and estimating parameters based on simulation and experimental results. The mechanical parameters of the swing, boom and stick joints, `Ai ; `Bi ; x i ; ffi i and fl i are given in table 2.1. The table also includes cylinder areas, A 1i and A 2i, and cylinder initial volumes, V h1i and V h2i. The cylinder leakages C tm ;C em1 and C em2 are assumed to be zero due to the difficulty in determining the values. The mass, center of mass and inertia tensors for each linkage are determined by Pro- Engineer based on three-dimensional drawings of the linkages. The mass of the swing

33 21 Table 2.1. Cylinder Physical Parameters Cylinder Physical Parameters `Ai (m) `Bi (m) x i (m) ffi i (rad) fl i (rad) A 1i (m 2 ) A 2i (m 2 ) V h1i (m 3 ) V h2i (m 3 ) Swing :995e 4 9:69e 4 Boom :93e 4 1:241e 3 Stick :851e 4 9:267e 4 arm is m 1 = 43:256 Kg. The position vector of the center of mass of the swing linkage with respect to the swing coordinate frame is 1 r 1 = [x 1 ; y 1 ; z 1 ; 1] T where x 1 = :316 m; y 1 = :124 m; z 1 = :29 m. The inertia tensor of the swing arm is given in equation I sw = :116 :515 :9 :515 2:26 : :9 : 2: (2.13) The mass of the boom arm is m 1 =45:783. The position vector of the center of mass of the boom linkage with respect to the boom coordinate frame is 2 r 2 =[x 2 ; y 2 ; z 2 ; 1] T where x 2 = :58 m; y 2 =:458 m; z 2 =: m. The inertia tensor of the boom arm is given in equation I bm = :367 1:15 : 1:15 15:226 : : : 15: (2.14) The mass of the stick arm is m 3 =27:958kg. The position vector of the center of mass of the stick linkage with respect to the stick coordinate frame is 3 r 3 =[x 3 ; y 3 ; z 3 ; 1] T where x 3 = :416 m; y 3 =:278 m; z 3 =: m. The inertia tensor of the stick arm is given in equation I stnl = :125 :365 : :356 7:73 : : : 7: (2.15) These valves are for an unloaded stick. If a 5 lb weight is added to the stick the following values are used. The mass is m 3 =52:51 kg. The center of mass position

34 22 vector used with the 5 lb weight is 3 r 3 =[x 3 ; y 3 ; z 3 ; 1] T where x 3 = :195 m; y 3 = :456m; z 3 =:m. The inertia tensor of the loaded stick arm is given in equation I stl = :782 :214 : :214 8:216 : : : 8: (2.16) The two parameters that are estimated based on experimental results are the bulk modulus of the hydraulic fluid and the joint damping. The bulk modulus is adjusted until the natural frequency of the simulation model matches that of the experimental setup under similar conditions. The value of the bulk modulus used is fi e = Pa. The damping at each joint is found in a similar manner. The value of the joint damping is adjusted until the transient behavior of the simulation matches that of the experimental data. In reality, due to the fact that friction and leakages are very difficult to measure, the joint damping parameter is essentially a lumped damping and leakage term since the leakage coefficients are set to zero. The values for the joint damping are b 1 = 5 Nm rads ; b 2 = 4 Nm rads and b 3 = 3 Nm rads. s s s The valve parameters are obtained through off-line testing and using the performance specifications given by the manufacturer. The servo valve models used for the swing and stick circuits are obtained from Bu [3]. The flow coefficient values are k q1 =3: m 3 =(Vs p Pa) and k q2 = 3: m 3 =(Vs p Pa). The natural frequency is 1 Hertz and the damping ratio is.7. The cartridge valve models are also obtained through off-line testing as well as performance specifications supplied by the manufacturer. A complete flow mapping is obtained for each valve through the use of a turbine flowmeter as well as using the cylinder position sensor for very low flows below the range of the flowmeter. The flowmeter setup can be seen in Fig The flow meter is equipped with a one-way check valve to protect the flowmeter as well as a needle valve with which to adjust the pressure drop across the valve. The valve driver adjustments of gain, deadband and dither current were tuned by setting the dither duty cycle approximately the same

35 23 Flow (gpm) Valve 1:HECT Flow vs. Pressure.V 1.V 1.25V 1.5V 1.75V 2.V 2.25V 2.5V 3.V 4.V 5.V 6.V 7.V 8.V 9.V 1.V Pressure (KPa) Figure Valve 1:HECT Flow Mapping f v1 ( P v1 ;x v1 ) for each valve and then tuning the deadband and gain to provide a flow of 2 gpm with a command voltage of 4 Volts and a flow of 6 gpm for a command of 8 Volts. Thus, two reference points are used to tune the two valve driver adjustments and in doing so, an attempt is made to calibrate the valves similarly. The valve mapping is generated by running three tests at each combination of command voltage and pressure drop and averaging the three trials. This is repeated numerous times for each valve. Valve 3, the REGEN valve is mapped in both directions. An example of the valve mapping for valve 1, HECT, f v1 ( P v1 ;x v1 ) is shown in Fig The remaining valve mappings can be seen in appendix A.3. obtained from the manufacturers specifications and are given below. 1 8:4 1 6 s 2 +:851s +1 The valve dynamics are (2.17) 2.4. Model Validation The simulation model is validated based on comparison of simulation results and

36 24 BM Ang(rad) BM Vel (rad/s) HE Pres () Model Validation Boom No Load Sim Ang Ex Ang Sim Ang Vel Ex Ang Vel Sim HE Ex HE Sim RE Ex HE Figure Boom -No Load experimental results. Each circuit is simulated with a simple step command with and without the 5 pound weight. These results are compared to actual experimental results from the electrohydraulic arm. The results show that the simulation model is a good match to the actual robot arm. Fig shows the comparison of cylinder displacement, velocity and pressures for the unloaded boom circuit. The complete model validation results are available in appendix A.4. The validated model can now be used for the controller design and testing in chapters 3 and 4. The programmable valve utilized on the boom circuit provides an number of unique features and advantages over a conventional valve. The disadvantages come in the increased complexity of the controller and in the additional sensors required for high-performance control. Chapters 3 and 4 look at two possible techniques for controlling the programmable valve. Chapter 3 takes a very simple approach that minimizes the need for additional sensors and computation power of the controller through a relatively simple controller design. Chapter 4 investigates the achievable performance with full state feedback and a larger computational capacity of the con-

37 25 troller making use of an adaptive robust controller. The next two chapters proceed through the controller development, simulation and experimental testing for each of these controllers.

38 26 3. PRESSURE FEEDBACK CONTROLLER The programmable valve offers many advantages over a conventional proportional directional control valve. The cost of these advantages is the increased complexity of the controller. Instead of a single control input there are now five control inputs to be determined. The individual control of the five cartridge valves must be coordinated in such a way that not only the task level performance requirements (i.e., cylinder position or velocity tracking) can be satisfied, but also secondary goals such as energy saving can be delivered. Depending on the tasks to be performed, different coordination strategies may have to be used. This chapter focuses on the limited sensory feedback situation when the cylinder position or velocity feedback information is not available. The lack of position or velocity sensors is a very common problem, particularly on construction equipment such as excavators and backhoes. The extra cost of sensors is prohibitive as well as the high likelihood of sensor failure in such a harsh environment. These factors make the possibility of improved control with limited sensory feedback very attractive. This chapter proposes a controller design that can improve performance with limited sensory feedback. The controller design methodology is to split the controller into two parts, a cylinder level controller and a valve level controller. The cylinder level determines which valves are to be used to control the cylinder and the valve level controller specifies how those valves are used. The high level, or cylinder level, controller determines which valves should be utilized in a given situation. The cylinder level controller analyzes the pertinent cylinder information and specifies the most effective and efficient use of the programmable valve. The determination is based on the desired cylinder velocity, cylinder pressures and cylinder loading. The valve usage information is passed along to low-level

39 27 controller. The low-level, or valve level, controller attempts to track the desired cylinder velocity. The controller makes use of a pressure-compensated inverse valve mapping because steady-state accuracy can only be achieved by taking into account the nonlinear valve mappings. This technique assumes that an accurate valve mapping for each valve exists and the head-end and rod-end cylinder pressures are available with little or no time delay. Using the known desired flow and the pressure drop across a valve, the needed command voltage can be backed out of the inverted valve mapping. This technique is able to essentially cancel the non-linear valve flow and results in a relatively linear system with good steady-state velocity tracking but poor transient performance of the lightly damped system. The obvious solution to improving the transient performance of the cylinder is to introduce a controller using output feedback. The problem with this approach is that cylinder position and velocity feedback are rarely available on hydraulic equipment, particularly construction equipment due to the added cost as well as the high potential of damage to the delicate sensors. The most cost effective approach is to take advantage of the fact that cylinder pressure sensors are available and attempt to improve the transient performance with the use of pressure feedback only. Pressure sensors are required with the use of the programmable valve and the pressure compensated inverse valve mappings and are consequently available for pressure feedback. Theoretically, pressure feedback should be able to improve the transient performance of the cylinder. This chapter presents the control design model as well as the controller design and testing of a pressure feedback controller for use with the programmable valve on the boom circuit Pressure Feedback Control Development Model The controller design is initiated with the development of a first principles model of a cylinder. The actual system is a coupled MIMO robot arm and without knowing