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**EEEB443 Control & Drives 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 2008 EEEB443 - Control & Drives Dr. Ungku Anisa, July 2008

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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 2008 EEEB443 - Control & Drives

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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 Reference signal Output signal + Controller Plant Sensor Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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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 2008 EEEB443 - Control & Drives

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**Closed Loop Control of DC Drives**

For DC Drive, this can be: Controlled rectifier or DC-DC converter 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 2008 EEEB443 - Control & Drives

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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 Current Control Loop Speed Control Loop Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Current Control for DC Drives with Choppers**

Current control loop is used to control torque via armature current (ia) 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 2008 EEEB443 - Control & Drives

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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 vc vc is then passed to a PWM circuit to produce the switching signal q. q = 1 T1 ‘on’, T2 ‘off’ Va = Vdc q = 0 T1 ‘off’, T2 ‘on’ Va = 0 vc > Vtri vc < Vtri T1 ‘on’, Va = Vdc T2 ‘on’, Va = 0 Vdc Pulse Width Modulator (PWM) vc ia* PI + q T1 T2 D1 Va - D2 ia vtri ierr Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Current Control for Chopper Drives – PWM Controller**

In the PWM circuit: vc is compared with a triangular waveform if vc > Vtri ‘on’ signal is produced (q = 1) if vc < Vtri ‘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 Vtri vc > Vtri vc < Vtri Ttri ton 1 vc Vdc vc > Vtri vc < Vtri q va q = 1 T1 ‘on’, va = Vdc q = 0 T2 ‘on’, va = 0 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives Dr. Ungku Anisa, July 2008

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**Current Control for Chopper Drives – PWM Controller**

Ttri ton 1 vc Vdc Va In the PWM circuit: Average value of q over a cycle determines duty cycle of chopper: Average armature voltage: q va va switches between Vdc and 0 average armature voltage Va depends on duty cycle (i.e. how long T1 is on) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Current Control for Chopper Drives – PWM Controller**

PWM controls chopper duty cycle once in every cycle Frequency of Va fixed by frequency of Vtri 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 2008 EEEB443 - Control & Drives

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**Current Control for Chopper Drives – Hysteresis Controller**

ia ia* - ia ia ia* + ia Instantaneous current control Current controlled within a narrow band of excursion from the desired value ia* Hysteresis window determines allowable deviation of ia Vdc ia* q T1 T2 D1 + Va - D2 ia ierr ia* q ia ia Hysteresis Controller Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Current Control for Chopper Drives – Hysteresis Controller**

Actual current ia compared with reference current ia* to obtain error signal ierr If ia ia* + ia q = 0, T2 ‘on’ and Va = 0 If ia ia* - ia q = 1, T1 ‘on’ and Va = Vdc Value of ia can be externally set or made to be a fraction of ia Chopper switching frequency is not fixed ia ia* + ia ia* q ia ia ia ia* - ia ia ia* + ia ia ia* - ia q = 1 T1 ‘on’, va = Vdc q = 0 T2 ‘on’, va = 0 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Current Control for Chopper Drives – Qualitative Comparison**

Characteristics Hysteresis Controller PWM Controller Switching frequency Varying Fixed (follows sawtooth waveform frequency i.e. carrier frequency) Switching losses High (due to varying switching frequency) Low Speed of response Fastest (due to instantanous change in current) Fast Ripple current Adjustable (depends on hysteresis window ia ) Filter size Depends on ia Small Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives Preferred method !

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**Closed Loop Control for DC Drives with Choppers**

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

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**Closed Loop Control for DC Drives with Choppers**

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

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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 vc and average armature voltage Va for PWM method Need transfer function for PWM-controlled chopper vtri ia* Pulse Width Modulator (PWM) Chopper DC motor + vc q Va ia PI ia Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Two-quadrant Chopper**

Need to obtain linear relationship between control input vc and average armature voltage Va for PWM method Case 1: vc > Vtri vc < Vtri Vtri -Vtri vc T1 off all the time i.e. ton, T1 = 0 vc -Vtri Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Two-quadrant Chopper**

Case 2: Vtri -Vtri vc vc > Vtri vc < Vtri T1 on ½ cycle i.e. ton, T1 = 0.5Ttri 0.5 vc -Vtri Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Two-quadrant Chopper**

Case 3: vc > Vtri vc < Vtri Vtri -Vtri vc T1 on all the time i.e. ton, T1 = Ttri 1 Vtri 0.5 vc -Vtri Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Two-quadrant Chopper**

Relationship between and vc : (2) For the two-quadrant chopper: (3) Hence, considering only the term due to vc, the two–quadrant chopper gain is: (4) 0.5 vc -Vtri +Vtri 1 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Four-quadrant Chopper**

Recap Chopper operation: Positive current: Va = Vdc when T1 and T2 on Va = 0 when current freewheels through T2 and D4 + Va - T1 D1 T2 D2 D3 D4 T3 T4 + Vdc - Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Four-quadrant Chopper**

Recap Chopper operation: Positive current: Va = Vdc when T1 and T2 on Va = 0 when current freewheels through T2 and D4 Negative current: Va = -Vdc when T3 and T4 on Va = 0 when current freewheels through T4 and D2 Output voltage can swing between: Vdc and -Vdc Vdc and 0 + Va - T1 D1 T2 D2 D3 D4 T3 T4 + Vdc - Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Four-quadrant Chopper**

Need to obtain linear relationship between control input vc and average armature voltage Va 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 Vdc and -Vdc or Vdc and 0. + Vdc − + Va - T1 D1 T2 D2 D3 D4 T3 T4 Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives Leg A Leg B

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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 vc Switching of Leg A and Leg B are always complementary vc > Vtri vc < Vtri + Va - T1 D1 T2 D2 D3 D4 T3 T4 + Vdc − vc vtri q Leg A q = 1,q =0 T1 on, T2 on Va= Vdc q = 0, q =1 T4 on, T3 on Va= -Vdc Leg B Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)**

Bipolar Switching PWM Va = Va+- Va- Leg A q 2vtri vc + Vdc − D1 D3 T1 T3 + Va - Va+ Vdc vtri Va- Vdc T4 T2 D2 D4 Va Vdc -Vdc vc q Leg B Va+ Va- Va jumps between +Vdc and –Vdc Bipolar Switching PWM Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of PWM-Controlled Four-quadrant Chopper (Bipolar Switching)**

Bipolar Switching PWM 2vtri vc 2vtri vc vc > Vtri vc < Vtri q Vdc q Vdc Va+ Vdc Va- Vdc Va = Va+- Va- Va Vdc -Vdc Va jumps between +Vdc and –Vdc Bipolar Switching PWM Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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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) (8) Hence, average voltage across the motor: (9) Subt. (6) into (9) Bipolar Switching PWM 2vtri vc Vdc Va+ Vdc Va- Vdc Va Vdc -Vdc Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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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 vc > Vtri vc < Vtri + Va - T1 D1 T2 D2 D3 D4 T3 T4 + Vdc − vc vtri qa -vc qb Leg A -vc > Vtri -vc < Vtri Leg B Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching)**

Unipolar Switching PWM 2Vtri vc -vc qa Leg A vtri + Vdc − Va+ Vdc D1 D3 vc T1 T3 + Va - Va- Vdc vtri T4 T2 D2 D4 -vc Va Vdc qb Va+ Va- Leg B Va = Va+- Va- Va jumps between +Vdc and 0 Unipolar Switching PWM Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Unipolar Switching PWM**

Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) Unipolar Switching PWM 2Vtri vc -vc 2Vtri vc -vc vc > Vtri vc < Vtri qb Vdc -vc > Vtri -vc < Vtri qa Vdc Va+ Vdc Va- Vdc Va = Va+- Va- Va Vdc Va jumps between +Vdc and 0 Unipolar Switching PWM Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Unipolar Switching PWM**

Transfer Function PWM-Controlled Four-quadrant Chopper (Unipolar Switching) Each leg is a two-quadrant chopper. Output of Leg A (average): (10) where (11) Output of Leg B (average): (12) (13) Hence, average voltage across motor armature: (14) Unipolar Switching PWM 2Vtri vc -vc Va+ Vdc Va- Vdc Va Vdc Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives Same as Bipolar Switching Scheme!

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**PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching**

Bipolar Switching PWM Unipolar Switching PWM 2Vtri vc -vc 2vtri vc Va+ Vdc Va+ Vdc Va- Vdc Va- Vdc Va Vdc -Vdc Va Vdc Output voltage swings from Vdc and –Vdc Output voltage frequency equal to frequency of triangle voltage (ftri) Output voltage swings from Vdc and 0 Output voltage frequency equal to times frequency of triangle voltage (ftri) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**ftri = frequency of Vtri**

PWM-Controlled Four-quadrant Chopper Comparison between Bipolar & Unipolar Switching Characteristics Bipolar Switching Unipolar Switching Output voltage swing Vdc and -Vdc Vdc and 0 Output voltage frequency ftri = frequency of Vtri 2ftri Current ripple = For same ftri and Vdc, unipolar scheme gives: better output voltage waveform (less ripple) lower current ripple better frequency response Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function PWM-Controlled Chopper: Two and Four Quadrant**

Gain of the PWM-controlled chopper: Two -quadrant: (15) Four–quadrant: (16) where Vdc = dc link voltage Vtri = maximum control voltage (i.e. peak of the triangular waveform) Chopper also has a delay: (17) where fc = carrier (triangular) waveform frequency Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Transfer Function of Subsystems**

PWM-controlled Chopper: (18) Note: Kr and Tr 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: Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Design of Controllers – Block Diagram of Motor Drive**

Current Control Loop Speed Control Loop 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 2008 EEEB443 - Control & Drives

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**Design of Controllers– Current Controller**

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

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**Design of Controllers– Current loop 1st order approximation**

Approximated by adding Tr to T1 (21) Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Design of Controllers– Current loop 1st order approximation**

where (22) (23) (24) 1st order approximation of current loop used in speed loop design. If more accurate speed controller design is required, values of Ki and Ti should be obtained experimentally. Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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**Design of Controllers– Speed Controller**

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

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**Design of Controllers– Speed Controller**

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

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References Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001. Mohan, Underland, Robbins, Power Electronics: Converters, Applications and Design, 2nd ed., John Wiley & Sons, USA, 1995. Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008. Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives

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