Preliminaries for Motor Control

Chapter 1

AC Motor Control andEV Applications

Brush and Commutator

Operation Sequence

Counter clockwise torque is max.Back emf is max.

Counter clockwise torque is max.Back emf is max.

Commutationtakes place.Disengaging/

Engaging

(b)

S N

(a) (c)

S N S N

Cross section of a PM DC Motor

xx

x x

x x

xx

PM

CommutatorArmaturecoil

Faraday’s Law

v

Ex

Ey

Bz

Back EMF

As the armature winding rotates in the DC field,the amount of flux passing through the armature winding varies. Hence, the voltage is developed as the rotor rotates.The polarity is opposite to the direction of current flow when motoring.

DC Motor Equivalent Circuit

Note that torque constant and back emf constant are the same.

Prove it.Hint: Derive from the power relationship. (Elec. Power= Mech. Power)

+-

+

-

+-

Field Weakening

Torque

Speed

decrease

Load curve

Power and Torque vs Speed

power

current

torque

ratedspeed

Practical DC Motor Control Circuit

DCMotor

L1 L2 L3

(a) (b)

Four Quadrant Operation

Motoring in the forward direction

Regeneration in the reverse direction

Motoringin the reverse direction

Regenerationin the forward direction

+-

+

-+-

+

-

+-

+

-+-

+

-

DC Motor Dynamic Model

++-

-

+

TL

PI+PI+ +-

--

DC Motor Speed Control Block Diagram

1. Determine current loop PI controller so that there is a slight overshoot to a step input.

2. Replace the current loop by 1. Determine velocity loop PI controller so that it is critically damped.

3. Find a response for step speed command *=1500rpm with load TL = 30 us (t-2).

-

Current Controller

++-

-

Speed Control Loop and Bode Plot

Gain

0 dB

-20 dB

PI controller 1st order filter(current controller) Inertial Load

speedSpeed

command

-40 dB

D

E

(a)

(b)

PI and IP Controllers

++-

-

PI controller

speedSpeed

command

++-

-

IP controller

speedSpeed

command+

-+

+

(a)

(b)

00 0.2 0.4 0.6 0.8 1.0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Time (sec)

PI Controller

IP Controller PI Controller

IP Controller

(a) (b)

Time (sec)

Speed Responses and Current Commands

PI Controller with Reference Model

-

-

Reference Model

Integral control

Proportionalcontrol

+

+

+++

++

+

+

PI Controller with Reference Model

Disturbancerejection

Two Control Objectives

-++

+

Command Tracking :

Disturbance Rejection :

Sensitivity and Complementary Sensitivity Functions

-++

+

Sensitivity andComplementary SensitivityFunctions

Instability Mechanism

-

Assumption

180o phase delay11

12

13

14

++

+

Gain Margin and Phase Margin

-180o

PhaseMargin

GainMargin

0

Gain crossover angular frequency

phase crossover angular frequency

Input

Disturbance

Time (sec)

+-

-+ +Output

0 1 1.5 320.5 2.5

Role of the Integral Controller (Disturbance Rejection)

Current Loop Based on a Microcontroller

Hold element(current command)

-Computing cycle(current control)

Controlledsystem

Current detection

PWMexecution

Bode Plots of PI and PI with referencePI

PI with reference

PI

PI with reference

Disturbancerejection

Commandfollowing

PIPI with reference

Sec.

Double Ratio Rule

Sequence

Plant

Double Ration Rue

For 2nd Order System

Application of Double Ratio Rule

Double Ration Rue

For 2nd Order System

IMC Structure

-

-

Plant with disturbance

Feedback compensator

Feed forwardcompensator

+

+

++

Variations of Two DOF Structure

-

-

(a)

(b)-

-

+ ++

+

++

+

+

Load Torque Observer with an Artificial Delay

-

-

load torque

+

+

++

+

++

delay

artificial delay