Motion Control. Laboratory assignment. Case study. Lectures. compliance, backlash and nonlinear friction. control strategies to improve performance

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1 Advanced Control and Automation Motion Control Lectures traditional CNC control architecture modelling of components dynamic response of axes effects on contouring performance control strategies to improve performance Case study Two-axis profiling machine Laboratory assignment design and implement controller on X-Y table subject to compliance, backlash and nonlinear friction L1:1

2 Elements of a servo-controlled axis L1: Source: DYNAMIC SERVO ACTUATORS

3 L1:3 Mechanical elements Bearing Table Bearing Ballscrew Nut Gearbox or Belt Drive Guideway Motor References: Source: Position Measurement on Machine Tools by Jan Braasch Weck, Manfred. Handbook of machine tools, Volume 3, Automation and Controls. Wiley, [Eng Library: WECK] HMT Limited. Mechatronics and Machine Tools. McGraw Hill, [Eng Library: 61 MECH]

4 Conventional CNC control architecture Source: "SERCOS interface" presentation by Rigobert Kynast ( L1:4

5 Modern CNC control architecture L1:5

6 CNC issues axis position commands via high-speed bus L1:6

7 In some tracking systems contouring error is critical... Profiling machines laser plasma water-jet Non-circular machining High speed milling Pictures courtesy Farley LaserLab L1:7

8 Time (s) Contouring error Example: laser profiling cut 10 mm circle in 0.5 s trapezoidal velocity profiles V max = 5 m/min (83 mm/s) A max = 1.4 m/s X position (mm) X position (mm) L1:8 Y position (mm) Time (s) Y position (mm)

9 Contouring limitations bandwidth lag in axis response mismatch between axes nonlinearities actuator saturation, Coulomb friction vibrational modes L1: X position (mm) Y position (mm)

10 In low-feedrate machines disturbance rejection could be more important Grinding machine - tool cutter grinder low speed smooth operation need shiny surface finish L1:10

11 Ripple torque and friction L1:11 Torque disturbance caused by motor cogging or electrical poles PGX contour error: scale=0000, 3.8um/-.5um Soft Y (mm) Soft X (mm) Friction effects at axis reversals

12 Modelling of two-axis contouring machine Conventional architecture Electromechanical dynamics Current, velocity and position control loops Simple model for axis position dynamics Captures effects of tuneable parameters in CNC Allows analytical derivation of contouring performance Case study of profiling machine Linearised, continuous-time model in MATLAB Nonlinear, hybrid model in Simulink L1:1

13 Mechanical modelling x = Pθ L /π L1:13 Mechanical elements of rigid servo axis drive Only 1 DoF so refer all inertias, friction and forces to motor shaft Kinetic energy is θ M J Effective total inertia Referred inertias T = J θ + J θ + Mx M M L L J θ M M J N P θ L M M N θ M ( ) ( ) = + + π P = J + J N + M N θ = J θ π 1 1 M L M M

14 x = Pθ L /π Rate of energy dissipation is F = B θ θ + B θ θ + B x x ( ) ( ) ( ) M M M L L L S = B + BN + B N θ = Bθ π P M L S M M Rate of working of external forces is P W = τ θ F x = τ F N θ π M M L M L M L1:14

15 L1:15 x = Pθ L /π Mechanical elements of rigid servo axis drive θm τ Μ JM rigid connection Motor Load τ L θ Μ = θ L /N J eff B M B eff Dynamically equivalent model, referred to motor speed

16 x = PNθ M /π + δ L1:16 Nθ M k L θm Mechanical elements of compliant servo axis drive τ Μ τ L JM k, c compliant connection J eff B M Motor Load π θ L = x PN B eff PN k = kl π Dynamically equivalent model, referred to motor speed

17 Mechanical dynamics (rigid model) τ M τ L J θ M B θ = ω M M J ω = τ τ Bω M M L M Θ = M Ω = M Ω s M T T Js + B M L T M Ω M Θ M Θ L X T L + 1 Js + B 1 s N P π L1:17

18 e a Electrical model for DC PM servo motor + i a R a L a e b + τ m θ m, ω m Equation set: B KVL for armature circuit: di a e a = R a i a + L a + e b dt Back-emf: e b = K b ω m J τ l Motor torque characteristic: τ m = K ii a E a + 1 I a T M Ls a + Ra K i E b = K b Ω m L1:18

19 Electromechanical model of motor and load L1:19 E a + 1 I a E b Ls a + Ra ( ) ( ) KI T = Js + B Ω i a L M E K I = L s+ R I a b a a a a K i K b T M Ω M Θ M X T L + 1 Js + B Ls + R K T I = ( Js + B )( L s + R ) + K K a a i L Ω M Kb Js+ B Ea a a a i b 1 PN s π Js + B K i ΩM T L Kb Las R a I = a E + a Transfer function E a Ω M Ω M K = i E JL s + JR + BL s+ BR + K K ( ) a a a a a i b

20 Transfer function E a Ω M Ω M K = i E JL s + JR + BL s+ BR + K K ( ) a a a a a i b L1:0 Often the armature inductance L a is negligible Ω M K = M Ea TMs+ 1 1 B KK = + T J JR 1 1 = + T T i b M a mechanical time constant m em K T M M electromechanical time constant = = K i BR + K K JR a BR + K K a i b a i b Motor gain (rad/sv) Motor time constant (s)

21 Example product specs for brushed permanent magnet DC servo motor L1:1

22 Case study: Two-axis profiling machine x-axis DC servo motor drives belt sprocket after speed reduction through a belt drive y beam x drive tube drive side (rack on rail; pinion driven through spur gears by y-axis DC servo motor) torch box (attached to thin stainless steel belt) idle side (roller on flat track) L1: