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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

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**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

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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

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

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**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

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**dt di L i R v = Introduction Lf Rf if + ea _ La Ra ia Vt Vf**

Electric torque Armature back e.m.f.

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**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

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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

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**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)

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**Modeling of Converters and DC motor**

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

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**Modeling of Converters and DC motor**

Phase-controlled rectifier 3-phase supply + Vt Q1 Q2 Q3 Q4 T

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**Modeling of Converters and DC motor**

Phase-controlled rectifier F1 F2 R1 R2 + Va - 3-phase supply Q1 Q2 Q3 Q4 T

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**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 -

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**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

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**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

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**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

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**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

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**Modeling of Converters and DC motor**

Switch–mode converters Q1 Q2 Q3 Q4 T + Vt - T1

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**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

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**Modeling of Converters and DC motor**

Switch–mode converters Q1 Q2 Q3 Q4 T + Vt - T1 D1 T2 D2 D3 D4 T3 T4

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**Modeling of Converters and DC motor**

Switch–mode converters Switching at high frequency Reduces current ripple Increases control bandwidth Suitable for high performance applications

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**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

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**Modeling of Converters and DC motor**

Switch–mode converters – averaged model vc q Ttri d Vdc Vt

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**Modeling of Converters and DC motor**

Switch–mode converters – averaged model Vtri,p -Vtri,p vc d 1 0.5

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**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

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**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)

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**Modeling of Converters and DC motor**

DC motor – small signal model + -

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**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

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**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

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**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

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**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

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**CLOSED-LOOP SPEED CONTROL**

Torque controller design Tc vtri + Vdc − q – kt Torque controller + - Torque controller Converter DC motor

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**CLOSED-LOOP SPEED CONTROL**

Torque controller design Open-loop gain kpT= 90 kiT= 18000 compensated compensated

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**CLOSED-LOOP SPEED CONTROL**

Speed controller design Assume torque loop unity gain for speed bandwidth << Torque bandwidth Torque loop 1 Speed controller * T* T – +

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**CLOSED-LOOP SPEED CONTROL**

Speed controller Open-loop gain kps= 0.2 kis= 0.14 compensated compensated

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**CLOSED-LOOP SPEED CONTROL**

Large Signal Simulation results Speed Torque

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**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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