On Practical Applications of Active Disturbance Rejection Control

Transcription

1 2010 Chinese Control Conference On Practical Applications of Active Disturbance Rejection Control Qing Zheng Gannon University Zhiqiang Gao Cleveland State University

2 Outline Ø Introduction Ø Active Disturbance Rejection Control Ø Practical Applications Ø Conclusions 2

3 Introduction: The Three Paradigms Industry Control Practice Modern Control Active Theory Disturbance PID + Rejection Feedforward Model Based

4 The Industry Paradigm y& = p( y, y&, w, u, t) u= ( K e+ K e+ K e& ) + u p I D ff Disturbance Rejection: PID tuning

5 The Model Paradigm Modeling Plant: y& = p( y, y&, w, u, t) q( y, y& ) + u Design Goal: y& = g( y&, y) Known Control Law: u = qyy (&, ) + gyy (&, ) Examples: pole placement; feedback linearization; etc.

6 Between knowing none and knowing all u Plant y& = p( y, y&, w, u, t) u Primary Dynamics k y&= bu, b= T m u Secondary Dynamics y& = f( y, y&, w, t) + bu f( y, y&, w, t) = p( y, y&, w, u, t) bu

7 The Dist. Rej. Paradigm Total Disturbance Plant: y& = f ( yy, &, wt, ) + bu b = 1 Design Goal: y& = g( y&, y) Dist. Estimation: Control Law: f ˆ( t) f( y, y &, w,) t u = f ˆ( t) + g( y &, y)

8 Active Disturbance Rejection x& = x 1 2 x& = f + u 2 y = x1 Uncertain Nonlinear Time Varying Complex u= u fˆ 0 x& = x x& u y = x1 Fixed Linear Time Invariant Simple

9 The Extended State Observer Augmented plant in state space: y& = f( y, y&, w, t) + u x = y, x = y&, x = f x& 1 = x2 x& 2 = x3 + u, x& 3 = f& y = x1 Extended State Observer [Han,95] z& 1 = z2 β1g1( z1 y) z& 2 = z3 β2g2( z1 y) + u z& 3 = β3g3( z1 y) z x z x z x = f

10 Active Disturbance Rejection Control r Controller ADRC Structure z 3 u0 + = fˆ z, z u 1 ˆ 1/b u + ESO Idea u Estimate and cancel the generalized disturbance d + Plant u Reduce the plant to double integrators u Use a PD controller to control the double integrator plant + + y n u= u / bˆ x x 1 2 x3 z z z k k = 1 y = y& x 1 1 x 2 2 x 3 3 P D = f u1 = u0 z3 = ω 2 c = 2ω c y& = f( y, y&, d, t) + bu y& = f( y, y&, d, t) + u x& = x+ u 1 + f y = ω o 2 z& = z 1 + u 1+ 3 ω o ( y z 1) ω o fˆ = z [ ] y& u 0 [ 1 0] x u = k ( r z ) + k ( r& z ) + r& 0 P 1 D

11 Practical Applications Simulation and Hardware Tests 11

12 Application 1: Motion Control Ø In a typical application using motor as the power source, y& = f(, t y, y&, w) + bu (1) Ø In most motion control literature, the linear time-invariant approximation is used: a b y& = y& + u J J t t (2) 12

13 Application 1: Motion Control Control System Design Objectives: Ø Track the desired trajectory quickly and accurately; Ø Smoother control signal and lower level of wear and tear of actuators; Ø High degree of robustness; Ø Better external disturbance rejection capability; Ø Simplification of controller design and tuning 13

14 Application 1: Motion Control Output Tracking error Control signal 1.5 LADRC performance nominal plant with disturbance and increased inertia Time(s) Time(s) Time(s) 14

15 Application 2: Web Tension Regulation A Typical Web Winding System

16 Application 2: Web Tension Regulation 1 v & c = ( Ntc Ff + uc ) g M c v& e = ( Bfve + R ( tc tr ) + RKeue + R δe ) J 1 ( 2 ( ) 2 v& p = Bfvp + R tc tr + RKpup + R δ p ) J AE 1 t& = v c c ( v v e p ) x () t + N c Parameter variations and uncertainties External Disturbances Tension-velocity Coupling Nonlinear, sensitive to velocity variations n Nonlinear tension dynamics; n External Disturbance; n Large amount of parameter variations and uncertainties; n Tension-velocity strong coupling;

17 Application 2: Web Tension Regulation Two different ADRC solutions for the tension loop are investigated: open-loop (ADRC1) and closed-loop (ADRC2). 5 x 10-4 IC IC LBC ADRC1 Carriage Velocity Error(m/sec) 0 ADRC1 LBC Time sec Velocity tracking errors for IC, LBC and ADRC1. IC: the PID based industry controller, LBC: Lyapunov Based Controller 17

18 Application 2: Web Tension Regulation LBC ADRC1 ADRC2 Error of Tensions Lyapunov Based Controller (LBC) ADRC1 ADRC Time sec Tension tracking error for LBC, ADRC1, ADRC2 18

19 Application 3: DC-DC Power Converter Digitally Controlled Power Converter

20 Application 3: DC-DC Power Converter Linear model of H-bridge converter 20

21 Application 3: DC-DC Power Converter Load step-up (3A 36A) disturbance rejection. 21

22 Application 4: Continuous Stirred Tank Reactor (CSTR) F, C, T w in A, in in F, T j ρ, V, Cp mixer ρ, V, C w j pw F, T w w x& C x A, in 1 0 rx 1 V V VHrx + UA( x x ) T x u VρCp V UA( x x ) T x in 2 = + 0 w V V j w jρwc ρ pw F, C, T out A T CA, in x 1 y1 y2 = x2 CA, in [ ] T Ø MV: the reactant feed flow rate the coolant water mass rate Ø CV: the reactor concentration C A the reactor temperature T F in F w r = k x 0 E exp( ) Rx [ ] T [ u, u ] [ F, F ] 2 T T = x1, x2, x3 = CA, T, T j u = = 1 2 in w T 22

23 Application 4: CSTR Conversion Setpoint DDC time (second) Temperature(K) time (second) Output Response 23

24 Application 4: CSTR Fin(m 3 s -1 ) time (second) Fw(kgs -1 ) time (second) Control Signals 24

25 Application 5: MEMS Gyroscopes Mechanical gyroscope and Micro machined gyroscope

26 Application 5: Dynamics of MEMS Gyroscopes u Mathematical Model 2 K x& + 2ζωnx& + ωnx + ωxyy 2 Ω y& = ud( t) m 2 K y& + 2ζ yωyy& + ωyy + ωxyx + 2 Ω x& = us( t) m ω x, ω y are Quadrature errors caused by spring xy xy coupling terms 2Ωx&, 2Ωy& are Coriolis acceleration terms

27 Application 5: Control of MEMS Gyroscopes q Control Objectives Ø Force the drive axis to resonance; Ø Force the sense axis output to zero; Ø Rotation rate estimation. q Challenges Ø Structure uncertainty; Ø Mechanical couplings (stiffness and damping); Ø Time-Varying

28 Application 5: MEMS Gyroscopes 400 The output of the drive axis Output x The steady state drive axis output x 10-3 Output x Time(s) x 10-3 The output of the drive axis with the ADRC. 28

29 Application 5: MEMS Gyroscopes 400 The tracking error of the drive axis 200 Error The steady state tracking error of the drive axis x 10-3 Error Time(s) x 10-3 The tracking error of the drive axis. 29

30 Application 5: MEMS Gyroscopes 400 The tracking error of the drive axis 200 Error The steady state tracking error of the drive axis x 10-3 Error Time(s) The tracking error of the drive axis with parameter variations. x

31 Application 5: MEMS Gyroscopes The output of the drive axis Output x(mv) The steady state drive axis output Output x(mv) Time(s) reference output The drive axis output of the FPGA implementation. 31

32 Practical Applications Assembly Line 32

33 Application 1: Industrial Servo Drive 81% Reduction in maximum position error. 33

34 Application 1: Industrial Servo Drive 41% Reduction in RMS torque. 34

35 Application 1: Industrial Servo Drive 71% Reduction in jerk. 35

36 Application 2: Temperature Control in Hose Extrusion Energy savings in a Hose Extruder Line: over 200% in product quality and 58% in energy reduction. 36

37 Conclusions q ADRC Ø Does Not Require an Accurate Mathematical Model Ø Strong Disturbance Rejection Ability Ø Highly Robust Ø Easy to Use (after parameterization) Ø A Transformative Control Technology 37

38 Thank You! Questions? 38