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Closed-loop Control of DC Drives with Chopper By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 20081EEEB443 - Control & Drives

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Outline Closed Loop Control of DC Drives with Choppers Current Control for DC Drives with Choppers Pulse-Width-Modulation (PWM) Controller Hysteresis-Current Controller Comparison between PWM and Hysteresis Controller Transfer Function of PWM-Controlled Chopper Two-quadrant Four-quadrant Design of Controllers References Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives2

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Closed Loop Control of DC Drives Closed loop control is when the duty cycle is varied automatically by a controller to achieve a reference speed or torque This requires the use of sensors to feed back the actual motor speed and torque to be compared with the reference values Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives3 Controller Plant Sensor + Reference signal Output signal

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Closed Loop Control of DC Drives Feedback loops may be provided to satisfy one or more of the following: Protection Enhancement of speed response Improve steady-state accuracy Variables to be controlled in drives: Torque – achieved by controlling current Speed Position Dr. Ungku Anisa, July 20084EEEB443 - Control & Drives

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Closed Loop Control of DC Drives Cascade control structure Flexible – outer loops can be added/removed depending on control requirements. Control variable of inner loop (eg: speed, torque) can be limited by limiting its reference value Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives5 For DC Drive, this can be: Controlled rectifier or DC-DC converter

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Closed Loop Control for DC Drives with Choppers Outer speed loop very similar to that in the controlled rectifier dc drive Inner current control loop – different Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives6 Current Control Loop Speed Control Loop

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Current Control for DC Drives with Choppers Current control loop is used to control torque via armature current (i a ) Output of current controller determines duty cycle (i.e. switching) of DC-DC converter Current controller can be either: Pulse-Width-Modulation (PWM) Controller contain PI controllers, i.e. linear fixed switching frequency Hysteresis (bang-bang) controller on-off controllers, i.e. non-linear varying switching frequency Selection of controller affects current control loop transient response Hence, affects speed loop bandwidth. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives7

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Current Control for Chopper Drives – PWM Controller In two quadrant chopper, upper and lower switches are complementary Only ONE control signal required Current error is passed to PI controller to produce control voltage v c v c is then passed to a PWM circuit to produce the switching signal q. q = 1 T1 ‘on’, T2 ‘off’ V a = V dc q = 0 T1 ‘off’, T2 ‘on’ V a = 0 Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives8 i err V dc Pulse Width Modulator (PWM) vcvc ia*ia* PI + q T1 T2 D1 +Va-+Va- D2 iaia + V dc iaia v tri v c > V tri v c < V tri T1 ‘on’, V a = V dc T2 ‘on’, V a = 0

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Current Control for Chopper Drives – PWM Controller In the PWM circuit: v c is compared with a triangular waveform if v c > V tri ‘on’ signal is produced (q = 1) if v c < V tri ‘off’ signal is produced (q = 0) (1) Chopper switching frequency is fixed by triangular waveform frequency regardless of operating conditions Bandwith of current loop controller is limited by frequency of V tri Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives9 v c > V tri v c < V tri T tri t on 0 1 vcvc 0 V dc q vava q = 1 T1 ‘on’, v a = V dc q = 0 T2 ‘on’, v a = 0 v c > V tri v c < V tri

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In the PWM circuit: Average value of q over a cycle determines duty cycle of chopper: Average armature voltage: Current Control for Chopper Drives – PWM Controller Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives10 T tri t on 0 1 vcvc 0 V dc VaVa q vava v a switches between V dc and 0 average armature voltage V a depends on duty cycle (i.e. how long T1 is on)

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Current Control for Chopper Drives – PWM Controller PWM controls chopper duty cycle once in every cycle Frequency of V a fixed by frequency of V tri Hence, chopper is a variable voltage source with average current control Instantaneous current control is not exercised Current can exceed maximum armature current between two consecutive switching Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives11

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Current Control for Chopper Drives – Hysteresis Controller Instantaneous current control Current controlled within a narrow band of excursion from the desired value i a * Hysteresis window determines allowable deviation of i a Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives12 V dc ia*ia* q T1 T2 D1 +Va-+Va- D2 iaia + V dc i err iaia ia*ia* q iaia iaia iaia i a i a * - i a i a i a * + i a Hysteresis Controller

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Current Control for Chopper Drives – Hysteresis Controller Actual current i a compared with reference current i a * to obtain error signal i err If i a i a * + i a q = 0, T2 ‘on’ and V a = 0 If i a i a * - i a q = 1, T1 ‘on’ and V a = V dc Value of i a can be externally set or made to be a fraction of i a Chopper switching frequency is not fixed Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives13 ia*ia* q iaia iaia iaia q = 1 T1 ‘on’, v a = V dc i a i a * - i a q = 0 T2 ‘on’, v a = 0 i a i a * + i a i a i a * - i a i a i a * + i a

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Current Control for Chopper Drives – Qualitative Comparison Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives14 CharacteristicsHysteresis ControllerPWM Controller Switching frequency VaryingFixed (follows sawtooth waveform frequency i.e. carrier frequency) Switching lossesHigh (due to varying switching frequency) Low Speed of response Fastest (due to instantanous change in current) Fast Ripple currentAdjustable (depends on hysteresis window i a ) Fixed Filter size Depends on i a Small Preferred method !

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Closed Loop Control for DC Drives with Choppers Controller design procedure: 1. Obtain the transfer function of all drive subsystems a) DC Motor & Load b) Current feedback loop sensor c) Speed feedback loop sensor 2. Design torque (current) control loop first Two options to choose from: A. Hysteresis Controller – to design just choose value of i a B. PWM Controller (contains PI controller) i. determine transfer function of PWM-controlled chopper ii. design PI controller using the same procedure as in closed loop control using controlled rectifier Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives15 Exactly the same as before (i.e. transfer functions obtained in closed loop control using controlled rectifier)

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Closed Loop Control for DC Drives with Choppers Controller design procedure (continued): 3. Then design the speed control loop i. Obtain 1 st order model of the designed current controller ii. Design the speed PI controller using the same procedure as in closed loop control using controlled rectifier Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives16

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Transfer Function of PWM-Controlled Chopper PWM current controller is preferred over Hysteresis Controller Before we can design the PI controller, need to obtain linear relationship between control input v c and average armature voltage V a for PWM method Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives17 Pulse Width Modulator (PWM) vcvc ia*ia* PI + q iaia v tri Chopper DC motor VaVa iaia Need transfer function for PWM-controlled chopper

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Transfer Function of PWM-Controlled Two-quadrant Chopper Need to obtain linear relationship between control input v c and average armature voltage V a for PWM method Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives18 V tri -V tri vcvc v c > V tri v c < V tri vcvc -V tri Case 1: T1 off all the time i.e. t on, T1 = 0

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Transfer Function of PWM-Controlled Two-quadrant Chopper Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives19 V tri -V tri vcvc v c > V tri v c < V tri vcvc -V tri 0.5 Case 2: T1 on ½ cycle i.e. t on, T1 = 0.5T tri

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Transfer Function of PWM-Controlled Two-quadrant Chopper Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives20 V tri -V tri vcvc v c > V tri v c < V tri vcvc -V tri V tri Case 3: T1 on all the time i.e. t on, T1 = T tri

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Relationship between and v c : (2) For the two-quadrant chopper: (3) Hence, considering only the term due to v c, the two–quadrant chopper gain is: (4) Transfer Function of PWM-Controlled Two-quadrant Chopper Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives vcvc -V tri +V tri 1

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Transfer Function of PWM-Controlled Four-quadrant Chopper Recap Chopper operation: Positive current: V a = V dc when T1 and T2 on V a = 0 when current freewheels through T2 and D4 + V a - T1 D1 T2 D2 D3 D4 T3 T4 + V dc - Dr. Ungku Anisa, July EEEB443 - Control & Drives

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Transfer Function of PWM-Controlled Four-quadrant Chopper Recap Chopper operation: Positive current: V a = V dc when T1 and T2 on V a = 0 when current freewheels through T2 and D4 Negative current: V a = -V dc when T3 and T4 on V a = 0 when current freewheels through T4 and D2 Output voltage can swing between: V dc and -V dc V dc and 0 + V a - T1 D1 T2 D2 D3 D4 T3 T4 + V dc - Dr. Ungku Anisa, July EEEB443 - Control & Drives

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Transfer Function of PWM-Controlled Four-quadrant Chopper Need to obtain linear relationship between control input v c and average armature voltage V a for PWM method Four quadrant chopper has two legs, so it requires two switching signals (one for each leg) Depending on relationship between the two switching signals, 4-quadrant chopper has two switching schemes: Bipolar switching Unipolar switching Switching scheme determines output voltage swing between V dc and -V dc or V dc and 0. + V a - T1 D1 T2 D2 D3 D4 T3 T4 Leg ALeg B + V dc − Dr. Ungku Anisa, July EEEB443 - Control & Drives

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Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching) Bipolar Switching PWM Leg A and Leg B obtain switching signals from the same control signal v c Switching of Leg A and Leg B are always complementary + V a - T1 D1 T2 D2 D3 D4 T3 T4 + V dc − vcvc v tri q q Leg A Leg B Dr. Ungku Anisa, July v c > V tri v c < V tri q = 1, q =0 T1 on, T2 on V a = V dc q = 0, q =1 T4 on, T3 on V a = -V dc

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Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching) Bipolar Switching PWM + V a - T1 D1 T2 D2 D3 D4 T3 T4 + V dc − vcvc v tri q q Leg A Leg B Va+Va+ Va-Va- Va-Va- V dc 0 Va+Va+ 0 2v tri vcvc VaVa V dc -V dc V a jumps between +V dc and –V dc Bipolar Switching PWM Dr. Ungku Anisa, July EEEB443 - Control & Drives V a = V a + - V a -

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Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching) Bipolar Switching PWM Va-Va- V dc 0 q 0 2v tri vcvc VaVa V dc -V dc V a jumps between +V dc and –V dc Bipolar Switching PWM Dr. Ungku Anisa, July EEEB443 - Control & Drives V a = V a + - V a - qq V dc 0 2v tri vcvc Va+Va+ V dc 0 v c > V tri v c < V tri

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Transfer Function PWM-Controlled Four-quadrant Chopper (Bipolar Switching) Each leg is a two-quadrant chopper. Output of Leg A (average): (5) where (6) Output of Leg B (average): (7) where (8) Hence, average voltage across the motor: (9) Subt. (6) into (9) Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives28 V dc Va-Va- 0 VaVa -V dc 2v tri vcvc Bipolar Switching PWM Va+Va+ 0 V dc

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Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) Unipolar Switching PWM Leg B switching signals obtained from the inverse of control signal for Leg A Leg A Leg B + V a - T1 D1 T2 D2 D3 D4 T3 T4 + V dc − vcvc v tri qaqa -v c v tri qbqb Dr. Ungku Anisa, July EEEB443 - Control & Drives v c > V tri v c < V tri -v c > V tri -v c < V tri

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Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) Unipolar Switching PWM Leg A Leg B + V dc − vcvc v tri qaqa -v c v tri qbqb + V a - T1 D1 T2 D2 D3 D4 T3 T4 2V tri vcvc -v c Va+Va+ Va-Va- V a jumps between +V dc and 0 Unipolar Switching PWM Va+Va+ V dc 0 Va-Va- 0 VaVa 0 Dr. Ungku Anisa, July EEEB443 - Control & Drives V a = V a + - V a -

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Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) Unipolar Switching PWM 2V tri vcvc -v c V a jumps between +V dc and 0 Unipolar Switching PWM VaVa V dc 0 Dr. Ungku Anisa, July EEEB443 - Control & Drives 2V tri vcvc -v c qaqa V dc 0 Va+Va+ 0 qbqb 0 Va-Va- 0 V a = V a + - V a - v c > V tri v c < V tri -v c > V tri -v c < V tri

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Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) 2V tri vcvc -v c Va+Va+ V dc 0 Va-Va- 0 VaVa 0 Each leg is a two-quadrant chopper. Output of Leg A (average): (10) where (11) Output of Leg B (average): (12) where (13) Hence, average voltage across motor armature: (14) Same as Bipolar Switching Scheme! Unipolar Switching PWM Dr. Ungku Anisa, July EEEB443 - Control & Drives

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PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching Bipolar Switching PWM Unipolar Switching PWM 2V tri vcvc -v c Va+Va+ V dc 0 Va-Va- 0 VaVa 0 Dr. Ungku Anisa, July EEEB443 - Control & Drives Va-Va- V dc 0 2v tri vcvc Va+Va+ V dc 0 VaVa -V dc Output voltage swings from V dc and –V dc Output voltage frequency equal to frequency of triangle voltage (f tri ) Output voltage swings from V dc and 0 Output voltage frequency equal to 2 times frequency of triangle voltage (f tri )

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PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching Current ripple = For same f tri and V dc, unipolar scheme gives: better output voltage waveform (less ripple) lower current ripple better frequency response Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives34 CharacteristicsBipolar SwitchingUnipolar Switching Output voltage swing V dc and -V dc V dc and 0 Output voltage frequency f tri = frequency of V tri 2f tri

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Gain of the PWM-controlled chopper: Two -quadrant: (15) Four–quadrant: (16) where V dc = dc link voltage V tri = maximum control voltage (i.e. peak of the triangular waveform) Chopper also has a delay: (17) where f c = carrier (triangular) waveform frequency Transfer Function PWM-Controlled Chopper: Two and Four Quadrant Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives35

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PWM-controlled Chopper: (18) Note: K r and T r as given in equations (15) – (17) above. Other subsystem transfer functions are as observed in ‘Closed-loop Control of DC Drives with Controlled Rectifier’. DC Motor and Load: Current Feedback: Speed feedback: Transfer Function of Subsystems Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives36

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Design of Controllers – Block Diagram of Motor Drive Assume that we are using PWM controlled chopper Control loop design starts from inner (fastest) loop to outer(slowest) loop Only have to solve for one controller at a time Not all drive applications require speed control (outer loop) Performance of outer loop depends on inner loop Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives37 Speed Control Loop Current Control Loop

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PI type current controller: (19) Loop gain function: (20) Design procedure - same as for current controller in closed- loop control using controlled rectifiers Design of Controllers– Current Controller Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives38 DC Motor & Load PWM-controlled Chopper

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Approximated by adding T r to T 1 (21) Design of Controllers– Current loop 1 st order approximation Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives39

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Design of Controllers– Current loop 1 st order approximation where (22) (23) (24) 1 st order approximation of current loop used in speed loop design. If more accurate speed controller design is required, values of K i and T i should be obtained experimentally. Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives40

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PI type current controller: (25) Assume there is unity speed feedback: (26) Design of Controllers– Speed Controller Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives41 DC Motor & Load 1 st order approximation of current loop

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1 Loop gain function: (27) Design procedure - same as for speed controller in closed-loop control using controlled rectifiers Design of Controllers– Speed Controller Dr. Ungku Anisa, July 2008EEEB443 - Control & Drives42

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References Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, Mohan, Underland, Robbins, Power Electronics: Converters, Applications and Design, 2 nd ed., John Wiley & Sons, USA, Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, Dr. Ungku Anisa, July EEEB443 - Control & Drives

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