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A 2-day course on POWER ELECTRONICS AND APPLICATIONS ( DC Motor Drives) Universiti Putra Malaysia August, 2004 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 Dominates variable speed applications before PE converters were introduced DC motor: industry workhorse for decades 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 Several limitations: Advantage: Precise torque and speed control without sophisticated electronics Regular MaintenanceExpensive HeavySpeed limitations Sparking

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

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Introduction Electric torque Armature back e.m.f. LfLf RfRf ifif +ea_+ea_ LaLa RaRa iaia +Vt_+Vt_ +Vf_+Vf_ dt di LiRv f fff

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

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

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MODELING OF CONVERTERS AND DC MOTOR Used to obtain variable armature voltage POWER ELECTRONICS CONVERTERS 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) T Q1 Q2 Q3Q4 3-phase supply +Vt+Vt iaia

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Phase-controlled rectifier Q1 Q2 Q3Q4 T 3-phase supply 3- phase supply +Vt+Vt Modeling of Converters and DC motor

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Phase-controlled rectifier Q1 Q2 Q3Q4 T F1 F2 R1 R2 + V a - 3-phase supply Modeling of Converters and DC motor

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Phase-controlled rectifier (continuous current) Firing circuit –firing angle control Establish relation between v c and V t firing circuit current controller controlled rectifier +Vt–+Vt– vcvc i ref + - Modeling of Converters and DC motor

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

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Phase-controlled rectifier (continuous current) Steady state: linear gain amplifier Cosine wave–crossing method Modeling of Converters and DC motor Transient: sampler with zero order hold T G H (s) converter T – 10 ms for 1-phase 50 Hz system – 3.33 ms for 3-phase 50 Hz system

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

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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

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Switch–mode converters Q1 Q2 Q3Q4 T +Vt-+Vt- T1 Modeling of Converters and DC motor

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Switch–mode converters +Vt-+Vt- T1 D1 T2 D2 Q1 Q2 Q3Q4 T Q1 T1 and D2 Q2 D1 and T2 Modeling of Converters and DC motor

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Switch–mode converters Q1 Q2 Q3Q4 T + V t - T1 D1 T2 D2 D3 D4 T3 T4 Modeling of Converters and DC motor

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

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Switch–mode converters - modeling + V dc − V dc vcvc v tri q when v c > v tri, upper switch ON when v c < v tri, lower switch ON Modeling of Converters and DC motor

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vcvc q T tri d Switch–mode converters – averaged model Modeling of Converters and DC motor V dc VtVt

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V tri,p -V tri,p vcvc d Switch–mode converters – averaged model Modeling of Converters and DC motor

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DC motor – small signal model Modeling of Converters and DC motor Extract the dc and ac components by introducing small perturbations in V t, i a, e a, T e, T L and m T e = k t i a e e = k t ac components dc components

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DC motor – small signal model Modeling of Converters and DC motor Perform Laplace Transformation on ac components V t (s) = I a (s)R a + L a sIa + E a (s) T e (s) = k E I a (s) E a (s) = k E (s) T e (s) = T L (s) + B (s) + sJ (s)

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

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CLOSED-LOOP SPEED CONTROL Cascade control structure 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 1/s converter torque controller speed controller position controller tacho Motor ** T* ** k T

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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 (>65 o ) 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 Ra = 2 La = 5.2 mH J = 152 x 10 –6 kg.m 2 B = 1 x10 –4 kg.m 2 /sec k t = 0.1 Nm/A k e = 0.1 V/(rad/s) V d = 60 VV tri = 5 V f s = 33 kHz Permanent magnet motor’s parameters Closed-loop speed control – an example PI controllers Switching signals from comparison of v c and triangular waveform

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CLOSED-LOOP SPEED CONTROL Torque controller design TcTc v tri + V dc − q q + – ktkt Torque controller Torque controller Converter - + DC motor

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CLOSED-LOOP SPEED CONTROL Torque controller design Open-loop gain compensated k pT = 90 k iT = 18000

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

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CLOSED-LOOP SPEED CONTROL Speed controller Open-loop gain compensated k ps = 0.2 k is = 0.14 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 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 Speed control by: armature voltage (0 b ) and field flux ( b )

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