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| 15 Application Note AN-1090 IRMCF3xx Series Controller Dynamics and Tuning By Eddy Ho, International Rectifier Table of Contents Page Introduction .......................................................................................................... 2 Current Controller................................................................................................. 2 Speed Controller .................................................................................................. 6 Field-Weakening Controller ................................................................................ 10 Critical Over Voltage Protection ......................................................................... 12 Interior Permanent Magnet Motor Control .......................................................... 14 This application note describes how to tune the embedded control loops on the IRMCF3xx series of control IC's. This covers the IRMCF312, IRMCF311 and IRMCF343 digital control IC's for air-conditioning systems and the IRMCF341 IC for washing machine applications. The control loops include the ID and IQ current control loops, the velocity control loop, the field weakening loop, IPM control and bus voltage protection. The note describes the equations used to derive the control loop constants and experimental methods to tune control constant www.irf.com AN-1090 1 15 Introduction This application note describes how to tune the embedded control loops on the IRMCF3xx series of control IC's. This covers the IRMCF312, IRMCF311 and IRMCF343 digital control IC's for airconditioning systems and the IRMCF341 IC for washing machine applications. The control loops include the ID and IQ current control loops, the velocity control loop, the field weakening loop, IPM control and bus voltage protection. The note describes the equations used to derive the control loop constants and experimental methods to tune control constants. There are 3 main control loops associated with IRMCK3xx series products. These control loops are current control loop, speed control loop and Field-weakening control loop. The following table summarizes the parameter dependence of each control loop. Parameters Motor Inductance Motor Resistance Voltage constant (Ke) System Inertia Current Controller Yes Yes No No Speed Controller No No Yes Yes Field-Weakening Controller Yes No Yes No Motor parameters are required (Parameter Configurator) for drive setup. These parameters are normally obtained from motor data sheet. IR Sensorless motor controller can tolerate +/-10 % motor parameter error without noticeable performance degradation. Increased parameter mismatch between motor and controller will result in degradation of torque per Amp capability. The degree of degradation is dependent on the operating conditions (speed, load) and motor characteristics (motor parameters and saturation). Current Controller The iMotion current controller utilizes Field-Oriented synchronously rotating reference frame type regulators. Field-Orientation provides significant simplification to the control dynamics of the current loop. There are two current regulators (one for d-channel and one for q-channel) employed for current regulation. The q-channel (torque) control structure is identical to d-channel (flux). The current control dynamics of d-channel is depicted in Figure 1. The motor can be represented by a first order lag with time constant T = L/R. This time constant involves motor inductance and equivalent resistance (R: cable + winding). For a surface mounted permanent magnet motor, the d and q channel inductances are almost equal. In the case of Interior permanent magnet motor, the q-channel inductance is normally higher than the d-channel inductance. In the current control dynamic diagram Figure 1, forward gain A translates digital controller output to voltage (include inverter gain) and feedback gain B translates current feedback (Ampere) to internal digital counts via A/D converter. The calculation of the controller gains (KxIreg, KpIreg_D) is done by using pole-zero cancellation technique as illustrated in Figure 2 where the current controller is rearranged to give transfer function block C(S). Setting KpIreg_D/KxIreg of C(S) to the time constant of the motor (T), the controller zero will cancel off the motor pole (pole-zero cancellation). Therefore, the controller dynamics can be further simplified as shown in Figure 3. The equivalent transfer function of Figure 3 is a first order lag with time constant Tc. By selecting appropriate current regulator response (typically 0.5 to 1 msec, entry of parameter configurator, Current Reg BW = 1/Tc) for a particular application, the current regulator gains can be readily obtained. It may be noticed that using pole zero cancellation technique, motor inductance enters into proportional gain calculation and resistance enters into integral gain calculation. www.irf.com AN-1090 2 15 KxIreg Current Command Controller Motor V A + - 1 S + + 1 R (1 + S T) I KpIreg_D B Figure 1. Current Control Dynamics Controller Current Command Motor V A + - KxIreg (1 + S (KpIreg_D/KxIreg)) 1 R (1 + S T) I S C(S) B Figure 2. Pole Zero Cancellation Controller Current Command + - Motor V A KxIreg 1 R I 1 1 + S Tc S B Tc = R/ (KxIreg*A*B) Figure 3. Simplified Current Control Dynamics Due to Pole Zero Cancellation www.irf.com AN-1090 3 15 Based on the pole-zero cancellation technique, the controller gains are evaluated by: K plreg = K xlreg = L q Current Re gBW A B R Current Re gBW 25 T A B Where A and B are the internal digital controller scaling (A*B = .006016) and T is the controller sampling time introduced for sampling compensation. The following gain calculation illustrates a drive application setup with Parameter configurator entries shown below: The current regulator gains are calculated as: K plreg = K plreg _ D K xlreg = 0.04 1500 = 9973 0.006016 0.04 1500 = = 9973 0.006016 6.1 1500 25 0.0001 = 4867 0.006016 The current controller in the Sensorless FOC block module directly uses these gains. MCE designer provides current loop diagnostic test function. This test provides the response of the current control loop and also the steady state accuracy. www.irf.com AN-1090 4 15 Once current regulator diagnostic is executed, step current response can be observed from trace function or current probes on w-phase. It is recommended to use current probe to observe step current response. Figure 4 shows (current probe) the step current response of w-phase when Current Reg diagnostic function is executed. In this figure, 25% step rated motor current is commanded. The step level can be controlled by parameter ParkI (inside Current Reg Diagnostic function). Figure 5 shows the expanded version of Figure 4. The measured current loop response is critically damped at 0.65 msec time constant (0 - 66.3% of final steady value), which is approximately equal to the anticipated current regulator bandwidth response (1/1500 = 0.667msec). 25% 0% Figure 4. Step Current Response 0.65 msec Figure 5. Step Current Response (Expanded Time Scale) www.irf.com AN-1090 5 15 Speed Controller The speed controller is the most outer-loop controller in a cascaded speed drive system. Figure 6 shows the cascaded control dynamics of the speed control loop. In practice, the inner current loop has much higher control bandwidth than the speed controller, therefore for speed control dynamic purpose, the inner current loop can be ignored as shown in Figure 7. Parameter M (Figure 7) relates command current digital counts to actual current in Amps. The motor mechanical dynamic is a first order function with mechanical time constant equals to J/F (Inertia/Friction). Pole-zero cancellation technique (outlined in current regulator tuning section) can be used to simplify tuning of the speed controller proportional and integral gains (KpSreg, KxSreg). In practice, information on mechanical friction (F) is difficult to obtain. In addition, temperature dependent friction characteristic is present in some applications. Therefore, manual speed tuning may be required to achieve optimal speed response. Some applications cannot tolerate high speed regulator bandwidth due to mechanical resonance present in mechanical arrangement. Controller Speed Regulator + Speed Command + KpSreg Speed Estimator KpIreg B Motor Load - KxSreg KxIreg Current Regulator 1 1 S + A + V 1 R (1 + S T) I Kt + 1 S + + + - 1/J F 1 S Speed Filter J - Inertia F - Friction Kt - Torque constant A, B, C - Conversion Gains SpdFiltBW Figure 6. Cascaded Control Dynamics controller Motor Speed Regulator + Speed Command + - KxSreg Load 1/J - 1 S + M + + Kt 1 Speed S F KpSreg J - Inertia F - Friction Kt - Torque constant C, M - Conversion Gains Filter C SpdFiltBW Figure 7. Simplified Speed Control Loop Dynamics www.irf.com AN-1090 6 15 As mentioned earlier, information on mechanical parameters (Friction and Inertia) may be inaccurate and Parameter Configurator will output less optimal gains for the controller. Manual tuning of speed regulator can be used to optimize speed performance. Figure 8 shows speed response (trace buffer speed feedback signal) of a high inertia fan under speed ramping. As can be seen, the speed response shows oscillatory behavior due to non optimized gain values. Ramp Speed response 3400 Speed (Digital counts) 3200 3000 2800 2600 2400 2200 1 100 199 298 397 496 595 694 793 892 991 Time (0.55 sec/Div) Figure 8. Ramp Speed Response There are many different approaches of tuning PI regulator for various applications. The following steps provide an example guide line of speed regulator tuning for fan applications. 1) Tuning of KpSreg. Run drive at a convenient speed say 30% rated rpm. Perform small step (30 to 35% rated rpm) speed response with KxSreg set to zero. The step response can be achieved by using a fast speed ramp setting (AccelRate). Under such condition, first order speed response is expected as shown in Figure 9. This figure shows the speed responses using 3 different proportional gains (KpSreg = Kp1, Kp2, Kp3). Step Speed Response 3400 3200 3000 2800 2600 2400 Increase KpSreg Kp1 Kp2 Kp 3 Speed (Digital Count) 1 201 401 601 801 1001 Time (0.167 sec/Div) Figure 9. Step Speed Response under Different KpSreg Gains www.irf.com AN-1090 7 15 Adjust KpSreg until the desired transient response (Speed regulator bandwidth) is obtained. For this fan application with high inertia to friction ratio, Kp3 is selected to yield approximately 0.2 sec first order time constant. 2) Tuning of KxSreg. After the desired proportional gain (KpSreg) is selected (step 1), please resume nominal ramp rate and speed regulator integral gain (KxSreg). Under such circumstance (with KpSreg = Kp3 and KxSreg = Kx1), issue a ramp speed command under the same speed range (30 to 35%) as illustrated in step 1. Figure 10 shows ramp speed responses under 3 different integral gains (Kx1, Kx2 and Kx3). The response with the original (imported from Parameter Configurator) integral gain (Kx1) exhibits oscillatory behavior. The integral gain is being reduced (Kx2 and Kx3) just enough to remove speed oscillation. For this fan application, the response obtained is acceptable with KxSreg = Kx3. Ramp Speed Response 3600 Speed (200 Digital Counts/Div) 3400 3200 3000 2800 2600 2400 1 100 199 298 397 496 595 694 793 892 991 Time (0.275 sec/Div) Figure 10. Ramp Speed Response under Different KxSreg Gains Reduce KxSreg Kx1 Kx2 Kx3 3) Figure 11 shows ramp speed response with non-optimized (KpSreg = Kp1, KxSreg = Kx1) and optimized (KpSreg = Kp3, KxSreg = Kx3) speed regulator gains. A tighter control response is exemplified with the gain optimization. www.irf.com AN-1090 8 15 Ramp Speed Reponse 3400 Speed (100 Digital Counts/Div) 3200 3000 2800 2600 2400 2200 1 100 199 298 397 496 595 694 793 892 991 Time (0.55 sec/Div) Optimized Figure 11. Comparison of Optimized and Non-optimized Speed Response 4) It may be noticed that there is still slight overshoot on the optimized Ramp Speed response (Figure 11). Most applications can tolerate a slight overshoot (<10%). Increasing KpSreg or reducing speed ramp rate as shown in Figure 12 can further reduce speed overshoot. It is recommended to keep overshoot to minimal possible for applications (i.e. Washer Spin Mode), which require Field-Weakening range of more than 1.5. Speed Overshoot Reduction Speed (100 Digital Counts/Div) 3200 3000 2800 Increase KpSreg Reduce Ramp 2600 2400 2200 1 201 401 601 801 1001 Time (0.275 sec/Div) Figure 12. Speed Overshoot Reduction www.irf.com AN-1090 9 15 Field-Weakening Controller Field weakening is required for wide speed range applications. Back EMF (BEMF) of a motor increases with speed up to the point that inverter output voltage reaches its maximum level. Further increase in motor speed requires flux weakening to maintain the motor terminal voltage at its maximum possible level as shown in Figure 13. Motor Flux Motor Voltage Inverter voltage Limit Crossover Speed Speed Figure 13. Field-Weakening Characteristics Figure 14 shows a block representation of the Field-Weakening Controller dynamics. The output of the controller (Fwk_Id) represents a d-axis current component, which opposed the rotor magnet flux (Flux). By injecting a negative d-axis current, the resultant flux can be reduced and hence the motor voltage can be limited to stay within the ceiling voltage of the inverter output. The control loop gain increases with motor frequency as shown in Figure 14. Inside the FieldWeakening controller, gain modulation is used to decouple the variation of loop gain due to motor frequency. Controller Motor Flux Modulation + level FieldWeakening Controller + Motor Frequency Fwk_Id B Ld + Voltage to modulation conversion Figure 14. Field-Weakening Control Dynamics Figure 15 shows the Field-weakening controller. This controller is implemented in the MCE application. As can be seen from this figure, when modulation exceed a prescribed level specified by FwkLvl, a negative d-axis current (Fwk_Id) will start and lowering down the main flux. The Field-Weakening controller acts as a modulation index limiter. The gain modulation block serves to compensate the increase in loop gain due to increase in motor frequency as mentioned earlier. www.irf.com AN-1090 10 15 Speed Gain Modulation FwkKi + FwkKxMod Integrate and Output limit Fwk_Id (to Inner-loop IdRefExt) FwkLvl - Gain - FwkLim Dv (Sensorless Foc output) modulation computation Qv (Sensorless Foc output) Figure 15. Field-Weakening Controller Block With gain modulation incorporated, the control loop gain is decoupled from motor frequency. Figure 16 shows a simplified representation of the Field-weakening control dynamic. The equivalent transfer function of Figure 16 is a first order lag system. Parameter M in Figure 16 is a function of motor inductance, nominal dc bus voltage and the motor crossover frequency (function of motor Ke). Parameter configurator sets the field-weakening controller gain (FwkKi) based on parameter M and a prescribed field-weakening loop response (0.25 sec). FwkKi Modulation + level - 1 S M Figure 16. Simplified Field-Weakening Control Dynamics The response of the Field-weakening loop can be observed from the command d-axis current (using MCEDesigner trace function). Under light Field-weakening condition (-10% rated motor current on field-weakening controller output current), a step change (-2%) in the modulation limit level (FwkLvl) is issued. When modulation limit reduces, the Field-Weakening controller increases d-axis motor current (negative) in order to reduce motor flux and satisfy the modulation limit (voltage limit). Figure 17 shows a step change in FwkLvl and the response of the command d-axis current. First order response is exemplified from Figure 17. The tuning of the FieldWeakening controller is straightforward since it only involves one controller gain. The response of the Field-Weakening controller should be high enough to catch up with speed changes. In practice, most appliance applications do not require high dynamic speed changes in FieldWeakening region. Therefore the response of Field-weakening can be relaxed (typically: 0.1 to 0.4 sec response time. Parameter configurator preset to 0.25sec). www.irf.com AN-1090 11 15 Figure 17. Field-Weakening Control Responses, Vertical: Id command (digital counts) Horizontal: Time (0.1 sec/ div) Critical Over Voltage Protection In order to achieve high-speed operation under limited voltage capability, motor flux is suppressed by injection of a negative d-axis current (Field-weakening) to the motor. In case of an inverter shunt down at high speeds, all inverter devices will be disabled and the negative d-axis field forcing will be lost. Under such circumstance, the motor flux will resume and motor voltage will build up according to motor Ke as shown in Figure 18. This is a critical over voltage condition in which the motor BEMF builds up and charges the dc bus capacitor voltage to an exceedingly large value. Motor Flux Speed Motor Voltage Voltage increase Inverter voltage Limit Speed Inverter shunt down Figure 18. Inverter Shunt Down during Field-Weakening In iMotion control IC (3xx series), the critical over voltage protection is implemented in MCE application software. Critical over voltage condition is detected by comparing dc bus voltage feedback to a configurable voltage level (configurable by Parameter Configurator: dc bus critical voltage). When critical over voltage is detected, command bit CriticalOv (inputs of MCE module www.irf.com AN-1090 12 15 Space Vector PWM) will be set. This will trigger a zero vector (low side devices turn-on) PWM state independent of any condition (including faults). The use of a zero vector enforces short circuit to the motor terminal and hence prohibits charging of dc bus capacitors. Figure 19 illustrates critical over voltage condition and the engagement of zero vector protection. Upon application of the zero vector, motor current will circulate within the motor windings and the rotational energy of the motor will be dissipated inside the motor (copper and core losses). Critical dc bus Over voltage Nominal dc bus voltage Motor W-phase Current Hor: 10 msec/ Div Inverter Shut down Zero Vector initiation Figure 19. Critical DC Bus Over Voltage (top: dc bus voltage, bottom: motor current) The interface between the critical over voltage detection and the Space Vector PWM module is shown in Figure 20. SVPWM module port_Ctrl0[1:0] pwm_lines[6] 00 01 10 11 = input = "Z" = "0" = "1" IC Pwm Pin Outs PWMUH User_U User_V User_W PwmPeriodConfig port_Ctrl0[3:2] u Duty v Ratio Modulator w PwmDeadTm PwmGuardBand Guard Band Protect UserVabEn User_Alpha From Sensorless FOC User_Beta From Sensorless FOC u ModScl TwoPhsCtrl[1] PwmPeriodConfig 2-phase PWM Enable Logic Space v Vector Modulator w (SVPWM) Guard Band Protect Gate Mux WH WL Guard Band Protect Gate Mux VH VL GCChargePD GCChargePW port_Ctrl0[7:6] 00 pwm_lines[9] 01 10 11 = input = "Z" = "0" = "1" pwmcfg[3] pwm_lines[7] 00 01 10 11 = input = "Z" = "0" = "1" UserVuvwEn pwmcfg[2] Gate Mux UH UL PWMUL port_Ctrl0[5:4] pwm_lines[8] 00 01 10 11 = input = "Z" = "0" = "1" PWMVH u Bootstrap v Precharge w PWMVL port_Ctrl0[9:8] pwm_lines[10] 00 01 10 11 = input = "Z" = "0" = "1" MotorSpeed Pwm2HiThr Pwm2LowThr TwoPhsCtrl[0] pwmCtrl PWMWH port_Ctrl0[11:10] pwm_lines[11] 00 01 10 11 = input = "Z" = "0" = "1" PWMWL CriticalOv MCE Application Critical Ov protection Figure 20. Critical Over Voltage Interface www.irf.com AN-1090 CriticalOv 13 15 In addition to the iMotion control IC, gate driver IC (IRS2631) of the iMotion chip set also provides over voltage protection. The gate driver IC can be configured to protect dc bus over voltage in the event of control IC failure using also the zero vector injection method. Interior Permanent Magnet Motor Control The motor torque developed by a permanent magnet motor is given by: Torque = P (FluxM Iq + (L d - L q ) Id Iq ) 2 Cylindrical Torque Reluctance Torque Where P Ld, Lq Id, Iq FluxM number of rotor poles d and q-axis inductance (d axis aligns to rotor magnet). d and q-axis current components. Flux linkage of permanent magnet There are two torque components associated with the motor torque equation. The first component (Cylindrical torque) is due to interaction between rotor magnet flux and stator q-axis current. The second component (reluctance torque) is due to motor saliency (difference in d and q inductance). This saliency term is negligible (Ld = Lq) in Surface Mounted Permanent magnet (SPM) motors. In the case of an Interior Permanent Magnet Motor (IPM) where Lq not equal to Ld, the torque per ampere rating is boosted by the saliency torque term. In motoring operation, a negative Id injection will contribute to the increase in reluctance torque. Figure 21a shows the current vector trajectory for optimal torque per ampere generation of an IPM motor. As current magnitude increases, the current angle advancement also increases which indicates an increase in d-axis current demand in the negative direction. The required current angle for optimal torque per ampere generation is depicted in Figure 21b. In iMotion control IC, this optimal current characteristics is approximated by a linear fit as shown in Figure 21b. Two parameters (AngDel and AngLim) are used to characterize the behavior of optimal current angle for generating maximum torque per ampere. Parameter AngDel fixes the slope of the linear line and parameter AngLim limits the maximum allowable angle advancement. Parameter configurator computes AngDel with 2 points (zero and rated current point). The implementation of this linear interpolation and the calculation of command d-q current are shown in Figure 22. www.irf.com AN-1090 14 15 q I Iq' Current Angle id' (a) d AngLim Current Angle (Deg) Current Angle (Deg) 90 0 Rated Amps Current Magnitude (b) 90 0 Rated Amps Current Magnitude (c) Figure 21. Current Angle at Maximum Torque per Ampere TrqRef Vector Rotator AngDel 0 AngLim + K + -AngLim 90 Deg IqRef_C Id_Decoupler To current regulator commands Figure 22. Current Decoupler for Optimal Torque per Ampere Operation www.irf.com AN-1090 15 |
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