f10 feedback control systems

7/31/2019 F10 Feedback Control Systems

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Drivetech, Inc. 1

Feedback Control System Theoriesapplied to Motor Control

(A Tutorial)

Dal Y. Ohm

Drivetech, Inc., Chantilly, Virginia

www.drivetechinc.com

Drivetech, Inc. 2

Block Diagram of Feedback Control

DC motor speed control example

Objective: Precise control of output in the presence ofdisturbance and plant parameter variations

Plant

(Load)

Actuator(motor &

electronics)

Controller

(PID control)

Reference Output

Sensor

(Encoder)

Disturbance


2/13

Drivetech, Inc. 3

Control Objectives

Regulation (Disturbance Rejection) Steady Target

Dynamic Tracking Changing Reference

Accuracy and Response Time Integral control

System Bandwidth

Disturbance rejection (location of poles) Tracking (affected by poles and zeros)

Drivetech, Inc. 4

Dynamic Model of DC motors

Armature (Stator) Dynamic Equations

Va = Ra Ia + La dIa/dt + Ke

Field Equation

= K If (wound field only)

Mechanical

T = K Ia = J d/dt + Td

PI(D) control

y(s) = Kp(1 + Ki/s + Kd s) e(s)

I,T

Current limit

V2V1

load


3/13

Drivetech, Inc. 5

Velocity Control of DC motors

PI control on second order plant

adds one integrator to get zero steady-state error

moves one pole (mechanical pole)

limited by electrical pole, load dynamics,

feedback accuracy and bw

LoadPWM

AmplifierPI(D)

*

Tach orEncoder

Td

Motor

Ke

+

-

Vemf

V* V T

Strategies for Better Performance

Improve feedback sensors

Higher resolution and reduced time delay

Position and velocity accuracy

Change of internal dynamics

Torque response

Torsional resonance

Compensation of system non-linearities Regulator structure

Optimal tuning

Drivetech, Inc. 6


4/13

Drivetech, Inc. 7

Current Control for DC motors

PID control (?)

J d/dt() = T - Td

limited improvement by D term due to noise

Armature current control (Ia* = k T*)

Ierr = Ia* - Ia Va = (Kp + Ki/s) Ierr

Nested vs Multi-variable control

Desired bandwidth

10x servo bandwidth!

Effects of Back emf

Drivetech, Inc. 8

Current controlled DC servo motors

High performance (bw) velocity control

Limited by current loop performance andload dynamics (Torsional resonance)

LoadPWM

AmplifierPI*

Tach or

Encoder

Td

Motor

Ke

+

-

Vemf

I*+ V TPI

-

I

V*


5/13

Drivetech, Inc. 9

Velocity Control of Brushless Motors

Commutation generates 3 phase sinusoidal voltage command based on rotor

angle

Absolute position sense required possible phase delay at high speed

6-step (trapezoidal (?)) control for low-cost drives

Td

Motor &Load

AC PWMAmplifierPI(D)

*

Positionsensor

Ke

+

-

V* VCommu-

tation

se

Drivetech, Inc. 10

Current controlled Brushless servo motors

AC current controller

performs current control & commutation

single or multiple PI controllers

Motor &Load

AC PWMAmplifierPI

*

Positionsensor

Ke

+

-

I*

Vabc

AC Current

Controller

se

Iabc


6/13

Drivetech, Inc. 11

Bode Plot and Closed-loop Performance

Closed-loop control is effective for signals < BW PWM & sampling frequency

1x, 2x, (1/2)x,.

Current ripple, desired bw, switching loss

100

101

102

103

104

10-6

10-4

10-2

100

102

Magnitude Response

100

101

102

103

104

-300

-250

-200

-150

-100

-50Phase Response

100

101

102

103

104

10-6

10-4

10-2

100

102

Magnitude Response

100

101

102

103

104

-300

-250

-200

-150

-100

-50

0Phase Response

Drivetech, Inc. 12

Current Magnitude Control

Used in 6-step PWM control with one sensor

Phase angle is not controlled

Difficulty in measuring accurate current at low cost

DC bus +

DC bus -

AC Motor

Q1

Q2

Q3

Q4

C

Q5

Q6

A

B

C

Rs

PI

-

V*Commu-

tation

I*

I

Vabc*


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Drivetech, Inc. 13

Hysteresis Control

Simple to implement

Switching frequency controlled by error band

Vb*Commutation

Ia*

Vc*Ic*

Va*

Ib*I*

+

+

+

-

-

-

--

Drivetech, Inc. 14

Phase Current Regulator

Ramp comparison PWM

Steady-state magnitude droop and phase delay

Phase advance

Possible problems at high modulation index

Commutation

PI(D)

PI(D)

PI(D) PWM

Ia*

Vc*Ic*

Vb*

Va*

Ib*I*

+

+

+

-

-

-

--


8/13

Drivetech, Inc. 15

Generation of Electromagnetic Torque

Doubly excited cylindrical machines

T = K Ms Mr sin rs

(Mutual) reaction torque

Condition for consistent torque production

DC machine flux fixed in space

AC machine rotating flux

Brushless

induction machine

Reaction Torque

S

N

NS

Ms

rs

Mr

Drivetech, Inc. 16

FOC (Field oriented Control) for AC motors

Synchronously rotating reference frame

Geo-centric vs Helio-centric view

AC motor current can be divided into twocomponents

Torque producing current component

Field flux current component

Independent control of two current components Operation is very similar to separately excited

DC motors


9/13

Drivetech, Inc. 17

Frame Transform (1) - Park

3 Phase to 2 Phase Transform S 1 cos120 cos120 Sa

S =1.5 0 -sin120 sin120 Sb

So 0.5 0.5 0.5 Sc

All polyphase currents produces

Rotating mag flux!

Equivalent 2-Phase Machine

Identical magnitude, Reversible

Not invariant power

Sa,S

S

Sb

Sc

Drivetech, Inc. 18

Frame Transform (2) - Clarke

Coordinate attached to the rotor

D-axis on rotor N pole

Q-axis on N-S mid point

d cos sin x

q = - sin cos y

x cos - sin d y = sin cos q x

+y

dq


10/13

Drivetech, Inc. 19

Dynamic Equations of Brushless Motors

Voltage Model in Synchronous Frame

Vq = (Rs + Ls p) Iq + Ls Id + m

Vd = (Rs + Ls p) Id - Ls Iq

Similar to DC Motor equation

m

+

Rs Ls

+-

VqIq +

Ls Id

Rs Ls

+-

VdId

Ls Iq

Drivetech, Inc. 20

Synchronous Regulator (SR)

Requires Coordinate transform

Nonzero Id* for phase advance or induction motorcontrol

SVM

Vc*

Vb*

Va*PI

I* = Iq*

+

-

T

Vq*

PIId* = 0

+

- Vd*

T-1


11/13

Drivetech, Inc. 21

Characteristics of SR

Inherent zero steady-state tracking error

Internal Model Principle

PI regulator step (1/s)

Double integrator control ramp (1/s2)

SR - sinusoidal [ 1 / (s2 + 2) ]

Simple to add disturbance feed-forward

Implementation in stationary frame possible

Drivetech, Inc. 22

Disturbance Feedforward Techniques

Compensates for Back emf and cross-coupling terms.

Disturbance compensation improves dynamicperformance

SVM

Vc*

Vb*

Va*PI

I* = Iq*

+

-

T

Vq*

PIId* = 0

+

- Vd*

Ld Id + m

- Lq Iq

T-1


12/13

Drivetech, Inc. 23

Space Vector Modulation

(A)

(B)

(C)

0 1 1 1 1 1 1 0

0 0 1 1 1 1 0 0

0 0 0 1 1 0 0 0

To Tx Ty TuTu Ty Tx To

Ts

Treats 3 Phase as a whole

Produces balanced 3 Phasevoltage

Voltage is projected into 3base vector and 2 zero vectors.

Added 3rd harmonic injection

Superior to conventional 3-phase sinusoidal pwm.

1

2

34

5

V1

V2V3

V4

V5 V6

(100)

(110)

Predictive Current Control

Select the present voltage vector that results in minimumcurrent error at next sampling time

Vs(n) = RsI(n) + Ls {Is*(n+1)-Is(n)}/Ts + Vemf(n)

Requires motor model & estimation of Vemf(n)

Not require Synchronous frame transform

Feed-forward alternative to Synchronous regulator

Many different techniques to select switching vectors

Suited for DSP implementation

Good performance with accurate motor model and delaycompensation.

Drivetech, Inc. 24


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Sensorless Control

Estimation of Flux Angle & Velocity

Available technologies Vemf detection (6-step)

Model-based, Observer, Sliding Mode Control

Carrier injection (IPM)

Performance BW limited, limited accuracy

Challenges at startup and near-zero speed, hightorque application

Model of nonlinearitieds & Hybrid approach Algorithm selection and tuning key to success

Drivetech, Inc. 25

Drivetech, Inc. 26

Conclusion

Application of feedback control principles tomotor drives

Velocity control limited by Plant dynamics & Feedback performance

Current control in drives improves Torque response time

Velocity control BW

Excellent performance with SR Torque per ampere performance & efficiency Disturbance feed-forward

Can be implemented with low-cost DSP & uC

f10 feedback control systems

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