AN93637 PSoC® 4 Sensorless Field-Oriented Control (FOC) Author: Bob Hu Associated Project: Yes Associated Part Family: CY8C42xx Software Version: PSoC Creator™ 3.1 or higher Related Application Notes: For a complete list of the application notes, click here. To get the latest version of this application note, or the associated project file, please visit http://www.cypress.com/go/AN93637. AN93637 shows how to implement sensorless field-oriented control (FOC) for a permanent magnet synchronous motor (PMSM) with a CY8C42xx device. A code example using the CY8CKIT-037 Motor Control Evaluation Kit is included to demonstrate sensorless FOC. Contents Introduction Introduction .......................................................................1 Motor Control Terms and Definitions .................................2 Sensorless FOC Basics ....................................................2 Code Example ...................................................................5 Features .......................................................................5 Design Overview ..........................................................6 Firmware ......................................................................8 CY8CKIT-037 Kit ..........................................................9 Operation.................................................................... 10 Performance ............................................................... 13 Design Details ................................................................. 14 Current Sampling ....................................................... 14 Transformations ......................................................... 20 Slide Mode Observer (SMO) ...................................... 21 PI Controllers.............................................................. 23 SVPWM Generation ................................................... 24 Summary ......................................................................... 27 Related Application Notes ............................................... 27 Appendix A: PMSM Model .............................................. 28 Appendix B: Slide Mode Observer (SMO) ....................... 31 Appendix C: SVPWM Theory .......................................... 32 Appendix D: Q Number Format (Fixed-Point Number) .... 35 Characteristics............................................................ 35 Conversion ................................................................. 36 Math Operations ......................................................... 36 Appendix E: Adapting the Design to Other Motors .......... 38 Appendix F: Tunable Parameters List ............................. 41 Worldwide Sales and Design Support ............................. 43 This application note shows how to control a permanent magnet synchronous motor (PMSM) with the sensorless ® field-oriented control (FOC) algorithm, using an ARM ® Cortex -M0-based PSoC 4 device. www.cypress.com The FOC algorithm is frequently used in motor control applications because it allows motors to operate with less noise and more stable torque output than other algorithms. Sensorless FOC adds the advantage of reducing the cost due to the absence of rotor position sensors. Sensorless FOC is used in many applications including consumer (air conditioner, refrigerator), industrial (blower, pump), and commercial (elevator, escalator) products. Sensorless FOC is calculation-intensive, and thus has been traditionally implemented with expensive digital signal processing (DSP) devices. However, with 32-bit ARM Cortex-M cores, it is possible to implement sensorless FOC with more cost-effective 32-bit MCUs. This application note assumes that you are familiar with PSoC 4 and the PSoC Creator IDE. If you are new to PSoC 4, see AN79953 – Getting Started with PSoC 4 and the PSoC 4200 family datasheet. If you are new to PSoC Creator, see the PSoC Creator home page. You should also understand motor control fundamentals; start with “electric motor” on Wikipedia. Finally, this application note includes a code example to be used with the Cypress CY8CKIT-037 Motor Control Evaluation Kit. This kit includes a 24-V 53-W PMSM motor. Note The CY8CKIT-037 kit board can operate at voltages as high as 48 V DC, and some components may operate at high temperatures. Use this kit with caution to avoid personal injury or equipment damage. Document No. 001-93637Rev. ** 1 PSoC® 4 Sensorless Field-Oriented Control (FOC) Motor Control Terms and Definitions BEMF: Back electromotive force. Commonly refers to the voltage that occurs in electric motors where there is relative motion between the armature of the motor and the magnetic field from the motor's field magnets or windings. See Appendix B. BLDC: Brushless DC motor. It has a trapezoidal BEMF; see Appendix E and Figure 38. PMSM: Permanent-magnet synchronous motor, or permanent-magnet motor (PMM). A synchronous motor that uses permanent magnets rather than windings in the rotor. It has a sinusoidal BEMF; see Appendix E and Figure 38. Sensorless FOC Basics This section introduces the hardware structure of a typical sensorless FOC system as well as a firmware overview of the FOC algorithm. If you are familiar with these concepts, you can skip this section and go to the Code Example section. Figure 1 shows the diagrams of the two types of PMSM motor; they differ in how magnets are placed in the rotor: Surface PMSM (SPMSM) – Left Interior PMSM (IPMSM) – Right Figure 1. Rotor Structure for SPMSM and IPMSM Source: http://www.hamaco.jp SPMSM is widely used due to the ease of manufacture and assembly, while IPMSM has a larger torque output with the same sized motor. The sensorless FOC algorithm varies depending on the motor type; this application note uses SPMSM, referred to as just “PMSM”. www.cypress.com Document No. 001-93637Rev. ** 2 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 2 shows the hardware block diagram of a typical sensorless FOC system. It consists of: Figure 2. Overview of a Typical Sensorless FOC System MCU Power Power Inverter Vdd PMSM Vbus, Vdriver Current sampling and signal conditioning circuit to determine the rotor position A PWMs Communication interface MCU B Inverter These components can be on the same controller board or separated in the system such as on an MCU board and an inverter board. PMSM C Motor Motor Figure 3 shows the details of the Inverter block shown in Figure 2. The inverter is composed of gate drivers and six MOSFETs (two for each motor phase). Turning different MOSFETs ON or OFF changes the current direction through the motor’s stator windings or phases. Opamps Opamps Signal Conditioning RR RR RR For example, turning ON Q1 and Q4 generates a current from phase A to phase B, while turning ON Q3 and Q2 reverses the current direction in those phases. Changing the current direction changes the stator flux direction and makes the rotor rotate. Sensing Resistors Communication Communication Interface Interface Controller Controller board board Figure 3. Details of Inverter Block PWMAH Gate PWMAL Driver AH AL PWMBH Gate PWMBL Driver BH BL PWMCH Gate PWMCL Driver CH CL Vbus Q1 AH Q3 BH Q2 AL Q5 CH Q4 BL Q6 CL B A C Vbus is a higher-voltage DC supply to power the motor. For example, it is 24 V in the CY8CKIT-037 kit. Note that the pairs of MOSFETs on the same phase (for example, Q1 and Q2) must not be turned ON at the same time – the resultant low resistance causes high currents that can damage the MOSFETs. www.cypress.com Document No. 001-93637Rev. ** 3 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 4 and Figure 5 show diagrams of the sensorless FOC algorithm and its calculation flow. The algorithm controls either the motor speed or motor torque using a proportional-integral (PI) controller based on a mathematical model of the PMSM (Appendix A describes the PMSM model). The control result is sent to a Space Vector Pulse Width Modulation (SVPWM) block (Appendix C). The SVPWM block generates three-phase voltages that change the stator currents. Figure 4. Sensorless FOC Control Block Diagram Sensorless FOC θ ω_ref Speed PI uα Inverse uβ Park Inverse Clarke ua ub uc SVPWM duty a duty b duty c P W M Inverter uq ud iq_ref id_ref iq Iq PI Park id Id PI iα iβ Clarke A D C iα iβ θ ω ia ib ic Speed and Position Estimation Motor Figure 5. Sensorless FOC Calculation Flow Ia Ib Ic Iα Clarke 3-Phase System Iβ Id Park Iq Ud PIs Uq Ua Ub Uc Uα Inverse Park Uβ Inverse Clarke 2-Phase System SVPWM 3-Phase System The Clarke and Park transformation calculations convert these three sampled motor phase currents into two values that are used by the PI controller. The Inverse Clarke and Inverse Park transformations are the opposites of the Clarke and Park transformations, respectively. Figure 6 shows the Clarke transformation, where the three motor phase currents ( , , ) are converted to and . The (a, b, c) frame is a three-phase stator reference frame, where the axes are 120° apart from each other. The transformation method is to project ( , , ) onto the (α, β) axes, which produce the outputs and . Duty a Duty b Duty c Figure 6. Clarke Transformation β b iβ is ib ic ia a iα α c www.cypress.com Document No. 001-93637Rev. ** 4 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 7 shows the details of the Park transformation. This transformation converts the current vectors from the Clarke transformation, and , to a frame on the rotating part of the motor. The axes of the rotating frame are called (d, q). The current vectors on these axes are called and . is d axis to the and the flux linkage vector of the rotor magnet. The is always aligned with , and the q axis is at 90° d axis. The rotor rotates at an angular speed , is the angle between the α and d axes. Figure 7. Park Transformation β ωr q In the (d, q) frame, the motor torque is proportional to . We can control to achieve the desired torque by using the proportional-integral (PI) controller. For details on the Clarke and Park transformations as well as the torque output, see Appendix A: PMSM Model. d iβ is Ψf id θr iq iα a α The angle used in the Park transformation is derived from the speed and position estimation. An algorithm called “Slide Mode Observer” (SMO) uses and to derive the value. Then, the angular speed is calculated based on . For more information, see Appendix B: Slide Mode Observer (SMO). Code Example This application note includes an example project to demonstrate sensorless FOC algorithm implemented with CY8C42xx devices. The code example is a complete design with all the code already written. It is intended to be used directly with the Cypress’s motor kit, CY8CKIT-037. This kit can be used with other motors if the motor’s power level is in the range supported by the CY8CKIT-037 kit. See Appendix E: Adapting the Design to Other Motors. Appendix F: Tunable Parameters List provides a quick reference for tuning the parameters for other motors. If the motor’s power level is greater than the range supported by this kit, you must design your custom control board with higher-power MOSFETS, power supply, and other components. The code example can still be used. Features Implements the sensorless FOC algorithm and closed-loop speed control in a multilayer, extensible, binary library architecture Estimates the rotor position with the Slide Mode Observer (SMO) algorithm Employs open-loop control at startup, which is changed to closed-loop control after the rotor position is determined Can adjust the motor speed by using the the potentiometer on the kit Uses the PSoC 4 internal opamps and the 888.89-Ksps successive approximation register (SAR) ADC for signal conditioning and measuring the motor phase current Supports motor speeds from 500 to 4000 RPM by default. Can support higher speeds in other motors by modifying the tuning parameters in the code example Provides control accuracy 5% over the default speed range. Using high-resolution sensing resistors and advanced control algorithms can improve the accuracy; this topic is outside the scope of this application note. www.cypress.com Document No. 001-93637Rev. ** 5 PSoC® 4 Sensorless Field-Oriented Control (FOC) Design Overview Figure 8 illustrates sensorless FOC implementation in PSoC 4. A 12-bit SAR ADC and two opamps are used to sample the motor phase currents (only two phase currents need be sampled; the third phase can be calculated from the other two.) The three TCPWMs generate six PWM outputs applied to the Inverter. A serial communication block (SCB) implements a UART to communicate with the host. Figure 9 is the corresponding implementation in PSoC Creator. For details, see Design Details. Figure 8. PSoC4 Sensorless FOC Implementation Block Diagram PSoC4 TCPWM Flash LPCOMP SRAM Cortex-M0 48MHz Ibus i SCB UART A B SAR ADC R Inverter Inverter Motor TCPWM iDAC < TCPWM C Opamp M U X Opamp Vbus POT R R R Figure 9. PSoC Creator Schematic Overview www.cypress.com Document No. 001-93637Rev. ** 6 PSoC® 4 Sensorless Field-Oriented Control (FOC) Table 1 shows the PSoC 4 resources that are used by this code example: Table 1. Resource Usage Summary www.cypress.com Item Used Available CPU Frequency 48 MHz 48 MHz PWM Frequency 10 kHz NA Flash (GCC compiler, size optimization) 17,216 bytes 32,768 bytes SRAM without stack and heap (GCC compiler, size optimization) 860 bytes NA SRAM in total (GCC compiler, size optimization) 2140 bytes 4096 bytes UDB 0 4 UDB Control Registers 1 4 UDB Status Registers 0 4 Interrupts 3 32 TCPWM Blocks 3 4 Opamps 2 2 Low-Power Comparators 1 2 8-bit current DAC (IDAC) 1 1 Document No. 001-93637Rev. ** 7 PSoC® 4 Sensorless Field-Oriented Control (FOC) Firmware Figure 10 shows the firmware execution flow. The FOC algorithm requires the PWM duty cycle to be updated every control cycle. Therefore, FOC calculations must be done in a periodic interrupt service routine (ISR). The ISR is triggered by the PWM every 100 µs (10-kHz PWM) – this is the control cycle period. Note that this interrupt should be high priority for effective duty cycle control – see SVPWM Generation. The cycle period can be decreased by increasing the PWM frequency. A shorter control period results in a higher-bandwidth control system with two benefits: Motor can be run faster Better response to load changes The communication and other functions that do not require real-time processing are executed in the main loop. Figure 10. Firmware Execution Flow Start Cymc_HAL_ADCReadSample Cymc_BCL_Clark System Initialization (main.c) Cymc_ACL_SMOCal interrupt signal PWM_MainLoop_ISR from PWM_A Main Loop (main.c) FOC_MainLoop_ISR (foc.c) Cymc_BCL_Park Cymc_GFL_PICal Cymc_BCL_InvPark Cymc_BCL_InvClark Cymc_BCL_SVPWM Cymc_HAL_PWMOutputUpdate The code example associated with the kit and this application note includes a multilayer, extensible, library architecture as Figure 11 shows. Figure 11. Sensorless FOC Motor Control Library Architecture www.cypress.com Document No. 001-93637Rev. ** 8 PSoC® 4 Sensorless Field-Oriented Control (FOC) CY8CKIT-037 Kit The Cypress kit CY8CKIT-037 is a motor-driver board designed to support three control algorithms: trapezoidal, FOC, and microstepping control for stepper motors. It has no MCU; it is a peripheral board to be used with the CY8CKIT-042 (Figure 12), through the Arduino-compatible interface. For more information, refer to the CY8CKIT-037 User Guide. Figure 12. CY8CKIT-037 (Top) and CY8CKIT-042 (Underneath) A PMSM, manufactured by Anaheim Automation, is included in this kit. Table 2 lists the motor parameters. See Appendix E: Adapting the Design to Other Motors for information on how to change the code example by changing the motor parameters listed in this table. Table 2. Parameters for CY8CKIT-037 Motor www.cypress.com Item Parameter Part Number BLY172S-24V-4000 Rated Torque (oz-in) 18.0 Rated Voltage (V) 24 Rated Power (watts) 53 Rated Speed (RPM) 4000 Torque Constant (oz-in/A) 5.03 Back EMF Voltage (V/kRPM) 4.14 Line-to-Line Resistance (ohm) 0.8 Line-to-Line Inductance (mH) 1.2 Rotor Inertia (oz-in-sec2) 0.000680 "L" Length (in) 2.37 Shaft Single Document No. 001-93637Rev. ** 9 PSoC® 4 Sensorless Field-Oriented Control (FOC) Operation Step 1 – Configure CY8CKIT -042 Select 3.3 V as the VDD power at jumper J9 on the CY8CKIT-042, as Figure 13 shows. Figure 13. CY8CKIT-042 Configuration Note In this application, the USB cable is used only for firmware programming, so it can be removed after programming. If you keep the cable connected, ensure that the other end is NOT connected to the PC. Connecting the cable to the PC causes the firmware to generate an “undervoltage” error, and the motor will not start. www.cypress.com Document No. 001-93637Rev. ** 10 PSoC® 4 Sensorless Field-Oriented Control (FOC) Step 2 – Configure CY8CKIT -037 Configure the board via jumpers J13-J24 as listed in the row “BLDC 2-SHUNT FOC” printed on the board. See Figure 14 and Figure 15. Figure 14.CY8CKIT-037 Configuration for Sensorless FOC Motor Control Figure 15. Jumper Table for CY8CKIT-037 Step 3 – Plug CY8CKIT-037 into CY8CKIT-042 Plug the CY8CKIT-037 into the CY8CKIT-042 via Arduino connectors J1-J4, as Figure 12 shows. www.cypress.com Document No. 001-93637Rev. ** 11 PSoC® 4 Sensorless Field-Oriented Control (FOC) Step 4 – Connect the Power Supply and Motor Connect the BLDC motor to J9 and J10 on CY8CKIT-037. The other motor cable routes the signals from the sensors inside the motor. (The kit hardware supports sensored BLDC motors and sensored FOC.) Because this is a sensorless example, we do not need to connect this cable. Connect the 24-V power adapter to J7. See Figure 16. Figure 16. Connect Motor and Power Supply S t e p 5 – B u i l d t h e P r o j e c t a n d P r o g r a m t h e P S o C 4 D e vi c e Open the sensorless FOC motor control code example project provided with this application note in PSoC Creator 3.1 or later. Select Build > Build Sensorless FOC Motor Control. When the build is complete, select Debug > Program to program the PSoC 4 device. www.cypress.com Document No. 001-93637Rev. ** 12 PSoC® 4 Sensorless Field-Oriented Control (FOC) Step 6 – Press the SW2 Button to Start Motor Rotation Press the SW2 button (Figure 17) to start the motor rotation. If the motor does not rotate and LED2 is blinking, an error has occurred. In this case, first confirm that steps 1 to 5 have been done correctly. Press the Reset button to clear the error status and press SW2 again. If LED2 still blinks, there must be a problem in the hardware or software. You can debug it using a multimeter or oscilloscope to observe the signals, or set breakpoints to monitor variables. You can also contact Cypress for technical support. Figure 17. Buttons and Status LED Reset LED2 SW2 Performance Figure 18 to Figure 20 show one of the phase currents for different motor speeds using the motor provided in the kit. Figure 21 shows the phase current during startup. Figure 18. Phase Current – 600 RPM Figure 19. Phase Current– 2000 RPM Figure 20. Phase Current– 4000 RPM Figure 21. Phase Current at Startup www.cypress.com Document No. 001-93637Rev. ** 13 PSoC® 4 Sensorless Field-Oriented Control (FOC) Design Details This section presents implementation details for each stage of the sensorless FOC processing listed in the PWM ISR (Figure 10), including current sampling, Clarke and Park transformations, SMO, PI controller, and SVPWM. Current Sampling PSoC Creator Schematic Figure 22 shows that four input channels are periodically sampled by the SAR ADC. The channels are: Two motor phase currents: OP_I_a_Vout_Filt and OP_I_b_Vout_Filt Bus voltage (OP_V_bus_Vout_Filt). This is the Inverter power supply (default 24 V) divided by resistors. Voltage input from variable resistor (potentiometer). Note that resistors and capacitors are included in the design but are not shown in this figure. For details, see the kit schematic. Figure 22. PSoC Creator Schematic – Current Sampling www.cypress.com Document No. 001-93637Rev. ** 14 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 23 and Figure 24 on page 16 show the SAR ADC configuration with the following features: Sampling clock is 16 MHz for an 888.89-ksps sampling rate. The actual sample rate shown in Figure 23 indicates that four channels are being sampled (888 / 4 = 222). Voltage reference is VDDA/2 to obtain a 0-to-VDDA input range. All channels are single-ended. The sampling result is unsigned. A hardware trigger starts sampling. After four channels are sampled, the ADC stops and waits for the next trigger signal. The trigger frequency is 10 kHz. The PWMs provide a common timing for ADC sampling, CPU interrupt, and MOSFET control – see Figure 9, Figure 10, and the SVPWM Generation section. Figure 23. SAR ADC Configuration, General Tab www.cypress.com Document No. 001-93637Rev. ** 15 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 24. SAR ADC Configuration, Channels Tab www.cypress.com Document No. 001-93637Rev. ** 16 PSoC® 4 Sensorless Field-Oriented Control (FOC) The motor phase current is converted to a voltage by the sensing resistors, as Figure 25 shows. The figure also shows that, because the sum of the three currents must be zero at the sampling point, we can sample just two of the currents and calculate the third. The opamp gains and the sensing resistor values are selected so that: The voltage stays in the ADC input range when the current is at the rated maximum. Sensing resistors are typically on the order of milliohms. The measurement of low currents is accurate. The sensing resistors have a tolerance of 1%. Figure 25. Dual-Shunt Current Sampling Opamp Ia A B C Ic=-(Ia+Ib) Opamp Ib R R R Figure 26 shows the schematic design for the CY8CKIT-037 kit. The kit board has 30-mΩ sensing resistors (not shown) and a 2.1-A rated current. Bias resistors (R40, R41) are included to handle positive and negative currents. Figure 26. CY8CKIT-037 Schematic: Signal Conditioning for Phase-A Current www.cypress.com Document No. 001-93637Rev. ** 17 PSoC® 4 Sensorless Field-Oriented Control (FOC) The PSoC 4 internal opamps are used. Figure 27 shows the configuration of each Opamp Component. Figure 27. PSoC 4 Internal Opamp Configuration Figure 28 shows the pin assignments for the SAR ADC and opamps. The opamp pins are direct connected to the internal opamps. Using these pins reduces the usage of analog routing resources as well as resistances between the pins and the opamp terminals. Figure 28. Pin Assignments for Opamp and SAR ADC www.cypress.com Document No. 001-93637Rev. ** 18 PSoC® 4 Sensorless Field-Oriented Control (FOC) Current Sampling Firmware The firmware for current sampling consists of initialization function calls and functions to read and use the sample data. The code example associated with the kit and this application note includes a Cypress-proprietary motor control library. This library manages the sensorless FOC procedure, as described in the Firmware section. Some system parameters such as DC bus voltage and sensing resistors value are defined as macros in the motor control library. For more information, see Appendix E: Adapting the Design to Other Motors. For system initialization, the Opamp Component API has a Start() function, as Code 1 shows. The SAR ADC is initialized by a motor control library function (see Figure 11). Code 1. Current Sampling Initialization /* main.c */ void main() { /* Initialize Opamps */ Opamp_A_Start(); Opamp_B_Start(); /* Initialize SAR ADC */ Cymc_HAL_ADCStart(); } /******************************************************/ /* Cymc_HAL_ADC.c */ void Cymc_HAL_ADCStart(); { /* start SAR ADC */ SADC_Start(); } Current sampling is done in the ISR, as Code 2 shows. A motor control library function (see Figure 11) is called to read the ADC raw data. Code 2. Current Sampling in the ISR /* foc.c */ CY_ISR(FOC_MainLoop_ISR) { . . . /* Read ADC and get phase current*/ Cymc_HAL_ADCReadSample(); . . . phaseCurrentU = adcRawData[ADC_IA_CHAN]; } /******************************************************/ /* Cymc_HAL_ADC.c */ void Cymc_HAL_ADCReadSample() { uint8 i = 0; for(i = 0; i < CHANNEL_NUM; i++) { adcRawData[i] = SADC_GetResult16(i) & (0x0FFF); } } www.cypress.com Document No. 001-93637Rev. ** 19 PSoC® 4 Sensorless Field-Oriented Control (FOC) Transformations Four structures are defined in the motor control library (Figure 11) for Clarke and Park transformations and the inverse transformations, as Code 3 shows. Four functions are defined to do the transformations. The structures and function prototypes are declared in the motor control library file Cymc_BCL_Transform.h: Code 3. Clarke and Park Transformation Structures and Function Prototypes /* Cymc_BCL_Transform.h */ /* struct definition for Clarke transformation*/ typedef struct { q15_t inU; /* phase-U variable q15_t inV; /* phase-V variable q15_t outAlpha; /* Output: α-axis variable q15_t outBeta; /* Output: β-axis variable } ClarkTrans; /* struct definition typedef struct { q15_t outU; q15_t outV; q15_t outW; q15_t InAlpha; q15_t InBeta; } InvClarkTrans; /* struct definition typedef struct { q15_t inAlpha; q15_t inBeta; q15_t outD; q15_t outQ; q15_t inSin; q15_t inCos; } ParkTrans; */ */ */ */ for inverse Clarke transformation */ /* /* /* /* /* Output: Output: Output: α-axis β-axis phase-U variable phase-V variable phase-W variable variable variable */ */ */ */ */ for Park transformation */ /* /* /* /* /* /* α-axis variable β-axis variable Output: d-axis variable Output: q-axis variable angle sin value angle cos value */ */ */ */ */ */ /* struct definition for inverse Park transformation */ typedef struct { q15_t outAlpha; /* α-axis variable */ q15_t outBeta; /* β-axis variable */ q15_t inD; /* Output: d-axis variable */ q15_t inQ; /* Output: q-axis variable */ q15_t inSin; /* angle sin value */ q15_t inCos; /* angle cos value */ } InvParkTrans; extern extern extern extern void void void void www.cypress.com Cymc_BCL_Clark(ClarkTrans *clark); Cymc_BCL_Park(ParkTrans *park); Cymc_BCL_InvPark(InvParkTrans *invPark); Cymc_BCL_InvClark(InvClarkTrans *invClark); Document No. 001-93637Rev. ** 20 PSoC® 4 Sensorless Field-Oriented Control (FOC) Code 4 shows how to use these functions: Code 4. Using Clarke and Park Transformation Functions /* foc.c */ CY_ISR(FOC_MainLoop_ISR) { . . . /* Clarke Transformation uvw -> αβ */ clarkTrans.inU = phaseCurrentU0 << 2; /* Phase U current */ clarkTrans.inV = phaseCurrentV0 << 2; /* Phase V current */ Cymc_BCL_Clark(&clarkTrans); . . . /* Park Transformation αβ -> dq */ parkTrans.inAlpha = clarkTrans.outAlpha; parkTrans.inBeta = clarkTrans.outBeta; Cymc_GFL_SinCosCal_Q15(curAngle, &parkTrans.inSin, &parkTrans.inCos); Cymc_BCL_Park(&parkTrans); . . . invParkTrans.inSin = parkTrans.inSin; invParkTrans.inCos = parkTrans.inCos; Cymc_BCL_InvPark(&invParkTrans); . . . invClarkTrans.InAlpha = invParkTrans.outAlpha; invClarkTrans.InBeta = invParkTrans.outBeta; Cymc_BCL_InvClark(&invClarkTrans); . . . } Slide Mode Observer (SMO) An introduction to SMO theory is in Appendix B: Slide Mode Observer (SMO). The structure and function prototypes for SMO calculation (Code 5) are defined in the motor control library (see Figure 11). Code 5. SMO Calculation Structure and Function Prototypes /* Cymc_ACL_SMO.h */ typedef struct { q15_t Vbus; q15_t volAlpha; q15_t volBeta; q15_t speedRef; q15_t Ggain; q15_t Fgain; q15_t slideCoff; q15_t slideError; q15_t curAlpha; q15_t curBeta; q15_t Theta; }SMO; /* /* /* /* /* /* /* /* /* /* /* DC-bus voltage */ α-axis stator voltage */ β-axis stator current */ Current speed reference */ control gain */ filter gain */ coefficient K for slide control */ error threshold for slide control */ α-axis stator current */ β-axis stator current */ Output: angle */ void Cymc_ACL_SMOCal(SMO *smo); void Cymc_ACL_SMOParamtersInit(floatRs, floatLs, floatTs, floatbaseFrequency, SMO *smo); www.cypress.com Document No. 001-93637Rev. ** 21 PSoC® 4 Sensorless Field-Oriented Control (FOC) A global variable of type SMO structure (Code 6) is also defined in the motor control library (see Figure 11). Code 6. SMO Structure Variable /* Cymc_MAL.h */ SMO smoEst; /* slide mode observer struct */ To use the SMO module, you must first call the motor control library function Cymc_MAL_MotorInit() in your initialization code. Code 7 shows initialization and usage of SMO: Code 7. SMO Initialization and Usage /* main.c */ void main() { . . . /* Initialize Motor Parameters */ Cymc_MAL_MotorInit(); . . . } /* Cymc_MAL.c */ void Cymc_MAL_MotorInit() { motor.Rs = M_RS; motor.Ls = M_LS; motor.Poles = M_POLES; motor.Ts = M_TS; motor.baseFrequency = M_BASEFREQUENCY; motor.ratedSpeedRPM = M_RATED_SPEED; /* Ω */ /* H */ /* S */ /* Hz */ /* RPM */ /* Initialize the SMO parameters */ Cymc_ACL_SMOParamtersInit(motor.Rs, motor.Ls, motor.Ts, motor.baseFrequency, &smoEst); smoEst.slideError = _FQ(0.5); /* see Appendix D */ } Code 8 shows how to use the SMO routines to obtain and use the angle information that is stored in the variable ‘curAngle’: Code 8. Using the SMO Module in the ISR /* foc.c */ CY_ISR(FOC_MainLoop_ISR) { . . . /* Position Calculation*/ smoEst.Vbus = _FQ(1.0); /* see Appendix D */ smoEst.speedRef = rampUp.output; smoEst.volAlpha = invParkTrans.outAlpha; smoEst.volBeta = invClarkTrans.InBeta; smoEst.curAlpha = clarkTrans.outAlpha; smoEst.curBeta = clarkTrans.outBeta; Cymc_ACL_SMOCal(&smoEst); . . . Cymc_GFL_SinCosCal_Q15(curAngle, &parkTrans.inSin, &parkTrans.inCos); . . . } www.cypress.com Document No. 001-93637Rev. ** 22 PSoC® 4 Sensorless Field-Oriented Control (FOC) PI Controllers The PI control equation for a continuous control system is: Where: Proportional factor Integration factor Error between actual value and reference Initial output at system startup Three parameters – motor speed, , and – are controlled by separate PI controllers. The speed PI controller uses the error between the calculated rotation speed and a given speed reference to calculate the control output, which in turn is the reference for the PI controller. The and PI controllers control and , respectively, using the errors for and . See Figure 4. th Code 9 shows how to implement PI control. Note that the speed PI control is only executed in every N control cycle. N is defined by the macro DEFAULT_SPEEDLOOPSCALER in Cymc_MAL.h, and saved in ‘speedLoopPrescaler’. The motor can be controlled in two modes: speed mode and torque mode. The speed mode controls the rotation speed in relation to a given speed reference. The torque mode controls the torque output in relation to a given torque reference. Depending on the mode selected, one of the references is used in the PI controller, as Code 9 shows. Code 9. PI Controllers /* foc.c */ CY_ISR(FOC_MainLoop_ISR) { . . . /* Speed PI Controller */ if(speedLoopCount == speedLoopPrescaler) { pidSpeed.ref = rampUp.output; /* motor.speedRef */ pidSpeed.fbk = speedEst.estimatedSpeed; Cymc_GFL_PICal(&pidSpeed); speedLoopCount = 0; updateSpeedrefFromVR(); } speedLoopCount++; /* Iq PI Controller */ /* select speed or torque control */ if(motor.runState == M_SPEEDLOOP) { pidIq.ref = pidSpeed.out; } else { pidIq.ref = motor.vqRef; } pidIq.fbk = parkTrans.outQ; Cymc_GFL_PICal(&pidIq); /* Id PI Controller */ pidId.ref = motor.vdRef; pidId.fbk = parkTrans.outD; Cymc_GFL_PICal(&pidId); . . . } www.cypress.com Document No. 001-93637Rev. ** 23 PSoC® 4 Sensorless Field-Oriented Control (FOC) SVPWM Generation PSoC Creator Schematic Design The SVPWM subsystem produces sinusoidal currents on the motor phases by changing the output duty cycles of the three PWMs (for details, see Appendix C: SVPWM Theory). The PWM outputs – two complementary outputs for each motor phase – turn the MOSFETs ON or OFF (see Figure 3). Figure 29 shows the SVPWM implementation in PSoC Creator. A common 48-MHz clock synchronizes the PWM outputs. The output enable (OE) feature of the output pins is enabled and controlled by the firmware through a control register. Figure 29. PSoC Creator Schematic: SVPWM and Timing Figure 30 shows the timing for all three PWMs as well as the details of PWM_A. In addition to the PWM signals, PWM_A generates the trigger signals for ADC sampling and CPU interrupt – see the Firmware section. ADC sampling is triggered by the PWM’s overflow event (‘ov’). The ADC takes approximately 4.5 µs to sample four channels, as described previously. ADC conversion must be completed before the PWM underflow event occurs. The interrupt is triggered by the PWM’s underflow event (‘un’). The result is that the ISR controls the PWM duty cycle on every cycle by updating the PWM compare buffer register (Figure 31). The register must be updated before the next underflow event occurs, or the duty cycle will be incorrect, which in turn causes an increased motor noise. Note that each PWM has a different duty cycle. Figure 30. PWM Timing and PWM_A Detail www.cypress.com Document No. 001-93637Rev. ** 24 PSoC® 4 Sensorless Field-Oriented Control (FOC) Figure 31 shows the configuration for PMW_A (phase A); it applies to all three PWM Components: The alignment mode is “Center align”. This produces the complementary PWM outputs ‘line’ and ‘line_n’. The outputs turn the MOSFETs of one of the motor phases ON and OFF (such as Q1 and Q2 in Figure 3). A deadband time is inserted to avoid turning ON both MOSFETs at the same time, which can damage the MOSFETs. In this code example, 40 cycles of a 48-MHz clock results in a dead time of 0.833 µs. The period value is the clock frequency divided by twice the desired PWM frequency minus 1. We double the desired PWM frequency because the count mode is up-down (see Figure 30). For a 48-MHz clock and a desired PWM frequency of 10 kHz, the period is (48,000,000 / (2 * 10,000)) - 1, or 2,399. To implement the duty cycle control technique described previously, we do the following: route the PWM_A ‘un’ output back to the ‘switch’ input of all PWMs (signal ‘PWM_UPDATE’ in Figure 29) check the “switch on rising edge” and “swap” boxes (Figure 31) Update the PWM compare buffer register in firmware. On each cycle, the PWM hardware copies (by swapping) the compare buffer register into the compare register, which changes the duty cycle. Figure 31. PWM_A Configuration Window www.cypress.com Document No. 001-93637Rev. ** 25 PSoC® 4 Sensorless Field-Oriented Control (FOC) Firmware implementation Code 10 shows how to initialize the PWMs and update them in the FOC ISR. Code 10. SVPWM Control /* main.c */ void main() { . . . /* TCPWM Init */ Cymc_HAL_PWMOutputDisable(); Cymc_HAL_PWMStart(); /* Motor Paramters Init */ Cymc_MAL_MotorInit(); /* PWM Main ISR Init */ PWM_MainLoop_ISR_StartEx(FOC_MainLoop_ISR); . . . } /**********************************************/ /* foc.c */ CY_ISR(FOC_MainLoop_ISR) { . . . /* SVPWM Calculation */ svpwmCal.Uu = invClarkTrans.outU; svpwmCal.Uv = invClarkTrans.outV; svpwmCal.Uw = invClarkTrans.outW; Cymc_BCL_SVPWM(&svpwmCal); /* Update PWM duty cycles */ pwmCmp[0] = svpwmCal.CmpU; pwmCmp[1] = svpwmCal.CmpV; pwmCmp[2] = svpwmCal.CmpW; Cymc_HAL_PWMOutputUpdate(); . . . } www.cypress.com Document No. 001-93637Rev. ** 26 PSoC® 4 Sensorless Field-Oriented Control (FOC) Summary Related Application Notes This application note has shown how to design a sensorless FOC control algorithm for a permanent magnet synchronous motor (PMSM), using a PSoC 4 CY8C42xx device. PSoC 4’s resources and flexible internal routing make it an excellent fit for motor control applications. For more information on motor control using PSoC 4, go to the Cypress website. AN88619 – PSoC4 Considerations 4100/4200 Hardware Design AN90799 – PSoC4 Interrupts AN80994 – PSoC3, PSoC4, and PSoC 5LP EMC Best Practices and Recommendations About the Author www.cypress.com Name: Bob Hu Title: Application Engineer Staff Background: Graduated from Shanghai Jiao Tong University with a master’s degree. He has worked at Cypress since 2009. Document No. 001-93637Rev. ** 27 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix A: PMSM Model This appendix presents the mathematical model of a permanent magnet synchronous motor (PMSM). To simplify the model, some assumptions are made: The PMSM motor winding connection is the “star” type. “Delta” type connections must be converted to the “star” type. Magnetic saturation is neglected. Eddy currents and hysteresis losses are negligible. Figure 32 illustrates the PMSM motor model in a threephase stator reference frame, also called the (a, b, c) frame. In this frame, the a, b, and c axes are aligned with the currents in the three phases of the PMSM stator, and are 120° apart from each other. is the flux linkage vector of the rotor magnet. The rotor rotates with an angular speed , and is the angle between and phase a. Figure 32. Three-Phase Stator Reference Frame b is Ψf ωr N The a, b, and c phases are each called “line”. The connection point of a, b, and c is called the neutral point. See Appendix B for information on usage of these terms. θr a S c The voltages on the stator windings are represented as: Stator voltage vector where: Stator resistance Stator current vector Stator flux linkages The stator winding flux linkage is the sum of the flux linkages from their own excitation, mutual flux linkages from other winding currents, and flux linkages from the rotor magnet. Because the current phases on the stator windings are 120° apart, the stator flux linkages are written as: where: Equivalent inductances of stator phases , Mutual equivalent inductances of stator phases Amplitude of rotor flux linkage Angle between www.cypress.com and phase a Document No. 001-93637Rev. ** 28 PSoC® 4 Sensorless Field-Oriented Control (FOC) The above model is of a high order, is strongly coupled, and has nonlinearity; analyzing it and controlling the torque and flux based on it is difficult. Therefore, the (d, q) frame is used to simplify the three-phase model. The (d, q) frame defines a rotating two-phase reference frame where the d axis is aligned with the rotor flux direction. Figure 33. Clarke Transformation β b iβ There are two transformations to convert the (a, b, c) frame to the (d, q) frame. The first one is a Clarke transformation – it converts the (a, b, c) frame to a twophase stationary reference frame (α, β) (Figure 33). ib is ic ia a iα α c The current vectors in the (α, β) frame are: For “star” type winding connections, the sum of the currents in the three phases is zero: Therefore, the current vectors in the (a, b, c) frame are transformed to the (α, β) frame as: The Park transformation then converts the (α, β) frame to the (d, q) frame. The (d, q) frame has two axes – direct and quadrature – that rotate with the same angle speed as the current vector. The direct axis is aligned with the rotor flux (Figure 34). The angle between the d axis and the α axis is . Figure 34. Park Transformation β ωr q d iβ is Ψf id θr iq iα a α The current vectors in the (d, q) frame are calculated as: The voltages in the (d, q) frame are calculated from and , as: www.cypress.com Document No. 001-93637Rev. ** 29 PSoC® 4 Sensorless Field-Oriented Control (FOC) and: The torque equation is expressed as: where: Inductances of direct and quadrature axes Note that for a SPMSM (Figure 1), independent of , and is equal to torque equation is simplified for SPMSM as: and are . Thus, the Number of pole pairs in rotor and are motor characteristics that are not affected by the motor rotation. Compared to the three-phase model, the torque is proportional only to the q-axis current , which is easier to control. www.cypress.com Document No. 001-93637Rev. ** 30 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix B: Slide Mode Observer (SMO) Obtaining the position of a rotating rotor is critical for FOC. The Park transformation (see Appendix A) requires the rotor position angle between the rotor flux linkage and the α axis. Originally, this information came from physical sensors, such as Hall-effect sensors, optical encoders, and so on. These sensors not only increase the system cost, but they also require maintenance. Later, the sensorless technique was developed to remove the need for sensors. Some high-precision applications such as robotics still require encoders. The idea of the sensorless technique is to estimate the angle based on the BEMF value in the (α, β) frame. The typical algorithm to do this is called a slide mode observer (SMO). In this algorithm, the two-phase voltages in the (α, β) frame is expressed as: Line-to-neutral resistance where: Line-to-neutral resistance Line-to-neutral inductance BEMF on (α, β) axes In the digital domain, the equation is changed to: where: Solving for Period of PWM on inverter : We now define two new parameters that are related to motor parameters: Note that and are motor characteristics that can be measured. is a constant system parameter, is the sampled result from the last control cycle, and is the calculation result of the last control cycle. Therefore, if given an estimated , an estimated current value can be calculated (“*” indicates an estimated value). Comparing with the actual current value sampled by the ADC, the error between these two values is used to adjust for a better estimation. Repeat this process until the error between and is small enough to meet the design requirements. Then, the estimated can represent the actual BEMF . The is obtained in the same manner. Because The angle and are expressed as: is calculated as: The angular speed is calculated by accumulating over m samples and multiplied by the speed constant : Thus, the position and speed information are calculated from the estimated BEMF. www.cypress.com Document No. 001-93637Rev. ** 31 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix C: SVPWM Theory In Figure 3, Q1, Q3, and Q5 are the upper MOSFETs of the inverter. If you consider the MOSFET ON state as “1” and the OFF state as “0”, there are eight combinations of ON/OFF states, which lead to eight inverter outputs. Table 3 lists the ON/OFF state combinations and their corresponding inverter outputs. , , and are the phase (line-toneutral) voltages (see Appendix A), while , , and are the line-to-line voltages. The values in each cell indicate the voltage as a percentage of the bus voltage, . For example, 2/3 means 2/3 of . Table 3. Output Combination in Three-Phase Frame Q1 Q3 Q5 (A) (B) (C) 1 0 0 2/3 -1/3 -1/3 1 0 -1 1 1 0 1/3 1/3 -2/3 0 1 -1 0 1 0 -1/3 2/3 -1/3 -1 1 0 0 1 1 -2/3 1/3 1/3 -1 0 1 0 0 1 -1/3 -1/3 2/3 0 -1 1 1 0 1 1/3 -2/3 1/3 1 -1 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 The eight combinations can be considered as six non-zero vectors and two zero vectors (000 and 111). As Figure 35 shows, the non-zero vectors are the axes of a hexagon; the angle between any two adjacent axes is 60 degrees. This divides the hexagon into six sectors (Roman numerals I to VI). The zero vectors are at the origin, and they generate zero voltage on the three phases. These eight vectors, called “basic space vectors,” are called , , , , , , and . A voltage vector is synthesized by one or two of the six nonzero basic space vectors. Figure 35. Basic Space Vectors U120(010) U60(110) II I III O111(111) O000(000) U180(011) IV U0(100) VI V U240(001) www.cypress.com U300(101) Document No. 001-93637Rev. ** 32 PSoC® 4 Sensorless Field-Oriented Control (FOC) For example, as Figure 36 shows, the voltage vector is in sector I, and the period of the PWM is . is the duration of ; is the duration of ; and is the duration of the two zero vectors. The vectors and compose a voltage vector, that can also be composed by basic space vectors and . Figure 36. Voltage Vector in Sector I β U60 Sector-I (U0,U60) Uβ Us U60 *T2/T θ π/3 T0 U0 *T1/T Uα U0 α can be expressed as: Therefore: Then: Where: www.cypress.com Document No. 001-93637Rev. ** 33 PSoC® 4 Sensorless Field-Oriented Control (FOC) Note that all basic space vectors are generated with a specific ON/OFF state of upper MOSFETs; the duration is actually the time of the PWM being high, or the duty cycle. Thus, generating a is related to a change in duty cycle of the PWMs applied to the inverter. In this example, both and require phase A to be turned ON, and requires phase B to be turned ON. Therefore: Depending on how you use zero vectors, the SVPWM has two output patterns: a five-phase pattern and a seven-phase pattern. The five-phase pattern uses only or .The seven-phase pattern uses both and , and their durations are equal. Figure 37 illustrates these two patterns. Note that in 5-phase SVPWM, phase A is always on or always off. Figure 37. Five- and Seven-Phase SVPWM in Sector I T U0 U60 5-phase SVPWM O111 O111 U60 U0 1 Phase A 0 Phase B Phase C T1/2 T2/2 T0/2 T0/2 T2/2 T1/2 7-phase SVPWM O000 U0 U60 O111 O111 U60 U0 O000 T2/2 T0/4 T0/4 T1/2 T2/2 T0/4 Phase A Phase B Phase C T0/4 T1/2 There is no difference in the synthesized voltage vector generated by these two methods. However, the five-phase pattern reduces the number of MOSFETs that are switching. This can reduce the switching losses in the power components, but it creates more harmonics than the seven-phase pattern. www.cypress.com Document No. 001-93637Rev. ** 34 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix D: Q Number Format (Fixed-Point Number) The Q number format is a well-known method to store and process floating-point numbers. It enables faster floating-point operations done by the CPU, so that a separate floating-point unit is not needed. However, some accuracy may be lost by using floating-point. The example project provided in this application note uses the Q number format. Although understanding the Q number format is not mandatory, gaining a fundamental knowledge of it will help you master the example code faster. An introduction to the Q number format can be found in Wikipedia. This appendix contains a copy of the “Q (number format)” page from the Wikipedia site, if you are not able to connect to the Internet but need to know about the Q number format when reading this application note. Note The following content is from Wikipedia. Cypress does not maintain this content for accuracy, nor guarantee that it is up to date. If you have access to the Internet, go to the Wikipedia website to read the latest version by clicking the following link or entering it in your browser. This material from Wikipedia is reproduced under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which you can view at the following URL: http://creativecommons.org/licenses/by-sa/3.0/. For more information, please see Wikipedia’s licensing statement at http://en.wikipedia.org/wiki/Wikipedia:Text_of_Creative_Commons_AttributionShareAlike_3.0_Unported_License. Your rights to this Wikipedia material are governed by the foregoing license. From Wikipedia, the free encyclopedia: Q (number format) on Wikipedia: http://en.wikipedia.org/wiki/Q_%28number_format%29 Q is a fixed point number format where the number of fractional bits (and optionally the number of integer bits) is specified. For example, a Q15 number has 15 fractional bits; a Q1.14 number has 1 integer bit and 14 fractional bits. Q format is often used in hardware that does not have a floating-point unit and in applications that require constant resolution. Characteristics Q format numbers are (notionally) fixed point numbers (but not actually a number itself); that is, they are stored and operated upon as regular binary numbers (i.e. signed integers), thus allowing standard integer hardware/ALU to perform rational number calculations. The number of integer bits, fractional bits and the underlying word size are to be chosen by the programmer on an application-specific basis—the programmer's choices of the foregoing will depend on the range and resolution needed for the numbers. Some DSP architectures offer native support for common formats, such as Q1.15. In this case, the processor can support arithmetic in one step, offering saturation (for addition and subtraction) and renormalization (for multiplication) in a single instruction. Most standard CPUs do not. If the architecture does not directly support the particular fixed point format chosen, the programmer will need to handle saturation and renormalization explicitly with bounds checking and bit shifting. There are 2 conflicting notations for fixed point. Both notations are written as Qm.n, where: Q designates that the number is in the Q format notation—the "Q" being reminiscent of the standard symbol for the set of rational numbers. m. (optional, assumed to be zero or one) is the number of bits set aside to designate the two's complement integer portion of the number, exclusive or inclusive of the sign bit (therefore if m is not specified it is taken as zero or one). n is the number of bits used to designate the fractional portion of the number, i.e. the number of bits to the right of the binary point. (If n = 0, the Q numbers are integers—the degenerate case). One convention includes the sign bit in the value of m, and the other convention does not. The choice of convention can be determined by summing m+n. If the value is equal to the register size, then the sign bit is included in the value of m. If it is one less than the register size, the sign bit is not included in the value of m. In addition, the letter U can be prefixed to the Q to indicate an unsigned value, such as UQ1.15, indicating values from 0.0 to +1.99997. Signed Q values are stored in 2's complement format, just like signed integer values on most processors. In 2's complement, the sign bit is extended to the register size. For a given Qm.n format, using an m+n+1 bit signed integer container with n fractional bits: www.cypress.com Document No. 001-93637Rev. ** 35 PSoC® 4 Sensorless Field-Oriented Control (FOC) its range is its resolution is For a given UQm.n format, using an m+n bit unsigned integer container with n fractional bits: its range is its resolution is For example, a Q14.1 format number: requires 14+1+1 = 16 bits 14 its range is [-2 , 2 its resolution is 2 14 −1 −1 - 2 ] = [-16384.0, +16383.5] = [0x8000, 0x8001 … 0xFFFF, 0x0000, 0x0001 … 0x7FFE, 0x7FFF] = 0.5 Unlike floating point numbers, the resolution of Q numbers will remain constant over the entire range. Conversion Float to Q To convert a number from floating point to Qm.n format: 1. Multiply the floating point number by 2 2. Round to the nearest integer n Q to float To convert a number from Qm.nformat to floating point: 1. Convert the number to floating point as if it were an integer 2. Multiply by 2 −n Math Operations Q numbers are a ratio of two integers: the numerator is kept in storage, the denominator is equal to 2n. Consider the following example: The Q8 denominator equals 28 = 256 1.5 equals 384/256 384 is stored, 256 is inferred because it is a Q8 number. If the Q number's base is to be maintained (n remains constant) the Q number math operations must keep the denominator constant. The following formulas shows math operations on the general Q numbers and . Because the denominator is a power of two the multiplication can be implemented as an arithmetic shift to the left and the division as an arithmetic shift to the right; on many processors shifts are faster than multiplication and division. To maintain accuracy the intermediate multiplication and division results must be double precision and care must be taken in rounding the intermediate result before converting back to the desired Q number. www.cypress.com Document No. 001-93637Rev. ** 36 PSoC® 4 Sensorless Field-Oriented Control (FOC) Using C the operations are (note that here, Q refers to the fractional part's number of bits): Addition signed int a, b, result; result = a + b; With saturation signed int a, b, result; signed long int tmp; tmp = a + b; if (tmp > 0x7FFFFFF) tmp = 0x7FFFFFFF; if (tmp < -1 * 0x7FFFFFFF) tmp = -1 * 0x7FFFFFFF; result = (signed int) tmp; Subtraction signed int a, b,result; result = a - b; Multiplication // precomputed value: #define K (1 << (Q-1)) signed int a, b, result; signed long int temp; temp = (long int)a * (long int)b; // result type is operand's type // Rounding; mid values are rounded up temp += K; // Correct by dividing by base result = temp >> Q; D i vi s i o n signed int a, b, result; signed long int temp; // pre-multiply by the base (Upscale to Q16 so that the result will be in Q8 format) temp = (long int)a << Q; // So the result will be rounded ; mid values are rounded up. temp += b/2; result = temp/b; Text is available under the Creative Commons Attribution-ShareAlike License. www.cypress.com Document No. 001-93637Rev. ** 37 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix E: Adapting the Design to Other Motors This appendix helps you to drive other motors with the code example provided with this application note. You should follow the operation guide step by step. A bold font indicates a mandatory action or critical information that requires more attention. Hardware: CY8CKIT-037 or your own motor driver board Firmware: Sensorless FOC project from the latest version of this application note Equipment: Oscilloscope, multimeter, PC, USB cable for CY8CKIT-042 or MiniProg3 for programming your own board Operation guide: 1. Check the power range and motor type. a. Power range CY8CKIT-037 supports a 12-V to 48-VDC supply voltage with up to 2 A input DC current. You should use the kit only in this power range; using the kit out of this power range may damage it. b. Motor type A motor with sinusoidal back electromotive force (BEMF) is recommended. A motor with trapezoidal BEMF may not rotate or achieve the desired performance with the sensorless FOC project. Figure 38 illustrates these two BEMF types. To measure BEMF, connect the ground of the oscilloscope probe to one motor phase and the probe to another motor phase. Leave the other motor phases floating. Rotate the motor either by hand or by using another motor. You should see the BEMF waveform on the oscilloscope. The sinusoidal BEMF contains the complete angle information, which can be calculated with the SMO algorithm. The trapezoidal BEMF is almost flat at the wave crest and trough and therefore is missing sufficient angle information. As a result, the SMO algorithm cannot reliably retrieve the angle from this waveform, which may halt the motor rotation. Figure 38. Sinusoidal BEMF Versus Trapezoidal BEMF (a) Sinusoidal BEMF 2. (b) Trapezoidal BEMF Change the parameters in the example project. a. Change the parameters for the motor. These parameters are defined in the MotorController structure and initialized in the Cymc_MAL_MotorInit function (Cymc_MAL.c). You should change them based on your motor specifications. float Rs Motor line-to-line resistance, unit: ohm float Ls Motor line-to-line inductance, unit: henry uint8 Poles Motor poles count float baseFrequency www.cypress.com float Ts PWM period, uint16 ratedSpeedRPM Rated speed based on motor specification, unit: RPM Document No. 001-93637Rev. ** , unit: second 38 PSoC® 4 Sensorless Field-Oriented Control (FOC) b. Change the macro definitions for the system parameters. These macro definitions are related to system parameters, such as DC bus voltage (Vbus, see Figure 3), device VDD, and so on. You should change them (Cymc_MAL.h) if the default values are different from your system. #define #define #define #define #define #define #define c. DC_BUS VDD SENSING_RESISTOR OPAMP_GAIN DC_BUS_SCALER MAX_PHASE_CURRENT ADC_RESOLUTION (uint16)(24) (3300) (uint16)(30) (uint16)(10000/2400) (uint16)((590+5490)/590) (uint16)(5) (4096) /* /* /* /* /* /* V */ mV */ mOhm */ 10K / 2.4K */ (R9 + R10) / R10 */ A */ Change the parameters for the sensorless algorithm (SMO). You may need to change two parameters in the SMO controller if the SMO cannot calculate the angle reliably with your motor. You can change them in the Cymc_MAL_MotorInit function (Cymc_MAL.c). q15_t slideCoff q15_t slideError d. Coefficient K for slide control Error threshold for slide control Change the parameters for the PI controllers. You may need to change the PI coefficient parameters in the PI controller if the PI controller does not work well with your motor. You can change them in the Cymc_MAL_MotorInit function (Cymc_MAL.c) for the three PI controllers: speed PI, Id PI, and Iq PI. q15_t q15_t q15_t q15_t q15_t 3. kr kp ki outMax outMin Reference set point weighting Proportional loop gain Integral gain Output upper limit Output lower limit Set up the hardware. If you are using the CY8CKIT-037 kit, you can use the adapter provided with the kit for any motor whose maximum power is 24 V DC / 2.1 A. If a different voltage (such as 48 V) or current (such as 3 A) is required, connect the DC voltage source to the J8 connector (yellow marker in Figure 39) instead of the supplied power adapter. Figure 39.Connector for DC Power Input 4. Program the CY8CKIT-042 and observe the performance. www.cypress.com Document No. 001-93637Rev. ** 39 PSoC® 4 Sensorless Field-Oriented Control (FOC) 5. Tune the SMO module if the motor does not rotate. a. The motor starts up in open-loop control and then switches to closed-loop speed control later. If switching to the closed loop control fails (motor halts very soon after the rotation starts), you may need to tune the SMO module. Try the following methods: i. Confirm that the motor parameters are set correctly in step 2.a. ii. Change the smoEst.slideError parameter to a larger value. When the value of this variable is larger, it is easier to switch to closed loop however the rotor angle calculation is less accurate. b. If the motor rotates with a vibration, try tuning the Kp and Ki parameters in the PI controller. The larger the Kp value, the faster the system closes in on the reference value; however it may make the system unstable. The Ki value can reduce the static error and make the system stable; however a larger Ki may make the integration value saturate. www.cypress.com Document No. 001-93637Rev. ** 40 PSoC® 4 Sensorless Field-Oriented Control (FOC) Appendix F: Tunable Parameters List Variable’s Name in Project Name: motor Type:structMotorController Location:Cymc_MAL.c Comments: Motor parameters and running status Name: rampUp Type:StructRampUp Location:Cymc_MAL.c Comments: Motor parameters struct Name: pidSpeed Type:StructPIController Location:Cymc_MAL.c Comments: PID controller for speed Name: pidId Type:StructPIController Location:Cymc_MAL.c Comments: PID controller for d-axis current Name: pidIq Type:StructPIController Location:Cymc_MAL.c Comments: PID controller for q-axis current Name: smoEst Type: structSMO Location: Cymc_MAL.c Comments: Only list tunable parameters in the SMO structure www.cypress.com Structure Member float Rs float Ls uint8 Poles float baseFrequency float Ts uint16 speedRPM uint16 ratedSpeedRPM uint8 runState q15_t speedRef q15_t vdRef q15_t vqRef q15_t RefSpeed Comments Motor line-to-line resistance, unit: ohm Motor line-to-line inductance, unit: henry Motor poles count q15_t delayPrescaler Delay prescaler q15_t stepSpeed Step pace for speed increasing q15_t output Output speed in open-loop startup q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t q15_t Reference setpoint Feedback Controller output Referencesetpoint weighting Proportional loop gain Integral gain Output upper limit Output lower limit Reference setpoint Feedback Controller output Referencesetpoint weighting Proportional loop gain Integral gain Output upper limit Output lower limit Reference setpoint Feedback Controller output Referencesetpoint weighting Proportional loop gain Integral gain Output upper limit Output lower limit DC-bus voltage Voltage on α-axis Voltage on β-axis Current speed reference Control gain Filter gain Coefficient K for slide control Error threshold for slide control α-axis stator current β-axis stator current Output: angle ref fbk out kr kp ki outMax outMin ref fbk out kr kp ki outMax outMin ref fbk out kr kp ki outMax outMin Vbus volAlpha volBeta speedRef Ggain Fgain slideCoff slideError curAlpha curBeta Theta PWM period, , unit: second Current rotation speed, unit: RPM Rated speed based on motor specification, unit: RPM Motor run state Speed reference vd reference vq reference Speed reference Document No. 001-93637Rev. ** 41 PSoC® 4 Sensorless Field-Oriented Control (FOC) Document History ® Document Title: AN93637 – PSoC 4 Sensorless Field-Oriented Control (FOC) Document Number:001-93637 Revision ** ECN 4556106 www.cypress.com Orig. of Change BOBH Submission Date 04/01/2015 Description of Change New application note Document No. 001-93637Rev. ** 42 PSoC® 4 Sensorless Field-Oriented Control (FOC) Worldwide Sales and Design Support Cypress maintains a worldwide network of offices, solution centers, manufacturer’s representatives, and distributors. To find the office closest to you, visit us at Cypress Locations. PSoC® Solutions Products Automotive cypress.com/go/automotive psoc.cypress.com/solutions Clocks & Buffers cypress.com/go/clocks PSoC 1 | PSoC 3 | PSoC 4 | PSoC 5LP Interface cypress.com/go/interface Lighting & Power Control cypress.com/go/powerpsoc Memory cypress.com/go/memory PSoC cypress.com/go/psoc Touch Sensing cypress.com/go/touch USB Controllers cypress.com/go/usb Wireless/RF cypress.com/go/wireless Cypress Developer Community Community | Forums | Blogs | Video |Training Technical Support cypress.com/go/support PSoC is a registered trademark and PSoC Creator is a trademark of Cypress Semiconductor Corp. All other trademarks or registered trademarks referenced herein are the property of their respective owners. Cypress Semiconductor 198 Champion Court San Jose, CA 95134-1709 Phone Fax Website : 408-943-2600 : 408-943-4730 : www.cypress.com © Cypress Semiconductor Corporation, 2015. The information contained herein is subject to change without notice. Cypress Semiconductor Corporation assumes no responsibility for the use of any circuitry other than circuitry embodied in a Cypress product. Nor does it convey or imply any license under patent or other rights. Cypress products are not warranted nor intended to be used for medical, life support, life saving, critical control or safety applications, unless pursuant to an express written agreement with Cypress. Furthermore, Cypress does not authorize its products for use as critical components in life-support systems where a malfunction or failure may reasonably be expected to result in significant injury to the user. The inclusion of Cypress products in life-support systems application implies that the manufacturer assumes all risk of such use and in doing so indemnifies Cypress against all charges. This Source Code (software and/or firmware) is owned by Cypress Semiconductor Corporation (Cypress) and is protected by and subject to worldwide patent protection (United States and foreign), United States copyright laws and international treaty provisions. Cypress hereby grants to licensee a personal, non-exclusive, non-transferable license to copy, use, modify, create derivative works of, and compile the Cypress Source Code and derivative works for the sole purpose of creating custom software and or firmware in support of licensee product to be used only in conjunction with a Cypress integrated circuit as specified in the applicable agreement. Any reproduction, modification, translation, compilation, or representation of this Source Code except as specified above is prohibited without the express written permission of Cypress. Disclaimer: CYPRESS MAKES NO WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, WITH REGARD TO THIS MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. Cypress reserves the right to make changes without further notice to the materials described herein. Cypress does not assume any liability arising out of the application or use of any product or circuit described herein. Cypress does not authorize its products for use as critical components in life-support systems where a malfunction or failure may reasonably be expected to result in significant injury to the user. The inclusion of Cypress’ product in a life-support systems application implies that the manufacturer assumes all risk of such use and in doing so indemnifies Cypress against all charges. Use may be limited by and subject to the applicable Cypress software license agreement. www.cypress.com Document No. 001-93637Rev. ** 43

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