Closed-loop Control of DC Drives with Controlled Rectifier
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Dr. Ungku Anisa, July 2008
Dr. Ungku Anisa, July 2008
Outline
Closed Loop Control of DC DrivesClosed-loop Control with Controlled RectifierTwo-quadrant
Transfer Functions of SubsystemsDesign of ControllersClosed-loop Control with Field WeakeningTwo-quadrant
Closed-loop Control with Controlled RectifierFour-quadrant
References*
Closed Loop Control of DC Drives
Feedback loops may be provided to satisfy one or more of the following:ProtectionEnhancement of response fast response with small overshootImprove steady-state accuracyVariables to be controlled in drives:Torque achieved by controlling currentSpeedPosition*
Closed Loop Control of DC Drives
Cascade control structureFlexible 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 valueTorque loop is fastest, speed loop slower and position loop - slowest*
Closed Loop Control of DC Drives
Cascade control structure:Inner Torque (Current) Control Loop:Maintains current within a safe limitAccelerates and decelerates the drive at maximum permissible current and torque during transient operations*
Torque (Current) Control Loop
Closed Loop Control of DC Drives
Cascade control structureSpeed Control Loop:Ensures that the actual speed is always equal to reference speed *Provides fast response to changes in *, TL and supply voltage (i.e. any transients are overcome within the shortest feasible time) without exceeding motor and converter capability*
Speed Control Loop
Closed Loop Control with Controlled Rectifiers Two-quadrant
Two-quadrant Three-phase Controlled Rectifier*
Current Control Loop
Speed Control Loop
Closed Loop Control with Controlled Rectifiers Two-quadrant
Actual motor speed m measured using the tachogenerator (Tach) is filtered to produce feedback signal mrThe reference speed r* is compared to mr to obtain a speed error signalThe speed (PI) controller processes the speed error and produces the torque command Te*Te* is limited by the limiter to keep within the safe current limits and the armature current command ia* is producedia* is compared to actual current ia to obtain a current error signalThe current (PI) controller processes the error to alter the control signal vc vc modifies the firing angle to be sent to the converter to obtained the motor armature voltage for the desired motor operation speed*
Closed Loop Control with Controlled Rectifiers Two-quadrant
Design of speed and current controller (gain and time constants) is crucial in meeting the dynamic specifications of the drive systemController design procedure:Obtain the transfer function of all drive subsystems
Design torque (current) control loop first
Then design the speed control loop
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Transfer Function of Subsystems
DC Motor and Load
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Transfer Function of Subsystems
DC Motor and Load
(1)
where(2)
(3)
This is achieved through redrawing of the DC motor and load block diagram.*
Transfer Function of Subsystems
DC Motor and Load
- mechanical motor time constant: (4)
- motor and load friction coefficient: (5)
In (3),(6)
(7)
Note: J = motor inertia, B1 = motor friction coefficient,
BL = load friction coefficient
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Transfer Function of Subsystems
Three-phase Converter
(8)
where vc = control signal (output of current controller)
Vcm = maximum value of the control voltage
Thus, dc output voltage of the three-phase converter(9)
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Transfer Function of Subsystems
Three-phase Converter
(10)
where V = rms line-to-line voltage
Converter also has a delay(11)
where fs = supply voltage frequency
Hence, the converter transfer function(12)
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Transfer Function of Subsystems
Current and Speed Feedback
(13)
where K = gain, T = time constant
Most high performance systems use dc tachogenerator and low-pass filterFilter time constant < 10 ms*
Design of Controllers
Block Diagram of Motor Drive
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Speed Control Loop
Current Control Loop
(15)
From the open loop gain, the system is of 4th order (due to 4 poles of system)Design of Controllers
Current Controller
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DC Motor & Load
Converter
Controller
Design of Controllers
Current Controller
(16)
Hence, the open loop gain function becomes:
i.e. system zero cancels the controller pole at origin.
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(17)
Design of Controllers
Current Controller
(18)
Hence, the open loop gain function becomes:
i.e. controller zero cancels one of the system poles.
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Design of Controllers
Current Controller
(19)
where (20)
The system is now of 2nd order.From the closed loop transfer function: ,the closed loop characteristic equation is:
or when expanded becomes: (21)
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Design of Controllers
Current Controller
(22)
(23)
So, for a given value of :use (22) to calculate n Then use (23) to calculate the controller gain KC*
Design of Controllers
Current loop 1st order approximation
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2nd order current loop model
(24)
Design of Controllers
Current loop 1st order approximation
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Full derivation available here.
1st order approximation of current loop
Design of Controllers
Current loop 1st order approximation
where (26)
(27)
(28)
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.*
(30)
Design of Controllers
Speed Controller
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DC Motor & Load
1st order approximation of current loop
(31)
From the loop gain, the system is of 3rd order.If designing without computers, simplification is needed.Design of Controllers
Speed Controller
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DC Motor & Load
1st order approximation of current loop
1
Design of Controllers
Speed Controller
(32)
Hence, design the speed controller such that:(33)
The open loop gain function becomes:
i.e. controller zero cancels one of the system poles.
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Design of Controllers
Speed Controller
(34)
where (35)
The controller is now of 2nd order.From the closed loop transfer function: ,the closed loop characteristic equation is:
or when expanded becomes: (36)
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Design of Controllers
Speed Controller
(37)
(38)
So, for a given value of :use (37) to calculate n Then use (38) to calculate the controller gain KS*
Closed Loop Control with Field Weakening Two-quadrant
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Closed Loop Control with Field Weakening Two-quadrant
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Field weakening
Closed Loop Control with Field Weakening Two-quadrant
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Induced emf controller
(PI-type with limiter)
Field weakening
Field current controller
(PI-type)
Field current reference
Estimated machine -induced emf
Induced emf reference
Closed Loop Control with Field Weakening Two-quadrant
The estimated machine-induced emf is obtained from:(the estimated emf is machine-parameter sensitive and must be adaptive)
The reference induced emf e* is compared to e to obtain the induced emf error signal (for speed above base speed, e* kept constant at rated emf value so that 1/)The induced emf (PI) controller processes the error and produces the field current reference if* if* is limited by the limiter to keep within the safe field current limitsif* is compared to actual field current if to obtain a current error signalThe field current (PI) controller processes the error to alter the control signal vcf (similar to armature current ia control loop) vc modifies the firing angle f to be sent to the converter to obtained the motor field voltage for the desired motor field flux*
Closed Loop Control with Controlled Rectifiers Four-quadrant
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Closed Loop Control with Controlled Rectifiers Four-quadrant
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Inputs to Selector block
References
Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control, Prentice-Hall, New Jersey, 2001.Rashid, M.H, Power Electronics: Circuit, Devices and Applictions, 3rd ed., Pearson, New-Jersey, 2004.Nik Idris, N. R., Short Course Notes on Electrical Drives, UNITEN/UTM, 2008.*
DC Motor and Load Transfer Function - Decoupling of Induced EMF Loop
Step 1:Step 2:*
DC Motor and Load Transfer Function - Decoupling of Induced EMF Loop
Step 3:Step 4:*
Back
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Vm
Input voltage
to rectifier
Cosine wave compared with
control voltage vc
Results of
comparison
trigger SCRs
Output voltage
of rectifier
Vcmcos() = vc
Cosine voltage
Back
Vcm
vc
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*
Back
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