AN1017 Sinusoidal Control of PMSM Motors with dsPIC30F DSC Author: Jorge Zambada Microchip Technology Inc. INTRODUCTION This application note describes a method of driving a sensored Permanent Magnet Synchronous Motor (PMSM) with sinusoidal currents controlled by a dsPIC30F Digital Signal Controller (DSC). The motor control firmware uses the dsPIC30F peripherals while the mathematical computations are performed by the DSP engine. The firmware is written in ‘C’ language, with some subroutines in assembly to take advantage of the special DSP operations of the dsPIC30F. APPLICATION FEATURES • Sinusoidal current generation for controlling PMSM motor phases using Space Vector Modulation (SVM) • Synchronization of sinusoidal voltages to PMSM motor position • Four-quadrant operation allowing forward, reverse and braking operation • Closed-loop speed regulation using digital Proportional Integral Derivative (PID) control • Phase advance operation for increased speed range • Fractional math operations performed by the DSP engine of the dsPIC® DSC MOTOR CONTROL WITH DIGITAL SIGNAL CONTROLLERS for motor control: Motor Control Pulse Width Modulation (MCPWM) and high-speed A/D Converter. The DSP engine of the dsPIC30F2010 supports the necessary fast mathematical operations. The dsPIC30F2010 family member is a 28-pin 16-bit DSC specifically designed for low-cost/high efficiency motor control applications. The dsPIC30F2010 provides these key features: • 30 MIPS processing performance • Six independent or three complementary pairs of dedicated Motor Control PWM outputs • Six-input, 1 Msps ADC with simultaneous sampling capability from up to four inputs • Multiple serial communications: UART, I2C™ and SPI • Small package (6 mm x 6 mm QFN) for embedded control applications • DSP engine for fast response in control loops HARDWARE REQUIRED You will need the following hardware to implement the described motor control application: • PICDEM™ MCLV Development Board (Figure 1) • Hurst DMB0224C10002 BLDC Motor • 24 VDC Power Supply You can purchase these items from Microchip as a complete kit or as individual components. Check the Development Tools section of the Microchip web site for ordering information. FIGURE 1: PICDEM™ MCLV DEVELOPMENT BOARD The dsPIC30F Motor Control family is specifically designed to control the most popular types of motors, including AC Induction Motors (ACIM), Brushed DC Motors (BDC), Brushless DC Motors (BLDC) and Permanent Magnet Synchronous Motors (PMSM), to list a few. Several application notes have been published for ACIM operation (AN984, AN908 and GS004) and Brushless DC Motor Control operation (AN901, AN957 and AN992) based on the dsPIC30F motor control family. These application notes are available on the the Microchip web site (www.microchip.com). This application note demonstrates how the dsPIC30F2010 is used to control a sensored PMSM motor with sinusoidal voltages. The design takes advantage of dsPIC30F peripherals specifically suited © 2005 Microchip Technology Inc. DS01017A-page 1 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC It is strongly recommended that you read the “PICDEM™ MCLV Development Board User’s Guide” (DS51554) to fully understand the hardware topology being used in this application note. This User’s Guide can be downloaded from the Microchip web site. On the low side, the voltage limit is 10V. On the high side, the voltage limit is 48V. It is important to note that the heat sink on the IGBTs have very limited heat dissipation, so high power requirements may not be easily met with the PICDEM™ MCLV development board. Figure 2 is a simplified system block diagram for a Sinusoidal PMSM motor control application. This diagram will help you develop your own hardware. To use the PICDEM™ MCLV development board for this application, use the jumper settings shown in Table 1 and the motor connections shown in Table 2 and Table 3. FIGURE 2: TABLE 1: SYSTEM BLOCK DIAGRAM dsPIC30F2010 PWM3H PWM3L Phase A PWM2H 3-Phase Phase B Inverter Phase C PWM2L 3-Phase PMSM Motor PWM1H PWM1L IBUS AN1 R14 AN2 RC14 Reference Speed S2 R26 +5V RB4/IC7 RB5/IC8 Hall A R21 Position for Sinusoidal Control (dsPIC® DSC Sensored) Jumpers J7, J8, J11 Open J12, J13, J14 Open J15, J16, J17, J10 Open J19 Short TABLE 2: Start/Stop RB3/CN5 PICDEM™ MCLV DEVELOPMENT BOARD JUMPER SETTINGS CONNECTIONS FOR MOTOR WINDINGS* R24 R23 R20 Hall B R22 Hall C R25 Connector J9 Position for Sinusoidal Control (dsPIC® DSC Sensored) M3 Phase A (White) M2 Phase B (Black) Salient aspects of this topology are: M1 Phase C (Red) • Potentiometer R14 selects the desired speed (Reference Speed) • Rotor position is detected using Hall effect sensors connected to pins RB3, RB4 and RB5 • Current feedback is provided through a simple operational amplifier circuit • Fault input is received through a comparator circuit connected with the current feedback circuit. The current is sensed using a 0.1 ohm resistor (R26) G You can easily adjust the values of the resistors to accommodate the current capabilities of the motor being used for your application. The motor drive circuit, on the other hand, is designed to drive a 24V PMSM motor. You can change the hardware to meet the drive requirement of a specific motor. Note: Refer to the “PICDEM™ MCLV Development Board User’s Guide” (DS51554) for details on how to change the hardware for use with motors greater or less than 24V. DS01017A-page 2 Ground (Green) if available TABLE 3: MOTOR CONNECTIONS FOR HALL SENSORS* Connector J9 +5V Position for Sinusoidal Control (dsPIC® DSC Sensored) Red GND Black HA White HB Brown HC Green * The colors referenced in Tables 2 and 3 for the motor windings and hall sensors, respectively, pertain to the Hurst 24V motor available from Microchip. The ground wire is sometimes not available on some motors. After your code is developed and you have downloaded it to the dsPIC30F, you will need to press switch S2 to start and stop the motor. The potentiomer marked REF (R14) sets the required speed and direction of rotation of the motor. The motor does not need to stop to change direction of rotation. © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC PROGRAMMING THE dsPIC30F2010 WITH THE dsPICDEM™ MCLV DEVELOPMENT BOARD For a good introduction to BLDC motors and their basic operating principles, see also AN885 “Brushless DC (BLDC) Motor Fundamentals” (DS00885) . The dsPICDEM MCLV development board allows you to program the dsPIC30F2010 in-circuit. To program the part, you must set DIP switch S4 to the PRGM position. When programming is complete, you must set the DIP switch to the DEBUG position to execute the code. If the IDC2 is connected to the PICDEM™ MCLV development board as a debugger, the connector at J6 should be attached. If you use MPLAB® ICD 2 as a debugger, the RJ11 cable should be connected to the board (J6). If you use MPLAB ICD 2 as a programmer only, the RJ11 cable should be connected for programming the part and unplugged for normal program execution. FIGURE 3: The following configuration allows the application to work on a PICDEM™ MCLV development board: Oscillator Source: Primary Oscillator Primary Oscillator Mode: XT w/PLL 16x Comm Channel Select: EMUC2 and EMUD2 Other settings can be enabled or disabled as needed, or modified in the application. BACKGROUND Many consumer and industrial applications use the BLDC motor because of its compact size, controllability and high efficiency. Increasingly, it is used in automotive applications as part of a strategy to eliminate belts and hydraulic systems, to increase functionality and to improve fuel economy. In high-performance applications, such as machine tools and low noise fan applications, the production of smooth torque is crucial. The main disadvantage of BLDC motors, when low torque ripple and quieter operation are required, is the non-sinusoidal distribution of the stator windings. BLDC motors with non-sinusoidal winding distribution generate trapezoidal back-EMF, as shown in Figure 3. Trapezoidal Back-EMF BLDC motors are specifically designed to be driven with square voltages synchronized with the motor’s angular position. This control method is commonly called six-step commutation. It is assumed that you are familiar with the six-step commutation technique, so no further elaboration is offered in this application note. However, for more detailed information on how to operate a BLDC motor with six-step commutation, you can refer to these additional Microchip application notes: 0 TRAPESOIDAL BACK-EMF 60 120 180 240 300 0 60 Phase A Phase B Phase C Trapezoidal distribution of the motor windings of a BLDC motor leads to torque ripple during motor operation since the current generation is also trapezoidal. This torque ripple produces a small speed oscillation, which generates audible noise. On the other hand, sinusoidal Back-EMF BLDC motors, also known as Permanent Magnet Synchronous Motors (PMSM) produce sinusoidal currents, which reduce the torque ripple, thus minimizing the audible noise. Figure 4 shows the sinusoidal back-EMF voltages generated by a motor with sinusoidal winding distribution. FIGURE 4: 0 SINUSOIDAL BACK-EMF 60 120 180 240 300 0 60 Phase A Phase B Phase C This application note assumes a 3-Phase PMSM motor with sinusoidal back-EMF and three Hall effect sensors. • AN857 “Brushless DC Motor Control Made Easy” (DS00857) • AN957 “Sensored BLDC Motor Control Using dsPIC30F2010” (DS00957) © 2005 Microchip Technology Inc. DS01017A-page 3 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC SENSORED OPERATION OF BLDC MOTORS To allow correct commutation of the motor, the absolute position within an electrical cycle must be measured. Three Hall effect sensors provide rotor position information. These sensors are distributed along the stator in such a way that they generate six different logic states per electrical cycle. The ratio between the electrical cycles and mechanical revolutions depends on the number of motor pole pairs. For instance, the motor used in this application note has five pole pairs, so every mechanical revolution requires five electrical cycles. For conventional energization (six-step commutation), six equally spaced commutations are required per electrical cycle. This is usually implemented using three Hall effect or optical switches with a suitable disk on the rotor. Continuous position information is not required. Only detection of the required commutation instances is required. Figure 5 shows the three sensor outputs along with the corresponding voltage driving each motor winding. FIGURE 5: SIX-STEP COMMUTATION FOR TRAPEZOIDAL BLDC MOTORS 0 60 120 180 240 300 0 You can see that the voltage does not vary for each particular sector until a new motor position or combination of Hall effect sensor is detected. For the technique described in this application note, the three Hall effect sensors detect the rotor position, as in the six-step technique. However, instead of generating square waves, a continuous changing voltage is generated with a sine-wave shape. Figure 6 shows the resulting sinusoidal voltage generation. The relation is shown between the phase voltages and the three Hall effect sensors. The amplitude of the sinusoidal voltages determines the speed for a specific mechanical load in the motor. FIGURE 6: VOLTAGE GENERATION FOR SINUSOIDAL BLDC MOTORS 0 60 120 180 240 300 0 60 HALL A HALL B 60 HALL C HALL A +V HALL B VOLTAGE A Float -V +V HALL C VOLTAGE B Float -V +V +V VOLTAGE A Float -V VOLTAGE C Float -V +V VOLTAGE B Float -V +V VOLTAGE C Float -V DS01017A-page 4 © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC IMPLEMENTATION OF SINUSOIDAL VOLTAGE CONTROL control loop only controls Amplitude. The value of Phase from the Phase Advance block is derived from Hall effect sensor information to maintain the sinusoidal voltage alignment to the rotor. Figure 7 is a block diagram representation of the application software. When the motor is running, Measured Speed is subtracted from Reference Speed (desired speed) and the resulting error is processed by the PID controller to generate the amplitude of the sine wave. The Reference Speed is set by an external potentiometer, while the measured speed is derived from a Hall effect sensor. Using the software block diagram as a point of reference, the following sections of this application note describe the software functionality in detail. The description starts with the Main State machine, which interacts with all the other software blocks using global variables. Then the description focuses on speed measurements (Reference Speed and Measured Speed), leading to an explanation of the software implementation of the PID controller. This discussion includes some background information on PID control. Once Amplitude is known, two additional parameters are needed for sine generation. One parameter is the Period of the sine wave, which is taken from one of the Hall effect sensors. The other parameter is the Phase, which is calculated using Phase Advance, depending on speed range requirements and the rotor position from the Hall effect sensors. Next, calculation of the parameters for generating three-phase sine waves is discussed, starting with the rotor sector and phase advance calculations. And finally, sinusoidal voltage generation using space vector modulation, with Amplitude, Phase and Period as parameters, concludes the discussion. The Amplitude variable sets the amount of motor current and the resulting torque. An increase in torque corresponds to an increase in speed. The speed FIGURE 7: SOFTWARE BLOCK DIAGRAM dsPIC® DSC Software Duty Cycles Reference Speed Error +- PID Amplitude Sine-Wave Generation Phase 3-Phase Voltages MCPWM 10-Bit ADC +5v Period 3-Phase Inverter BLDC Fault Measured Speed Phase Advance Maximum Phase Advance Rotor Sector Rotor Direction Speed Sector Calculation Calculation Start/ Stop Angular Position Main State Machine © 2005 Microchip Technology Inc. Input Capture GPIO Period Hall Sensors Low-Pass Passive Filters DS01017A-page 5 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC MAIN STATE MACHINE The state diagram shown in Figure 8 illustrates how each interrupt (shown with heavy, dark lines) interacts with the motor control software. At Power-on Reset, the software initializes all the software variables and enables all the peripherals to be used by the application. After the variables and peripherals are initialized, the software enters the Motor Stopped state and remains there until a Start command is executed from the external push button (S2 pressed). When S2 is pressed, the RunMotor() subroutine is called, and the first process within this subroutine (ChargeBootstraps()) is executed. The inverter circuit uses N-channel MOSFETs for the upper and lower devices. The bootstrap circuit generates a floating voltage source for the gate drive of the upper devices. The bootstrap supply voltage can be 15V greater than the inverter voltage rail to ensure that the upper devices turn on. The ChargeBootstraps() subroutine is needed to charge the bootstrap capacitors each time the motor is energized for the first time before running the motor. The ChargeBootstraps() TABLE 4: subroutine turns on the lower transistors for 10 ms, to ensure voltage on these capacitors, and then transfers control of the outputs to the PWM module. Next, the variables used for controlling the motor are initialized. Then the PID coefficients, error accumulation and controller output variables used in the PID Speed Controller are initialized. In the RunMotor() subroutine, the timer counters are also initialized to zero, and the variables to capture the Hall effect sensor period are also initialized. At the end of the subroutine, the interrupt flags are cleared and the interrupts are enabled. Once the variables have been initialized in the RunMotor() subroutine, all other activities within the state machine are performed by Interrupt Service Routines (ISRs). Table 4 summarizes the Interrupt Service Routines, indicates when they are called and provides a brief description of the operations executed in each particular ISR. If S2 is pressed while the motor is running, the StopMotor() subroutine disables all the interrupts and stops the motor. SUMMARY OF INTERRUPT SERVICE ROUTINES Interrupt When Called Operations Performed A/D 20 kHz • Reads new Reference Speed value from AN2 PWM 20 kHz • Generates sine wave using SVM T1 1 kHz • • • • CN5 Every Hall A transition • Calculates rotor position • Determines rotor mechanical direction • Synchronizes sine-wave pointer to rotor position IC7 Every Hall B transition • • • • IC8 Every Hall C transition • Calculates rotor position • Determines rotor mechanical direction • Synchronizes sine-wave pointer to rotor position DS01017A-page 6 Measures Speed Calculation using IC7 data Executes PID control Calculates Phase Advance Provides Motor Stalled protection Calculates rotor position Determines rotor mechanical direction Captures Hall transition timing using IC Synchronizes sine-wave pointer to rotor position © 2005 Microchip Technology Inc. MAIN STATE MACHINE DIAGRAM es se d Pr I nt er ru Enable Peripherals and Interrupts Calculate Phase Advance if enabled pt 1m s) Reset Phase to agree with motor position Motor Running rrup Inte I C7 B Ha l l d not tor Mo 10 ms for Motor Stalled Protection g vin mo has A Hall effect sensor interrupt ms been generated within 10 CN5 Interr upt (Hall A) IC 8 se es Pr 2 S In t er ru pt ( Ha l lC Calculate rotor position from Hall effect sensors Calculate rotor direction from Hall effect sensor change ) t Disable interrupts and stop the motor pt rru Initialize PID Controller parameters te In Motor Stopped A/ D Execute PID Speed Controller Calculate actual speed from IC buffered M PW Read Reference Speed from AN2 Initialize value for running the motor Initialize variables and peripherals Generate new Sine point using SVM Increment phase of Sine Wave Charge Bootstrap Capacitors S2 0 ms (ea ch for 10 terr upt g movin T1 In Initialize variables and peripherals not Motor Synchronize sine-wave phase with rotor position Calculate rotor position from Hall effect sensors Reset DS01017A-page 7 Capture IC Event Calculate rotor direction from Hall effect sensor change Calculate rotor position from Hall effect sensors Calculate rotor direction from Hall effect sensor change Synchronize sine-wave phase with rotor position Synchronize sine-wave phase with rotor position SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC © 2005 Microchip Technology Inc. FIGURE 8: SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC SPEED CALCULATION Measured Speed Calculation The actual speed of the motor is calculated from one Hall effect sensor (Hall B). The calculation uses an Input Capture channel (IC7 input pin) to measure the time between two consecutive transitions in Hall effect sensor B. The timing diagram in Figure 9 shows the capture events and the variables used to store two consecutive captures to measure the time between Hall effect sensor B transitions. In the same figure, the mechanical rotation angle is plotted for the five polepair motor used to see the relationship between Hall effect sensor B signal and the actual mechanical movement. Reference Speed Calculation The Reference Speed variable (see Figure 7) is read by the A/D interrupt using the A/D converter (AN2 input pin). The A/D converter is configured to generate interrupts at the PWM rate (20 kHz in this application). Within the A/D ISR, the A/D conversion buffer is copied into a variable (RefSpeed) in signed fractional format. This variable represents the desired speed from -1.0 to 0.99997. Table 5 summarizes the minimum and maximum value of this variable and their interpretation for the motor used in this application note. TABLE 5: EXAMPLES OF REFERENCE SPEED CALCULATIONS RefSpeed Variable Hex Value Fractional Value Desired Speed in RPM Min Value 0x8000 -1.0 6000 RPM Reverse Max Value 0x7FFF 0.99997 6000 RPM Forward FIGURE 9: TIME RELATIONSHIP BETWEEN HALL B AND MOTOR MECHANICAL POSITION PastCapture = IC7BUF ActualCapture = IC7BUF Electrical Degrees 0 180 0 180 0 36 72 108 0 180 0 180 0 180 0 144 180 216 252 288 324 360 HALL B Motor Position (Rotor Angle) Mechanical Degrees DS01017A-page 8 © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC The variable used to store the time between transitions is called Period and is calculated in the Timer 1 ISR. This ISR is generated every 1 millisecond and executes the speed controller. The formula used to calculate the actual speed of the motor is: Period = ActualCapture – PastCapture where ActualCapture and PastCapture contain timing information of two consecutive Hall effect sensor B transitions as shown in Figure 9. Period is used for calculating the step size of the pointer used to generate the sine wave, since the generated sinusoidal voltages need to be of the same frequency compared to the Hall effect sensor information. For Speed calculation, the following formula is used to convert Hall effect sensor time between transitions (Period) to the measured speed (MeasuredSpeed): MINPERIOD MeasuredSpeed = FractionalDivide ⎛⎝ -----------------------------------⎞⎠ Period TABLE 6: MINPERIOD is a constant value calculated to give a fractional value of 0.99997, if a maximum speed of 6000 RPM is detected from the Hall effect sensor. The MINPERIOD formula is: MINPERIOD = (Timer 1 Input Clock) x 60 (Max Speed in RPM) x (Motor Poles) (20 MHz/64) x 60 = 6000 RPM x 10 = 312 Table 6 provides examples of speed calculation (MeasuredSpeed) from the input capture values stored in PastCapture and ActualCapture. The sign is added to the MeasuredSpeed depending on variable CurrentDirection, which is calculated in the Hall effect sensor interrupts. CurrentDirection is calculated based on two consecutive combinations from the Hall effect sensors (or two consecutive sectors). If the motor is moving forwards (CW), the MeasuredSpeed is kept positive. If the motor is moving backward (CCW), MeasuredSpeed is converted to a negative value. EXAMPLES OF MEASURED SPEED CALCULATIONS MeasuredSpeed ActualCapture 0x0000 PastCapture 0xFEC7 Period 0x0139 Hexadecimal Fractional RPM 0x7F97 0.99679 5990.4 0x2000 0x1D8E 0x0272 0xFCB 0.49838 2995.2 0x4000 0xC5EE 0x7A12 0x0147 0.00998 60 © 2005 Microchip Technology Inc. DS01017A-page 9 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC PID SPEED CONTROLLER The PID speed controller is executed in the T1 interrupt (Timer 1 ISR) every 1 millisecond. This subroutine is called SpeedControl() and uses both Reference Speed (RefSpeed) and the actual speed of the motor (MeasuredSpeed) in signed fractional format. MeasuredSpeed is subtracted from RefSpeed to determine the speed error (Error), which determines if the motor must speed up or slow down. To ensure smooth operation of the motor, the error value is parsed into proportional, integral and derivative components to produce a composite output that is used to compensate for the speed error. The PID controller implementation takes advantage of the MAC instruction of the dsPIC DSC for fast execution. The formula used to generate the controller output (ControlOutput) depends on three error values saved in the last three T1 interrupts (ControlDifference, ControlDifference and ControlDifference) and the PID coefficients (PIDCoefficients, PIDCoefficients and PIDCoefficients). The formula is: ControlOutput = ControlOutput + ControlDifference x PIDCoefficients + ControlDifference x PIDCoefficients Table 7 provides a brief description of the PID control variables This implementation of the PID uses the MAC instruction along with the automatic saturation feature of the dsPIC DSC when performing MAC operation. When adjusting PID gains, the user is responsible for avoiding maximum values of the PID coefficients. These values represent fractional values and have to be within the following values: Kp + Ki + Kd < 0.9999 (0x7FFF) -Kp – 2*Kd > -1.0(0x8000) Kd < 0.9999(0x7FFF) Figure 10 is a flow chart that shows how the SpeedControl() function is implemented. Required_Direction is taken from the sign of the PID controller output (ControlOutput) and tells the software to run the motor CW or CCW. The following code sample shows how the required direction is calculated in the software: // ControlOutput determines the motor // required direction if (ControlOutput < 0) Required_Direction = CCW; else Required_Direction = CW; + ControlDifference x PIDCoefficients TABLE 7: PID CONTROL VARIABLES Variable Description ControlOutput The output of the controller in 16-bit signed fractional format ControlDifference Most recent calculated speed error (RefSpeed - MeasuredSpeed) ControlDifference Speed error in the previous T1 ISR (1 ms old) ControlDifference Speed error before ControlDifference (2 ms old) PIDCoefficients, PIDCoefficients and PIDCoeffients[2} Modified PID coefficients from regular PID form to filter-like PID implementation: PIDCoefficients = Kp + Ki = Kd PIDCoefficients = -Kp - 2Kd PIDCoefficients = Kd DS01017A-page 10 © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC FIGURE 10: SPEED CONTROL FLOW CHART SpeedControl() Initialize Pointers to Controller Variables Calculate most recent Error and store at ControlDifference Load Accumulator with last ControlOutput MAC (ControlDifference x PIDCoefficients (ControlDifference x PIDCoefficients (ControlDifference x PIDCoefficients Save old Errors in ControlDifference array Yes New ControllerOutput<0> Required Direction = CCW No Required Direction = CW Save old Errors in ControlDifference array End © 2005 Microchip Technology Inc. DS01017A-page 11 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC PID BACKGROUND ADJUSTING PID GAINS A complete discussion of Proportional Integral Derivative (PID) controllers is beyond the scope of this application note. However, some PID operation basics are relevant. The P gain of a PID controller sets the overall system response. When first tuning a controller, the I and D gains should be set to zero. The P gain can then be increased until the system responds well to set-point changes without excessive overshoot or oscillations. Using lower values of P gain will ‘loosely’ control the system, while higher values will give ‘tighter’ control. At this point, the system will probably not converge to the set-point. A PID controller responds to an error signal in a closed control loop and attempts to adjust the controlled quantity to achieve the desired system response. The controlled parameter can be any measurable system quantity such as speed, torque or flux. The benefit of the PID controller is that it can be adjusted empirically by adjusting one or more gain values and observing the change in system response. A digital PID controller is executed at a periodic sampling interval. It is assumed that the controller is executed frequently enough so that the system can be properly controlled. The error signal is formed by subtracting the desired setting of the parameter to be controlled from the actual measured value of that parameter. The sign of the error indicates the direction of change required by the control input. The Proportional (P) term of the controller is formed by multiplying the error signal by a P gain, causing the PID controller to produce a control response that is a function of (i.e., proportional to) the error magnitude. As the error signal becomes larger, the P term of the controller becomes larger to provide more correction. The effect of the P term tends to reduce the overall error as time elapses. However, the P term has less effect as the error approaches zero. In most systems, the error of the controlled parameter gets very close to zero but does not converge. The result is a small remaining steady state error. After a reasonable P gain is selected, the I gain can be slowly increased to force the system error to zero. Only a small amount of I gain is required in most systems. Note that the effect of the I gain, if large enough, can overcome the action of the P term, slow the overall control response and cause the system to oscillate around the set-point. If oscillation occurs, reducing the I gain and increasing the P gain usually solves the problem. The D gain can speed up system response. However, it must be used carefully because it can produce large output swings, which potentially cause mechanical damage on the motor. The Integral (I) term of the controller is used to eliminate small steady state errors. The I term calculates a continuous running total of the error signal. Therefore, a small steady state error accumulates into a large error value over time. This accumulated error signal is multiplied by an I gain factor and becomes the I output term of the PID controller. The Differential (D) term of the PID controller is used to enhance the speed of the controller and responds to the rate of change of the error signal. The D term input is calculated by subtracting the present error value from a prior value. This delta error value is multiplied by a D gain factor that becomes the D output term of the PID controller. The D term of the controller produces more control output the faster the system error is changing. DS01017A-page 12 © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC ROTOR SECTOR CALCULATION The following code illustrates this process: Again referring to the software block diagram in Figure 2, the rotor sector value is needed for sinusoidal voltage generation. Rotor sector is the absolute position of the rotor, in electrical degrees, in 60-degree steps. That information is obtained by reading the digital value from the three Hall effect sensors. The Rotor Sector Calculation software block uses the three Hall effect sensor interrupts (CN5, IC8 and IC7 interrupts, as shown in Figure 8). The sector is calculated using the relationships shown in Table 8: TABLE 8: Hall C RELATIONSHIP OF SECTOR TO ANGULAR POSITION Hall B Hall A Sector 0 0 0 Invalid 0 0 1 4 0 1 0 2 0 1 1 3 1 0 0 0 1 0 1 5 1 1 0 1 1 1 1 Invalid For calculating the actual motor direction of rotation (Current_Direction) the last two consecutive sectors in the Hall effect sensor interrupts are compared. Table 9 summarizes the direction calculation based on the last two sectors. TABLE 9: CURRENT DIRECTION CALCULATION LastSector Sector Current_Direction 0 1 CCW 1 2 CCW 2 3 CCW 3 4 CCW 4 5 CCW 5 0 CCW 0 5 CW 1 0 CW 2 1 CW 3 2 CW 4 3 CW 5 4 CW The actual direction of motor rotation is used in the Speed Calculation block. If the actual direction is CCW, the speed is negative. © 2005 Microchip Technology Inc. // MeasuredSpeed sign adjustment based on // current motor direction of rotation if (Current_Direction == CCW) MeasuredSpeed = -MeasuredSpeed; The calculated Rotor Sector value is modified by the measured speed and maximum phase advance to set the phase angle of the sinusoidal voltage. PHASE ADVANCE Under normal conditions, motor speed is limited by the voltage supplied to the motor windings by the inverter. The voltage on the motor windings is usually synchronized with the rotor position, as shown by the relationship between Voltage A and Hall A in Figure 11. This condition creates a rotating electrical field in the stator that is 90 degrees ahead of the rotor magnetic field, which produces the maximum torque per amp from the motor. FIGURE 11: EFFECT OF PHASE ADVANCE ON DRIVE VOLTAGE 0 60 120 180 240 300 0 60 VOLTAGE A HALL A Θ VOLTAGE A With Phase Advance If the field generated in the stator is shifted by an angle theta, the resulting magnetic field between the stator and the rotor is increased. The addition of this phase advance creates a negative field in the rotor, which reduces the field produced by rotor permanent magnets. Some important effects of this phase shift include: • Phase advance increases the speed range over the nominal speed limit, since the resulting field vector is increased. • Phase advance weakens the rotor field since it produces a negative field in the rotor. Field weakening reduces the overall torque output available from the motor. • Motor current consumption, motor operating temperature and audible noise increase when phase advance is used because the stator field is working against the rotor field. DS01017A-page 13 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC SINE-WAVE GENERATION USING SPACE VECTOR MODULATION For applications where an increase in the speed range of the motor is required, phase advance is a recommended algorithm. This algorithm can be enabled by defining PHASE_ADVANCE in the SinusoidalBLDC v1.1.c file. This feature is disabled in the context of this application note. #define PHASE_ADVANCE TABLE 10: The final step in the sinusoidal control of a PMSM motor is to generate pulse-width modulation signals for the three-phase motor voltage signals. By using Space Vector Modulation (SVM), the process of generating the pulse width for each of the three phases reduces to a few simple equations. Each of the three inverter outputs can be in one of two states: either connected to the + bus rail or the - bus rail. Thus the output can be in eight possible states (23 = 8), as shown in Table 10. // for extended // speed ranges this // should be defined SPACE VECTOR MODULATION INVERTER STATES C B A Vab Vbc Vca Vds Vqs Vector 0 0 0 0 0 0 0 0 U(000) 0 0 1 VDC 0 -VDC 2/3Vdc 0 U0 0 1 1 0 VDC -VDC VDC/3 VDC/3 U60 0 1 0 -VDC VDC 0 -VDC/3 VDC/3 U120 1 1 0 -VDC 0 VDC -2VDC/3 0 U180 1 0 0 0 -VDC VDC -VDC/3 -VDC/3 U240 1 0 1 VDC -VDC 0 VDC/3 -VDC/3 U300 1 1 1 0 0 0 0 0 U(111) DS01017A-page 14 © 2005 Microchip Technology Inc. SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC The two states where all three outputs are connected to either the + bus or the - bus are considered null states because there is no line-to-line voltage across any of the phases. These are plotted at the origin of the SVM Star. The remaining six states are represented as vectors with 60 degree rotation between each state, as shown in Figure 12. FIGURE 12: SPACE VECTOR MODULATION U120(010) III U180(110) period. This configuration produces two pulses line-toline during each period. The effective switching frequency is doubled, reducing the ripple current while not increasing the switching losses in the power devices. FIGURE 14: PWM FOR PERIOD T 000 100 110 111 111 T0/4 T1/2 T2/2 T0/4 T0/4 110 100 000 PWM1 U60(011) II U(111) PWM2 I PWM3 U(000) U0(001) T2/2 T1/2 T0/4 T IV VI V U240(100) Figure 15 shows a complete electrical revolution with duty cycles using SVM. the values represent duty cycles between 0% and 100%. U300(101) Space Vector Modulation allows any resultant vector be represented by the sum of the components of the two adjacent vectors. In Figure 13, UOUT is the desired resultant. It lies in the sector between U60 and U0. If during a given PWM period T, U0 is output for T1/ T and U60 is output for T2/T, the average for the period will be UOUT. FIGURE 13: AVERAGE SPACE VECTOR MODULATION U60(011) T = T1 + T2 + T0 = PWM Period UOUT = UOUT T1 * U0 + T2 * U60 T T2/T * U60 T1/T * U0 U0(001) FIGURE 15: LINE-TO-GROUND VOLTAGES USING SVM 100% 50% 0% SVM Sector I II As shown in Figure 14, the PWM period T, the vector T1 is output for T1/T and the vector T2 is output for T2/ T. During the remaining time the null vectors are output. The dsPIC30F device is configured for center aligned PWM, which forces symmetry about the center of the © 2005 Microchip Technology Inc. IV V VI PWM1 PWM2 PWM3 The resulting line-to-line voltages are shown in Figure 16. Sinusoidal voltages with full amplitude are fed into the motor windings. FIGURE 16: The values for T1 and T2 are taken from a look up table containing 172 fractional sinusoidal values for 0 to 60 electrical degrees. As a result, for each of the six segments one axis is exactly opposite that segment, and the other two axes symmetrically bound the segment. The values of the vector components along those two bounding axis are equal to T1 and T2. For details of the calculations, refer to the SVM.c file that accompanies this application note. III LINE-TO-LINE VOLTAGES USING SVM +VDC 0V -VDC SVM Sector I II III IV V VI Va - Vb Vb - Vc Vc - Va DS01017A-page 15 SINUSOIDAL CONTROL OF PMSM MOTORS WITH DSPIC30F DSC CONCLUSION The dsPIC30F2010 provides an ideal low-cost solution for controlling a PMSM motor with sinusoidal voltages. Motor control peripherals, such as the MCPWM, in combination with processing power, makes possible several algorithms such as Space Vector Modulation for sine-wave generation, and PID loops for controlling motor speed. The dsPICDEM™ MCLV development board has the necessary hardware to run this application while maintaining low cost to the total system. Software files are contained in the AN1017.zip file and can be downloaded from the Microchip web site www.microchip.com REVISION HISTORY Revision A (December 2005) • Initial release of this document. DS01017A-page 16 © 2005 Microchip Technology Inc. Note the following details of the code protection feature on Microchip devices: • Microchip products meet the specification contained in their particular Microchip Data Sheet. • Microchip believes that its family of products is one of the most secure families of its kind on the market today, when used in the intended manner and under normal conditions. • There are dishonest and possibly illegal methods used to breach the code protection feature. All of these methods, to our knowledge, require using the Microchip products in a manner outside the operating specifications contained in Microchip’s Data Sheets. Most likely, the person doing so is engaged in theft of intellectual property. • Microchip is willing to work with the customer who is concerned about the integrity of their code. • Neither Microchip nor any other semiconductor manufacturer can guarantee the security of their code. Code protection does not mean that we are guaranteeing the product as “unbreakable.” Code protection is constantly evolving. We at Microchip are committed to continuously improving the code protection features of our products. Attempts to break Microchip’s code protection feature may be a violation of the Digital Millennium Copyright Act. If such acts allow unauthorized access to your software or other copyrighted work, you may have a right to sue for relief under that Act. Information contained in this publication regarding device applications and the like is provided only for your convenience and may be superseded by updates. It is your responsibility to ensure that your application meets with your specifications. MICROCHIP MAKES NO REPRESENTATIONS OR WARRANTIES OF ANY KIND WHETHER EXPRESS OR IMPLIED, WRITTEN OR ORAL, STATUTORY OR OTHERWISE, RELATED TO THE INFORMATION, INCLUDING BUT NOT LIMITED TO ITS CONDITION, QUALITY, PERFORMANCE, MERCHANTABILITY OR FITNESS FOR PURPOSE. Microchip disclaims all liability arising from this information and its use. Use of Microchip’s products as critical components in life support systems is not authorized except with express written approval by Microchip. No licenses are conveyed, implicitly or otherwise, under any Microchip intellectual property rights. Trademarks The Microchip name and logo, the Microchip logo, Accuron, dsPIC, KEELOQ, microID, MPLAB, PIC, PICmicro, PICSTART, PRO MATE, PowerSmart, rfPIC, and SmartShunt are registered trademarks of Microchip Technology Incorporated in the U.S.A. and other countries. AmpLab, FilterLab, Migratable Memory, MXDEV, MXLAB, PICMASTER, SEEVAL, SmartSensor and The Embedded Control Solutions Company are registered trademarks of Microchip Technology Incorporated in the U.S.A. Analog-for-the-Digital Age, Application Maestro, dsPICDEM, dsPICDEM.net, dsPICworks, ECAN, ECONOMONITOR, FanSense, FlexROM, fuzzyLAB, In-Circuit Serial Programming, ICSP, ICEPIC, Linear Active Thermistor, MPASM, MPLIB, MPLINK, MPSIM, PICkit, PICDEM, PICDEM.net, PICLAB, PICtail, PowerCal, PowerInfo, PowerMate, PowerTool, Real ICE, rfLAB, rfPICDEM, Select Mode, Smart Serial, SmartTel, Total Endurance, UNI/O, WiperLock and Zena are trademarks of Microchip Technology Incorporated in the U.S.A. and other countries. SQTP is a service mark of Microchip Technology Incorporated in the U.S.A. All other trademarks mentioned herein are property of their respective companies. © 2005, Microchip Technology Incorporated, Printed in the U.S.A., All Rights Reserved. Printed on recycled paper. Microchip received ISO/TS-16949:2002 quality system certification for its worldwide headquarters, design and wafer fabrication facilities in Chandler and Tempe, Arizona and Mountain View, California in October 2003. The Company’s quality system processes and procedures are for its PICmicro® 8-bit MCUs, KEELOQ® code hopping devices, Serial EEPROMs, microperipherals, nonvolatile memory and analog products. In addition, Microchip’s quality system for the design and manufacture of development systems is ISO 9001:2000 certified. © 2005 Microchip Technology Inc. Advance Information DS00000A-page 17 WORLDWIDE SALES AND SERVICE AMERICAS ASIA/PACIFIC ASIA/PACIFIC EUROPE Corporate Office 2355 West Chandler Blvd. Chandler, AZ 85224-6199 Tel: 480-792-7200 Fax: 480-792-7277 Technical Support: http://support.microchip.com Web Address: www.microchip.com Australia - Sydney Tel: 61-2-9868-6733 Fax: 61-2-9868-6755 India - Bangalore Tel: 91-80-2229-0061 Fax: 91-80-2229-0062 China - Beijing Tel: 86-10-8528-2100 Fax: 86-10-8528-2104 India - New Delhi Tel: 91-11-5160-8631 Fax: 91-11-5160-8632 Austria - Wels Tel: 43-7242-2244-399 Fax: 43-7242-2244-393 Denmark - Copenhagen Tel: 45-4450-2828 Fax: 45-4485-2829 China - Chengdu Tel: 86-28-8676-6200 Fax: 86-28-8676-6599 India - Pune Tel: 91-20-2566-1512 Fax: 91-20-2566-1513 France - Paris Tel: 33-1-69-53-63-20 Fax: 33-1-69-30-90-79 China - Fuzhou Tel: 86-591-8750-3506 Fax: 86-591-8750-3521 Japan - Yokohama Tel: 81-45-471- 6166 Fax: 81-45-471-6122 Germany - Munich Tel: 49-89-627-144-0 Fax: 49-89-627-144-44 China - Hong Kong SAR Tel: 852-2401-1200 Fax: 852-2401-3431 Korea - Gumi Tel: 82-54-473-4301 Fax: 82-54-473-4302 China - Qingdao Tel: 86-532-8502-7355 Fax: 86-532-8502-7205 Korea - Seoul Tel: 82-2-554-7200 Fax: 82-2-558-5932 or 82-2-558-5934 Atlanta Alpharetta, GA Tel: 770-640-0034 Fax: 770-640-0307 Boston Westborough, MA Tel: 774-760-0087 Fax: 774-760-0088 Chicago Itasca, IL Tel: 630-285-0071 Fax: 630-285-0075 Dallas Addison, TX Tel: 972-818-7423 Fax: 972-818-2924 Detroit Farmington Hills, MI Tel: 248-538-2250 Fax: 248-538-2260 Kokomo Kokomo, IN Tel: 765-864-8360 Fax: 765-864-8387 Los Angeles Mission Viejo, CA Tel: 949-462-9523 Fax: 949-462-9608 San Jose Mountain View, CA Tel: 650-215-1444 Fax: 650-961-0286 China - Shanghai Tel: 86-21-5407-5533 Fax: 86-21-5407-5066 China - Shenyang Tel: 86-24-2334-2829 Fax: 86-24-2334-2393 China - Shenzhen Tel: 86-755-8203-2660 Fax: 86-755-8203-1760 China - Shunde Tel: 86-757-2839-5507 Fax: 86-757-2839-5571 China - Wuhan Tel: 86-27-5980-5300 Fax: 86-27-5980-5118 China - Xian Tel: 86-29-8833-7250 Fax: 86-29-8833-7256 Malaysia - Penang Tel: 60-4-646-8870 Fax: 60-4-646-5086 Philippines - Manila Tel: 63-2-634-9065 Fax: 63-2-634-9069 Italy - Milan Tel: 39-0331-742611 Fax: 39-0331-466781 Netherlands - Drunen Tel: 31-416-690399 Fax: 31-416-690340 Spain - Madrid Tel: 34-91-708-08-90 Fax: 34-91-708-08-91 UK - Wokingham Tel: 44-118-921-5869 Fax: 44-118-921-5820 Singapore Tel: 65-6334-8870 Fax: 65-6334-8850 Taiwan - Hsin Chu Tel: 886-3-572-9526 Fax: 886-3-572-6459 Taiwan - Kaohsiung Tel: 886-7-536-4818 Fax: 886-7-536-4803 Taiwan - Taipei Tel: 886-2-2500-6610 Fax: 886-2-2508-0102 Thailand - Bangkok Tel: 66-2-694-1351 Fax: 66-2-694-1350 Toronto Mississauga, Ontario, Canada Tel: 905-673-0699 Fax: 905-673-6509 *DS01017A* 10/31/05 DS01017A-page 18 © 2005 Microchip Technology Inc.