# A 2-day course on POWER ELECTRONICS AND APPLICATIONS (DC Motor Drives) Universiti Putra Malaysia 11-12 August, 2004 Dr. Nik Rumzi Nik Idris Department.

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A 2-day course on POWER ELECTRONICS AND APPLICATIONS (DC Motor Drives) Universiti Putra Malaysia August, Dr. Nik Rumzi Nik Idris Department of Energy Conversion Universiti Teknologi Malaysia

Contents Introduction Trends in DC drives DC motors
Modeling of Converters and DC motor Phase-controlled Rectifier DC-DC converter (Switch-mode) Modeling of DC motor Closed-loop speed control Cascade Control Structure Closed-loop speed control - an example Torque loop Speed loop Summary

INTRODUCTION DC DRIVES: Electric drives that use DC motors as the prime movers DC motor: industry workhorse for decades Dominates variable speed applications before PE converters were introduced Will AC drive replaces DC drive ? Predicted 30 years ago AC will eventually replace DC – at a slow rate DC strong presence – easy control – huge numbers

Introduction DC Motors Advantage: Precise torque and speed control without sophisticated electronics Several limitations: Regular Maintenance Expensive Heavy Speed limitations Sparking

DC Motors Introduction Rotor: armature windings Stator: field windings
Current in Current out Stator: field windings Rotor: armature windings Mechanical commutator Large machine employs compensation windings

dt di L i R v = Introduction Lf Rf if + ea _ La Ra ia Vt Vf
Electric torque Armature back e.m.f.

Introduction Armature circuit: In steady state,
Therefore speed is given by, Three possible methods of speed control: Field flux Armature voltage Vt Armature resistance Ra

Introduction Armature voltage control : retain maximum torque capability Field flux control (i.e. flux reduced) : reduce maximum torque capability For wide range of speed control 0 to base  armature voltage, above base  field flux reduction Te Maximum Torque capability Armature voltage control Field flux control base

MODELING OF CONVERTERS AND DC MOTOR
POWER ELECTRONICS CONVERTERS Used to obtain variable armature voltage Efficient Ideal : lossless Phase-controlled rectifiers (AC  DC) DC-DC switch-mode converters(DC  DC)

Modeling of Converters and DC motor
Phase-controlled rectifier (AC–DC) 3-phase supply + Vt ia T Q1 Q2 Q3 Q4

Modeling of Converters and DC motor
Phase-controlled rectifier 3-phase supply + Vt Q1 Q2 Q3 Q4 T

Modeling of Converters and DC motor
Phase-controlled rectifier F1 F2 R1 R2 + Va - 3-phase supply Q1 Q2 Q3 Q4 T

Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current) Firing circuit –firing angle control  Establish relation between vc and Vt firing circuit current controller controlled rectifier + Vt vc iref -

Phase-controlled rectifier (continuous current)
Modeling of Converters and DC motor Phase-controlled rectifier (continuous current) Firing angle control linear firing angle control Cosine-wave crossing control

Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current) Steady state: linear gain amplifier Cosine wave–crossing method Transient: sampler with zero order hold T GH(s) converter T – 10 ms for 1-phase 50 Hz system – ms for 3-phase 50 Hz system

Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current) Output voltage Control signal Td Cosine-wave crossing Td – Delay in average output voltage generation 0 – 10 ms for 50 Hz single phase system

Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current) Model simplified to linear gain if bandwidth (e.g. current loop) much lower than sampling frequency  Low bandwidth – limited applications Low frequency voltage ripple  high current ripple  undesirable

Modeling of Converters and DC motor
Switch–mode converters Q1 Q2 Q3 Q4 T + Vt - T1

Modeling of Converters and DC motor
Switch–mode converters + Vt - T1 D1 T2 D2 Q1 Q2 Q3 Q4 T Q1  T1 and D2 Q2  D1 and T2

Modeling of Converters and DC motor
Switch–mode converters Q1 Q2 Q3 Q4 T + Vt - T1 D1 T2 D2 D3 D4 T3 T4

Modeling of Converters and DC motor
Switch–mode converters Switching at high frequency  Reduces current ripple  Increases control bandwidth Suitable for high performance applications

Modeling of Converters and DC motor
Switch–mode converters - modeling + Vdc vc vtri q when vc > vtri, upper switch ON when vc < vtri, lower switch ON

Modeling of Converters and DC motor
Switch–mode converters – averaged model vc q Ttri d Vdc Vt

Modeling of Converters and DC motor
Switch–mode converters – averaged model Vtri,p -Vtri,p vc d 1 0.5

Modeling of Converters and DC motor
DC motor – small signal model Te = kt ia ee = kt  Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m ac components dc components

Modeling of Converters and DC motor
DC motor – small signal model Perform Laplace Transformation on ac components Vt(s) = Ia(s)Ra + LasIa + Ea(s) Te(s) = kEIa(s) Ea(s) = kE(s) Te(s) = TL(s) + B(s) + sJ(s)

Modeling of Converters and DC motor
DC motor – small signal model + -

CLOSED-LOOP SPEED CONTROL
Cascade control structure 1/s converter torque controller speed position + - tacho Motor * T* * kT It is flexible – outer loop can be readily added or removed depending on the control requirements The control variable of inner loop (e.g. torque) can be limited by limiting its reference value

CLOSED-LOOP SPEED CONTROL
Design procedure in cascade control structure Inner loop (current or torque loop) the fastest – largest bandwidth The outer most loop (position loop) the slowest – smallest bandwidth Design starts from torque loop proceed towards outer loops

CLOSED-LOOP SPEED CONTROL
Closed-loop speed control – an example OBJECTIVES: Fast response – large bandwidth Minimum overshoot good phase margin (>65o) Zero steady state error – very large DC gain BODE PLOTS Obtain linear small signal model METHOD Design controllers based on linear small signal model Perform large signal simulation for controllers verification

CLOSED-LOOP SPEED CONTROL
Closed-loop speed control – an example Ra = 2  La = 5.2 mH J = 152 x 10–6 kg.m2 B = 1 x10–4 kg.m2/sec kt = 0.1 Nm/A ke = 0.1 V/(rad/s) Vd = 60 V Vtri = 5 V fs = 33 kHz Permanent magnet motor’s parameters PI controllers Switching signals from comparison of vc and triangular waveform

CLOSED-LOOP SPEED CONTROL
Torque controller design Tc vtri + Vdc q kt Torque controller + - Torque controller Converter DC motor

CLOSED-LOOP SPEED CONTROL
Torque controller design Open-loop gain kpT= 90 kiT= 18000 compensated compensated

CLOSED-LOOP SPEED CONTROL
Speed controller design Assume torque loop unity gain for speed bandwidth << Torque bandwidth Torque loop 1 Speed controller * T* T +

CLOSED-LOOP SPEED CONTROL
Speed controller Open-loop gain kps= 0.2 kis= 0.14 compensated compensated

CLOSED-LOOP SPEED CONTROL
Large Signal Simulation results Speed Torque

CLOSED-LOOP SPEED CONTROL – DESIGN EXAMPLE
SUMMARY Speed control by: armature voltage (0 b) and field flux (b) Power electronics converters – to obtain variable armature voltage Phase controlled rectifier – small bandwidth – large ripple Switch-mode DC-DC converter – large bandwidth – small ripple Controller design based on linear small signal model Power converters - averaged model DC motor – separately excited or permanent magnet Closed-loop speed control design based on Bode plots Verify with large signal simulation

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