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Hydraulic Servo Systems : Dynamic Properties and Control

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Hydraulic Servo Systems : Dynamic Properties and Control Hydraulic Servo Systems Dynamic Properties and Control by Closed loop stiffness for a Karlposition-Erik servo Rydberg with velocity feedback s2 2 K h s 1 K s K K qi K 2 K vfv f sav A K FL vfv h vfv h p qi S Kvfv 1 K fv Ksav c X K V A p ce t p 2 1 s Ap 4eKce s s2 2 Steady state loop gain [1/s] 1 h s 1 2 2 Ap Kvv Kvfv h Kvfv h Kqi 1 Sc Kvv Kvfv Kvv Ksav K f K V Ap Kvfv ce 1 t s K K (without velocity feedback) K-E Rydberg 4eKce Feedbacks in Electro-Hydraulicvv v Servo Systems 7 For the same amplitude margin, Kv must have the same value in the system with and without velocity feedback. Velocity feedback increases the steady state stiffness with the factor Kvfv.FL K æ V ö ce ç1+ t s÷ Karl-Erik Rydberg, Linköping University, Sweden 2 ç 21 ÷ Ap è 4be K ce ø Threshold Saturation - . u i i imax Kqi 1 xp xp c K r v 1 1 + + sav s + s2 2d ei Ap 1+ + h s + 1 s - - n wv 2 w wh h Velocity feedback Kfv Position feedback Closed loop stiffness for a position servoK fwith velocityFigure 12: A feedbacklinear valve controlled position servo with velocity feedback Am = 6 dB If the bandwidth of the valve is relatively high and threshold and saturation is neglected With velocity feedback, K = 20 1/s, K = 9.0 the velocity feedbackvv will givevfv the effect on the hydraulic resonance frequency and damping as shown in Figure 13. Without velocity feedback, Kv =20 1/s FL æ ö Kqi Kce hv =V 387t rad/s ç1+ s÷ Kvfv = 1 + Kfv Ksav 2 ç ÷ Ap Ap è 4be K ce ø - . 1/ Kvfv x x uc iv Kqi p 1 p + Ksav s2 2d Ap + + h s + 1 s - 2 K w Kvfv wh vfv h Position feedback Kf Karl-ErikFigure Rydberg, 13: Linköping A linear University, position Sweden servo with velocity feedback22 included From Figure 13 the new resonance frequency and damping (hv and hv) caused by the velocity feedback can be evaluated as 1 K qi K , , where the velocity loop gain is K 1 K K . hv h vfv hv h vfv fv sav A K vfv p +11 Designing the position control loop for the same amplitude margin as without velocity feedback gives the following relations: K qi Steady state loop gain without velocity feedback: K v K sa K f Ap K qi Steady state loop gain with velocity feedback: K vv K sav K f Ap K vfv A certain amplitude margin means that K v h h . In this case h h hv hv , which implies that K v K vv and thereby the servo amplifier gain K sav K sa K vfv . With velocity feedback, the servo amplifier gain (Ksav) can be increased in proportion to the velocity loop gain Kvfv and the servo amplifier gain without velocity feedback, Ksa. The open loop gain (Au(s)) for a position servo without (Kv = 20) and with velocity feefback (Kvfv = 10 and Kvv =20) is shown in Figure 14. K-E Rydberg Hydraulic Servo Systems – Dynamic Properties and Control ______________________________________________________________________ Linköping November 6, 2014 Revised October 27, 2016 Karl-Erik Rydberg Professor, PhD Department of Management and Engineering Linköping University SE-581 83 LINKÖPING ISBN: 978-91-7685-620-8 2 K-E Rydberg Hydraulic Servo Systems – Dynamic Properties and Control ______________________________________________________________________ Hydraulic Servo Systems – Dynamic Properties and Control Table of Contents Hydraulic Servo Systems - Dynamic Properties and Control .................................. 1 1 Introduction ................................................................................................ 5 1.1 What is a servo? ................................................................................................................... 5 1.2 Technology comparisons .................................................................................................. 5 1.3 Capabilities of electro-hydraulic servos ...................................................................... 7 1.4 Different electro-hydraulic concepts ............................................................................ 7 1.5 Servo system efficiency ..................................................................................................... 9 1.5.1 Servo valve efficiency ................................................................................................................. 9 2 Configuration of electro-hydraulic servos ..................................... 12 2.1 Position servo .................................................................................................................... 13 2.2 Velocity and force servos ............................................................................................... 13 3 Servo valves and their characteristics ............................................ 15 3.1 Number of lands and ports ............................................................................................ 15 3.2 Types of valve center ....................................................................................................... 16 3.2.1 Valve sleeve ............................................................................................................................... 17 3.3 Examples of electro-hydraulic servo valves ............................................................ 18 3.3.1 Type of feedback ..................................................................................................................... 18 3.3.2 Number of stages .................................................................................................................... 19 3.4 General steady state valve characteristics .............................................................. 24 3.4.1 Valve Coefficients ................................................................................................................... 25 3.5 Critical center four-way valve ...................................................................................... 26 3.5.1 Practical null coefficients for a critical center valve ............................................... 26 3.5.2 Leakage characteristics of a practical critical center four-way valve ........... 27 3.5.3 Blocked line pressure sensitivity curve ........................................................................ 27 3.5.4 Leakage flow curves .............................................................................................................. 28 3.5.5 Real flow gain characteristics ........................................................................................... 29 3.6 Open center spool valve ................................................................................................. 30 3.7 Three-way spool valve analysis ................................................................................... 32 3.8 Dynamic response of servo valves .............................................................................. 34 4 Position servos with valve-controlled cylinders ......................... 36 4.1 Asymmetric cylinder ....................................................................................................... 36 4.1.1 Example ....................................................................................................................................... 38 Variation in resonance frequency for an asymmetric cylinder with line volumes .......... 38 Parameters ...................................................................................................................................... 38 4.2 Valve controlled symmetric cylinder ........................................................................ 39 4.2.1 Servo system stability and bandwidth .......................................................................... 42 4.4 Influence from flow forces on valve spools ............................................................. 45 4.5 Position servo with mechanical springs at connectors ....................................... 47 4.5.1 Simulation of position servo with mechanical springs .......................................... 48 5.1 Four-way valve controlled motor with position feedback ................................. 52 5.2 Valve controlled motor for an angular velocity servo ......................................... 54 5.3 Pump controlled motor .................................................................................................. 56 3 K-E Rydberg Hydraulic Servo Systems – Dynamic Properties and Control ______________________________________________________________________ 5.4 Pump controlled motor with variable displacement ........................................... 58 5.5 Pump controlled symmetric cylinder ........................................................................ 59 6 Hydraulic systems with complex load dynamics ......................... 61 6.1 Loads with one degree of freedom ............................................................................. 62 6.2 Loads with two degrees of freedom ........................................................................... 64 7 Feedbacks in Electro-Hydraulic Servo Systems ........................... 75 7.1 Linear valve controlled position servo ..................................................................... 75 7.1.1 Influence of valve dynamics ............................................................................................... 76 7.1.2 Closed loop stiffness ............................................................................................................. 77 7.2 Valve controlled position servo with load pressure feedback .......................... 78 7.3 Valve controlled angular position servo with acc. feedback
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