AMCLIB User's Guide DSP56800E Document Number: DSP56800EAMCLIBUG Rev. 2, 10/2015 AMCLIB User's Guide, Rev. 2, 10/2015 2 Freescale Semiconductor, Inc. Contents Section number Title Page Chapter 1 Library 1.1 Introduction.................................................................................................................................................................... 5 1.2 Library integration into project (CodeWarrior™ Development Studio) .......................................................................7 Chapter 2 Algorithms in detail 2.1 AMCLIB_TrackObsrv................................................................................................................................................... 17 2.2 AMCLIB_AngleTrackObsrv..........................................................................................................................................21 2.3 AMCLIB_PMSMBemfObsrvDQ...................................................................................................................................27 AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 3 AMCLIB User's Guide, Rev. 2, 10/2015 4 Freescale Semiconductor, Inc. Chapter 1 Library 1.1 Introduction 1.1.1 Overview This user's guide describes the Advanced Motor Control Library (AMCLIB) for the family of DSP56800E core-based digital signal controllers. This library contains optimized functions. 1.1.2 Data types AMCLIB supports several data types: (un)signed integer, fractional, and accumulator. The integer data types are useful for general-purpose computation; they are familiar to the MPU and MCU programmers. The fractional data types enable powerful numeric and digital-signal-processing algorithms to be implemented. The accumulator data type is a combination of both; that means it has the integer and fractional portions. The following list shows the integer types defined in the libraries: • • • • Unsigned 16-bit integer —<0 ; 65535> with the minimum resolution of 1 Signed 16-bit integer —<-32768 ; 32767> with the minimum resolution of 1 Unsigned 32-bit integer —<0 ; 4294967295> with the minimum resolution of 1 Signed 32-bit integer —<-2147483648 ; 2147483647> with the minimum resolution of 1 The following list shows the fractional types defined in the libraries: • Fixed-point 16-bit fractional —<-1 ; 1 - 2-15> with the minimum resolution of 2-15 • Fixed-point 32-bit fractional —<-1 ; 1 - 2-31> with the minimum resolution of 2-31 AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 5 Introduction The following list shows the accumulator types defined in the libraries: • Fixed-point 16-bit accumulator —<-256.0 ; 256.0 - 2-7> with the minimum resolution of 2-7 • Fixed-point 32-bit accumulator —<-65536.0 ; 65536.0 - 2-15> with the minimum resolution of 2-15 1.1.3 API definition AMCLIB uses the types mentioned in the previous section. To enable simple usage of the algorithms, their names use set prefixes and postfixes to distinguish the functions' versions. See the following example: f32Result = MLIB_Mac_F32lss(f32Accum, f16Mult1, f16Mult2); where the function is compiled from four parts: • • • • MLIB—this is the library prefix Mac—the function name—Multiply-Accumulate F32—the function output type lss—the types of the function inputs; if all the inputs have the same type as the output, the inputs are not marked The input and output types are described in the following table: Table 1-1. Input/output types Type Output Input frac16_t F16 s frac32_t F32 l acc32_t A32 a 1.1.4 Supported compilers AMCLIB for the DSP56800E core is written in assembly language with C-callable interface. The library is built and tested using the following compilers: • CodeWarrior™ Development Studio For the CodeWarrior™ Development Studio, the library is delivered in the amclib.lib file. AMCLIB User's Guide, Rev. 2, 10/2015 6 Freescale Semiconductor, Inc. Chapter 1 Library The interfaces to the algorithms included in this library are combined into a single public interface include file, amclib.h. This is done to lower the number of files required to be included in your application. 1.1.5 Special issues 1. The equations describing the algorithms are symbolic. If there is positive 1, the number is the closest number to 1 that the resolution of the used fractional type allows. If there are maximum or minimum values mentioned, check the range allowed by the type of the particular function version. 2. The library functions require the core saturation mode to be turned off, otherwise the results can be incorrect. Several specific library functions are immune to the setting of the saturation mode. 3. The library functions round the result (the API contains Rnd) to the nearest (two's complement rounding) or to the nearest even number (convergent round). The mode used depends on the core option mode register (OMR) setting. See the core manual for details. 4. All non-inline functions are implemented without storing any of the volatile registers (refer to the compiler manual) used by the respective routine. Only the non-volatile registers (C10, D10, R5) are saved by pushing the registers on the stack. Therefore, if the particular registers initialized before the library function call are to be used after the function call, it is necessary to save them manually. 1.2 Library integration into project (CodeWarrior™ Development Studio) This section provides a step-by-step guide to quickly and easily integrate the AMCLIB into an empty project using CodeWarrior™ Development Studio. This example uses the MC56F8257 part, and the default installation path (C:\Freescale\FSLESL \DSP56800E_FSLESL_4.2) is supposed. If you have a different installation path, you must use that path instead. 1.2.1 New project To start working on an application, create a new project. If the project already exists and is open, skip to the next section. Follow the steps given below to create a new project. 1. Launch CodeWarrior™ Development Studio. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 7 Library integration into project (CodeWarrior™ Development Studio) 2. Choose File > New > Bareboard Project, so that the "New Bareboard Project" dialog appears. 3. Type a name of the project, for example, MyProject01. 4. If you don't use the default location, untick the “Use default location” checkbox, and type the path where you want to create the project folder; for example, C: \CWProjects\MyProject01, and click Next. See Figure 1-1. Figure 1-1. Project name and location 5. Expand the tree by clicking the 56800/E (DSC) and MC56F8257. Select the Application option and click Next. See Figure 1-2. Figure 1-2. Processor selection 6. Now select the connection that will be used to download and debug the application. In this case, select the option P&E USB MultiLink Universal[FX] / USB MultiLink and Freescale USB TAP, and click Next. See Figure 1-3. AMCLIB User's Guide, Rev. 2, 10/2015 8 Freescale Semiconductor, Inc. Chapter 1 Library Figure 1-3. Connection selection 7. From the options given, select the Simple Mixed Assembly and C language, and click Finish. See Figure 1-4. Figure 1-4. Language choice The new project is now visible in the left-hand part of CodeWarrior™ Development Studio. See Figure 1-5. Figure 1-5. Project folder 1.2.2 Library path variable To make the library integration easier, create a variable that will hold the information about the library path. 1. Right-click the MyProject01 node in the left-hand part and click Properties, or select Project > Properties from the menu. The project properties dialog appears. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 9 Library integration into project (CodeWarrior™ Development Studio) 2. Expand the Resource node and click Linked Resources. See Figure 1-6. Figure 1-6. Project properties 3. Click the 'New…' button on the right-hand side. 4. In the dialog that appears (see Figure 1-7), type this variable name into the Name box: FSLESL_LOC 5. Select the library parent folder by clicking 'Folder…' or just typing the following path into the Location box: C:\Freescale\FSLESL\DSP56800E_FSLESL_4.2_CW and click OK. 6. Click OK in the previous dialog. AMCLIB User's Guide, Rev. 2, 10/2015 10 Freescale Semiconductor, Inc. Chapter 1 Library Figure 1-7. New variable 1.2.3 Library folder addition To use the library, add it into the CodeWarrior Project tree dialog. 1. Right-click the MyProject01 node in the left-hand part and click New > Folder, or select File > New > Folder from the menu. A dialog appears. 2. Click Advanced to show the advanced options. 3. To link the library source, select the third option—Link to alternate location (Linked Folder). 4. Click Variables…, and select the FSLESL_LOC variable in the dialog that appears, click OK, and/or type the variable name into the box. See Figure 1-8. 5. Click Finish, and you will see the library folder linked in the project. See Figure 1-9 AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 11 Library integration into project (CodeWarrior™ Development Studio) Figure 1-8. Folder link Figure 1-9. Projects libraries paths 1.2.4 Library path setup AMCLIB requires MLIB and GFLIB and GMCLIB to be included too. Therefore, the following steps show the inclusion of all dependent modules. 1. Right-click the MyProject01 node in the left-hand part and click Properties, or select Project > Properties from the menu. A dialog with the project properties appears. AMCLIB User's Guide, Rev. 2, 10/2015 12 Freescale Semiconductor, Inc. Chapter 1 Library 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Expand the C/C++ Build node, and click Settings. In the right-hand tree, expand the DSC Linker node, and click Input. See Figure 1-11. In the third dialog Additional Libraries, click the 'Add…' icon, and a dialog appears. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box by adding one of the following: • ${FSLESL_LOC}\MLIB\mlib_SDM.lib—for small data model projects • ${FSLESL_LOC}\MLIB\mlib_LDM.lib—for large data model projects Tick the box Relative To, and select FSLESL_LOC next to the box. See Figure 1-9. Click OK. Click the 'Add…' icon in the third dialog Additional Libraries. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box by adding one of the following: • ${FSLESL_LOC}\GFLIB\gflib_SDM.lib—for small data model projects • ${FSLESL_LOC}\GFLIB\gflib_LDM.lib—for large data model projects Tick the box Relative To, and select FSLESL_LOC next to the box. Click OK. Click the 'Add…' icon in the Additional Libraries dialog. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box by adding one of the following: • ${FSLESL_LOC}\GMCLIB\gmclib_SDM.lib—for small data model projects • ${FSLESL_LOC}\GMCLIB\gmclib_LDM.lib—for large data model projects Tick the box Relative To, and select FSLESL_LOC next to the box. Click OK. Click the 'Add…' icon in the Additional Libraries dialog. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box by adding one of the following: • ${FSLESL_LOC}\AMCLIB\amclib_SDM.lib—for small data model projects • ${FSLESL_LOC}\AMCLIB\amclib_LDM.lib—for large data model projects Now, you will see the libraries added in the box. See Figure 1-11. Figure 1-10. Library file inclusion AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 13 Library integration into project (CodeWarrior™ Development Studio) Figure 1-11. Linker setting 16. In the tree under the DSC Compiler node, click Access Paths. 17. In the Search User Paths dialog (#include “…”), click the 'Add…' icon, and a dialog will appear. 18. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box to be: ${FSLESL_LOC}\MLIB\include. 19. Tick the box Relative To, and select FSLESL_LOC next to the box. See Figure 1-12. Click OK. 20. Click the 'Add…' icon in the Search User Paths dialog (#include “…”). 21. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box to be: ${FSLESL_LOC}\GFLIB\include. 22. Tick the box Relative To, and select FSLESL_LOC next to the box. Click OK. 23. Click the 'Add…' icon in the Search User Paths dialog (#include “…”). 24. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box to be: ${FSLESL_LOC}\GMCLIB\include. 25. Tick the box Relative To, and select FSLESL_LOC next to the box. Click OK. 26. Click the 'Add…' icon in the Search User Paths dialog (#include “…”). AMCLIB User's Guide, Rev. 2, 10/2015 14 Freescale Semiconductor, Inc. Chapter 1 Library 27. Look for the FSLESL_LOC variable by clicking Variables…, and then finish the path in the box to be: ${FSLESL_LOC}\AMCLIB\include. 28. Tick the box Relative To, and select FSLESL_LOC next to the box. Click OK. 29. Now you will see the paths added in the box. See Figure 1-13. Click OK. Figure 1-12. Library include path addition Figure 1-13. Compiler setting The final step is typing the #include syntax into the code. Include the library into the main.c file. In the left-hand dialog, open the Sources folder of the project, and doubleclick the main.c file. After the main.c file opens up, include the following lines into the #include section: #include #include #include #include "mlib.h" "gflib.h" "gmclib.h" "amclib.h" When you click the Build icon (hammer), the project will be compiled without errors. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 15 Library integration into project (CodeWarrior™ Development Studio) AMCLIB User's Guide, Rev. 2, 10/2015 16 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail 2.1 AMCLIB_TrackObsrv The AMCLIB_TrackObsrv function calculates a tracking observer for the determination of angular speed and position of the input error functional signal. The tracking-observer algorithm uses the phase-locked-loop mechanism. It is recommended to call this function at every sampling period. It requires a single input argument as a phase error. A phasetracking observer with a standard PI controller used as the loop compensator is shown in Figure 2-1. Figure 2-1. Block diagram of proposed PLL scheme for position estimation The depicted tracking observer structure has the following transfer function: Equation 1 The controller gains Kp and Ki are calculated by comparing the characteristic polynomial of the resulting transfer function to a standard second-order system polynomial. The essential equations for implementation of the tracking observer according to the block scheme in Figure 2-1 are as follows: AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 17 AMCLIB_TrackObsrv Equation 2 Equation 3 where: • • • • • • • • KP is the proportional gain KI is the integral gain Ts is the sampling period [s] e(k) is the position error in step k ω(k) is the rotor speed [rad / s] in step k ω(k - 1) is the rotor speed [rad / s] in step k - 1 θ(k) is the rotor angle [rad] in step k θ(k - 1) is the rotor angle [rad] in step k - 1 In the fractional arithmetic, Equation 1 on page 17 and Equation 2 on page 18 are as follows: Equation 4 Equation 5 where: • • • • • • • esc(k) is the scaled position error in step k ωsc(k) is the scaled rotor speed [rad / s] in step k ωsc(k - 1) is the scaled rotor speed [rad / s] in step k - 1 θsc(k) is the scaled rotor angle [rad] in step k θsc(k - 1) is the scaled rotor angle [rad] in step k - 1 ωmax is the maximum speed θmax is the maximum rotor angle (typically) 2.1.1 Available versions The function is available in the following versions: • Fractional output - the output is the fractional portion of the result; the result is within the range <-1 ; 1). AMCLIB User's Guide, Rev. 2, 10/2015 18 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail The available versions of the AMCLIB_TrackObsrv function are shown in the following table: Table 2-1. Init versions Function name AMCLIB_TrackObsrvInit_F16 Init angle frac16_t Parameters AMCLIB_TRACK_OBSRV_T_F32 * Result type void The input is a 16-bit fractional value of the angle normalized to the range <-1 ; 1) that represents an angle (in radians) within the range <-π ; π). Table 2-2. Function versions Function name AMCLIB_TrackObsrv_F16 Input type frac16_t Parameters AMCLIB_TRACK_OBSRV_T_F32 * Result type frac16_t Tracking observer with a 16-bit fractional position error input divided by π. The output from the obsever is a 16-bit fractional position normalized to the range <-1 ; 1) that represents an angle (in radians) within the range <-π ; π). 2.1.2 AMCLIB_TRACK_OBSRV_T_F32 Variable name Input type Description f32Theta frac32_t Estimated position as the output of the second numerical integrator. The parameter is within the range <-1 ; 1). Controlled by the algorithm. f32Speed frac32_t Estimated speed as the output of the first numerical integrator. The parameter is within the range <-1 ; 1). Controlled by the algorithm. f32I_1 frac32_t State variable in the controller part of the observer; integral part at step k - 1. The parameter is within the range <-1 ; 1). Controlled by the algorithm. f16IGain frac16_t The observer integral gain is set up according to Equation 4 on page 18 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. i16IGainSh int16_t The observer integral gain shift takes care of keeping the f16IGain variable within the fractional range <-1 ; 1). The shift is determined as: The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. f16PGain frac16_t The observer proportional gain is set up according to Equation 4 on page 18 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. i16PGainSh int16_t The observer proportional gain shift takes care of keeping the f16PGain variable within the fractional range <-1 ; 1). The shift is determined as: Table continues on the next page... AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 19 AMCLIB_TrackObsrv Variable name Input type Description The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. f16ThGain frac16_t The observer gain for the output position integrator is set up according to Equation 5 on page 18 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. i16ThGainSh int16_t The observer gain shift for the position integrator takes care of keeping the f16ThGain variable within the fractional range <-1 ; 1). The shift is determined as: The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. 2.1.3 Declaration The available AMCLIB_TrackObsrvInit functions have the following declarations: void AMCLIB_TrackObsrvInit_F16(frac16_t f16ThetaInit, AMCLIB_TRACK_OBSRV_T_F32 *psCtrl) The available AMCLIB_TrackObsrv functions have the following declarations: frac16_t AMCLIB_TrackObsrv_F16(frac16_t f16Error, AMCLIB_TRACK_OBSRV_T_F32 *psCtrl) 2.1.4 Function use The use of the AMCLIB_TrackObsrv function is shown in the following example: #include "amclib.h" static AMCLIB_TRACK_OBSRV_T_F32 sTo; static frac16_t f16ThetaError; static frac16_t f16PositionEstim; void Isr(void); void main(void) { sTo.f16IGain sTo.i16IGainSh sTo.f16PGain sTo.i16PGainSh sTo.f16ThGain sTo.i16ThGainSh = = = = = = FRAC16(0.6434); -9; FRAC16(0.6801); -2; FRAC16(0.6400); -4; AMCLIB_TrackObsrvInit_F16(FRAC16(0.0), &sTo); f16ThetaError = FRAC16(0.5); AMCLIB User's Guide, Rev. 2, 10/2015 20 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail } /* Periodical function or interrupt */ void Isr(void) { /* Tracking observer calculation */ f16PositionEstim = AMCLIB_TrackObsrv_F16(f16ThetaError, &sTo); } 2.2 AMCLIB_AngleTrackObsrv The AMCLIB_TrackObsrv function calculates an angle-tracking observer for determination of angular speed and position of the input signal. It requires two input arguments as sine and cosine samples. The practical implementation of the angle-tracking observer algorithm is described below. The angle-tracking observer compares values of the input signals - sin(θ), cos(θ) with their corresponding estimations. As in any common closed-loop systems, the intent is to minimize the observer error towards zero value. The observer error is given here by subtracting the estimated resolver rotor angle from the actual rotor angle. The tracking-observer algorithm uses the phase-locked loop mechanism. It is recommended to call this function at every sampling period. It requires a single input argument as phase error. A phase-tracking observer with standard PI controller used as the loop compensator is shown in Figure 2-2. Figure 2-2. Block diagram of proposed PLL scheme for position estimation Note that the mathematical expression of the observer error is known as the formula of the difference between two angles: AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 21 AMCLIB_AngleTrackObsrv Equation 6 If the deviation between the estimated and the actual angle is very small, then the observer error may be expressed using the following equation: Equation 7 The primary benefit of the angle-tracking observer utilization, in comparison with the trigonometric method, is its smoothing capability. This filtering is achieved by the integrator and the proportional and integral controllers, which are connected in series and closed by a unit feedback loop. This block diagram tracks the actual rotor angle and speed, and continuously updates their estimations. The angle-tracking observer transfer function is expressed as follows: Equation 8 The characteristic polynomial of the angle-tracking observer corresponds to the denominator of the following transfer function: Appropriate dynamic behavior of the angle-tracking observer is achieved by the placement of the poles of characteristic polynomial. This general method is based on matching the coefficients of characteristic polynomial with the coefficients of a general second-order system. The analog integrators in the previous figure (marked as 1 / s) are replaced by an equivalent of the discrete-time integrator using the backward Euler integration method. The discrete-time block diagram of the angle-tracking observer is shown in the following figure: AMCLIB User's Guide, Rev. 2, 10/2015 22 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail Figure 2-3. Block scheme of discrete-time tracking observer The essential equations for implementating the angle-tracking observer (according to this block scheme) are as follows: Equation 9 Equation 10 Equation 11 Equation 12 where: • • • • • • • • • • K1 is the integral gain of the I controller K2 is the proportional gain of the PI controller Ts is the sampling period [s] e(k) is the position error in step k ω(k) is the rotor speed [rad / s] in step k ω(k - 1) is the rotor speed [rad / s] in step k - 1 a(k) is the integral output of the PI controler [rad / s] in step k a(k - 1) is the integral output of the PI controler [rad / s] in step k - 1 θ(k) is the rotor angle [rad] in step k θ(k - 1) is the rotor angle [rad] in step k - 1 AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 23 AMCLIB_AngleTrackObsrv • θ̂(k) is the estimated rotor angle [rad] in step k • θ̂(k - 1) is the estimated rotor angle [rad] in step k - 1 In the fractional arithmetic, Equation 9 on page 23 to Equation 12 on page 23 are as follows: Equation 13 Equation 14 Equation 15 where: • • • • • • • • • • • esc(k) is the scaled position error in step k ωsc(k) is the scaled rotor speed [rad / s] in step k ωsc(k - 1) is the scaled rotor speed [rad / s] in step k - 1 asc(k) is the integral output of the PI controler [rad / s] in step k asc(k - 1) is the integral output of the PI controler [rad / s] in step k - 1 θsc(k) is the scaled rotor angle [rad] in step k θsc(k - 1) is the scaled rotor angle [rad] in step k - 1 θ̂sc(k) is the scaled rotor angle [rad] in step k θ̂sc(k - 1) is the scaled rotor angle [rad] in step k - 1 ωmax is the maximum speed θmax is the maximum rotor angle (typicaly π) 2.2.1 Available versions The function is available in the following versions: • Fractional output - the output is the fractional portion of the result; the result is within the range <-1 ; 1). AMCLIB User's Guide, Rev. 2, 10/2015 24 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail The available versions of the AMCLIB_AngleTrackObsrv function are shown in the following table: Table 2-3. Init versions Function name Init angle AMCLIB_AngleTrackObsrvInit_F16 frac16_t Parameters AMCLIB_ANGLE_TRACK_OBSRV_T_F32 * Result type void The input is a 16-bit fractional value of the angle normalized to the range <-1 ; 1) that represents an angle in (radians) within the range <-π ; π). Table 2-4. Function versions Function name AMCLIB_AngleTrackObsrv_F16 Input type Parameters GMCLIB_2COOR_SINCOS_T_F16 * Result type AMCLIB_ANGLE_TRACK_OB frac16_t SRV_T_F32 * Angle-tracking observer with a two-componenent (sin/cos) 16-bit fractional position input within the range <-1 ; 1). The output from the obsever is a 16-bit fractional position normalized to the range <-1 ; 1) that represents an angle (in radians) within the range <-π ; π). 2.2.2 AMCLIB_ANGLE_TRACK_OBSRV_T_F32 Variable name Input type Description f32Speed frac32_t Estimated speed as the output of the first numerical integrator. The parameter is within the range <-1 ; 1). Controlled by the AMCLIB_AngleTrackObsrv_F16 algorithm; cleared by the AMCLIB_AngleTrackObsrvInit_F16 function. f32A2 frac32_t Output of the second numerical integrator. The parameter is within the range <-1 ; 1). Controlled by the AMCLIB_AngleTrackObsrv_F16 and AMCLIB_AngleTrackObsrvInit_F16 algorithms. f16Theta frac16_t Estimated position as the output of the observer. The parameter is normalized to the range <-1 ; 1) that represents an angle (in radians) within the range <-π ; π). Controlled by the AMCLIB_AngleTrackObsrv_F16 and AMCLIB_AngleTrackObsrvInit_F16 algorithms. f16SinEstim frac16_t Sine of the estimated position as the output of the actual step. Keeps the sine of the position for the next step. The parameter is within the range <-1 ; 1). Controlled by the AMCLIB_AngleTrackObsrv_F16 and AMCLIB_AngleTrackObsrvInit_F16 algorithms. f16CosEstim frac16_t Cosine of the estimated position as the output of the actual step. Keeps the cosine of the position for the next step. The parameter is within the range <-1 ; 1). Controlled by the AMCLIB_AngleTrackObsrv_F16 and AMCLIB_AngleTrackObsrvInit_F16 algorithms. f16K1Gain frac16_t Observer K1 gain is set up according to Equation 13 on page 24 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. Table continues on the next page... AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 25 AMCLIB_AngleTrackObsrv Variable name i16K1GainSh Input type int16_t Description Observer K2 gain shift takes care of keeping the f16K1Gain variable within the fractional range <-1 ; 1). The shift is determined as: The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. f16K2Gain frac16_t Observer K2 gain is set up according to Equation 15 on page 24 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. i16K2GainSh int16_t Observer K2 gain shift takes care of keeping the f16K2Gain variable within the fractional range <-1 ; 1). The shift is determined as: The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. f16A2Gain frac16_t Observer A2 gain for the output position is set up according to Equation 14 on page 24 as: The parameter is a 16-bit fractional type within the range <0 ; 1). Set by the user. i16A2GainSh int16_t Observer A2 gain shift for the position integrator takes care of keeping the f16A2Gain variable within the fractional range <-1 ; 1). The shift is determined as: The parameter is a 16-bit integer type within the range <-15 ; 15>. Set by the user. 2.2.3 Declaration The available AMCLIB_AngleTrackObsrvInit functions have the following declarations: void AMCLIB_AngleTrackObsrvInit_F16(frac16_t f16ThetaInit, AMCLIB_ANGLE_TRACK_OBSRV_T_F32 *psCtrl) The available AMCLIB_AngleTrackObsrv functions have the following declarations: frac16_t AMCLIB_AngleTrackObsrv_F16(const GMCLIB_2COOR_SINCOS_T_F16 *psAnglePos, AMCLIB_ANGLE_TRACK_OBSRV_T_F32 *psCtrl) 2.2.4 Function use The use of the AMCLIB_AngleTrackObsrvInit and AMCLIB_AngleTrackObsrv functions is shown in the following example: AMCLIB User's Guide, Rev. 2, 10/2015 26 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail #include "amclib.h" static AMCLIB_ANGLE_TRACK_OBSRV_T_F32 sAto; static GMCLIB_2COOR_SINCOS_T_F16 sAnglePos; static frac16_t f16PositionEstim, f16PositionInit; void Isr(void); void main(void) { sAto.f16K1Gain sAto.i16K1GainSh sAto.f16K2Gain sAto.i16K2GainSh sAto.f16A2Gain sAto.i16A2GainSh = = = = = = FRAC16(0.6434); -9; FRAC16(0.6801); -2; FRAC16(0.6400); -4; f16PositionInit = FRAC16(0.0); AMCLIB_AngleTrackObsrvInit_F16(f16PositionInit, &sAto); } sAnglePos.f16Sin sAnglePos.f16Cos = FRAC16(0.0); = FRAC16(1.0); /* Periodical function or interrupt */ void Isr(void) { /* Angle tracking observer calculation */ f16PositionEstim = AMCLIB_AngleTrackObsrv_F16(&sAnglePos, &sAto); } 2.3 AMCLIB_PMSMBemfObsrvDQ The AMCLIB_PMSMBemfObsrvDQ function calculates the algorithm of back-electromotive force observer in a rotating reference frame. The method for estimating the rotor position and angular speed is based on the mathematical model of an interior PMSM motor with an extended electro-motive force function, which is realized in an estimated quasi-synchronous reference frame γ-δ as shown in Figure 2-4. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 27 AMCLIB_PMSMBemfObsrvDQ Figure 2-4. The estimated and real rotor dq synchronous reference frames The back-EMF observer detects the generated motor voltages induced by the permanent magnets. A tracking observer uses the back-EMF signals to calculate the position and speed of the rotor. The transformed model is then derived as follows: Equation 16 where: • • • • • • • • RS is the stator resistance LD and LQ are the D-axis and Q-axis inductances Ψm is the back-EMF constant ωr is the angular electrical rotor speed uγ and uδ are the estimated stator voltages iγ and iδ are the estimated stator currents θerror is the error between the actual D-Q frame and the estimated frame position s is the operator of the derivative The block diagram of the observer in the estimated reference frame is shown in Figure 2-5. The observer compensator is substituted by a standard PI controller. As shown in Figure 2-5, the observer model and hence also the PI controller gains in both axes are identical to each other. AMCLIB User's Guide, Rev. 2, 10/2015 28 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail Figure 2-5. Block diagram of proposed Luenberger-type stator current observer acting as state filter for back-EMF The position estimation can now be performed by extracting the θerror term from the model, and adjusting the position of the estimated reference frame to achieve θerror = 0. Because the θerror term is only included in the saliency-based EMF component of both uγ and uδ axis voltage equations, the Luenberger-based disturbance observer is designed to observe the uγ and uδ voltage components. The position displacement information θerror is then obtained from the estimated back-EMFs as follows: Equation 17 The estimated position can be obtained by driving the position of the estimated reference frame to achieve zero displacement θerror = 0. The phase-locked-loop mechanism can be adopted, where the loop compensator ensures correct tracking of the actual rotor flux position by keeping the error signal θerror zeroed, θerror = 0. A perfect match between the actual and estimated motor model parameters is assumed, and then the back-EMF transfer function can be simplified as follows: AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 29 AMCLIB_PMSMBemfObsrvDQ Equation 18 The appropriate dynamic behavior of the back-EMF observer is achieved by the placement of the poles of the stator current observer characteristic polynomial. This general method is based on matching the coefficients of the characteristic polynomial with the coefficients of the general second-order system. The back-EMF observer is a Luenberger-type observer with a motor model, which is implemented using the backward Euler transformation as follows: Equation 19 where: • • • • • • • i(k) = [iγ, iδ] is the stator current vector in the actual step i(k - 1) = [iγ, iδ] is the stator current vector in the previous step u(k) = [uγ, uδ] is the stator voltage vector in the actual step e(k) = [eγ, eδ] is the stator back-EMF voltage vector in the actual step i'(k) = [iγ, -iδ] is the complementary stator current vector in the actual step ωe(k) is the electrical angular speed in the actual step TS is the sampling time [s] This equation is transformed into the fractional arithmetic as follows: Equation 20 where: • • • • • • • • • • isc(k) = [iγ, iδ] is the scaled stator current vector in the actual step isc(k - 1) = [iγ, iδ] is the scaled stator current vector in the previous step usc(k) = [uγ, uδ] is the scaled stator voltage vector in the actual step esc(k) = [eγ, eδ] is the scaled stator back-EMF voltage vector in the actual step i'sc(k) = [iγ, -iδ] is the scaled complementary stator current vector in the actual step ωesc(k) is the scaled electrical angular speed in the actual step imax is the maximum current [A] emax is the maximum back-EMF voltage [V] umax is the maximum stator voltage [V] ωmax is the maximum electrical angular speed in [rad / s] AMCLIB User's Guide, Rev. 2, 10/2015 30 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail If the Luenberger-type stator current observer is properly designed in the stationary reference frame, the back-EMF can be estimated as a disturbance produced by the observer controller. However, this is only valid when the back-EMF term is not included in the observer model. The observer is a closed-loop current observer, therefore it acts as a state filter for the back-EMF term. The estimate of the extended EMF term can be derived from Equation 18 on page 30 as follows: Equation 21 The observer controller can be designed by comparing the closed-loop characteristic polynomial with that of a standard second-order system as follows: Equation 22 where: • • • • ω0 is the natural frequency of the closed-loop system (loop bandwith) ξ is the loop attenuation KP is the proporional gain kI is the integral gain 2.3.1 Available versions This function is available in the following versions: • Fractional output - the output is the fractional portion of the result; the result is within the range <-1 ; 1). The parameters use the accumulator types. • Accumulator output with floating-point inputs - the output is the accumulator result; the result is within the range <-1 ; 1). The inputs are 32-bit single precision floatingpoint values. The available versions of the AMCLIB_PMSMBemfObsrvDQ function are shown in the following table: Table 2-5. Init versions Function name AMCLIB_PMSMBemfObsrvDQInit_F16 Parameters AMCLIB_BEMF_OBSRV_DQ_T_A32 * Result type void Initialization does not have any input. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 31 AMCLIB_PMSMBemfObsrvDQ Table 2-6. Function versions Function name Input/output type Input AMCLIB_PMSMBemfObsrvDQ_F16 Result type GMCLIB_2COOR_DQ_T_F16 * frac16_t GMCLIB_2COOR_DQ_T_F16 * frac16_t Parameters AMCLIB_BEMF_OBSRV_DQ_T_A32 * Back-EMF observer with a 16-bit fractional input D-Q current and voltage, and a 16-bit electrical speed. All are within the range <-1 ; 1). 2.3.2 AMCLIB_BEMF_OBSRV_DQ_T_A32 type description Variable name Data type Description sEObsrv GMCLIB_2COOR_DQ_T_ Estimated back-EMF voltage structure. F32 sIObsrv GMCLIB_2COOR_DQ_T_ Estimated current structure. F32 sCtrl f32ID_1 frac32_t State variable in the alpha part of the observer, integral part at step k - 1. The variable is within the range <-1 ; 1). f32IQ_1 frac32_t State variable in the beta part of the observer, integral part at step k - 1. The variable is within the range <-1 ; 1). a32PGain acc32_t The observer proportional gain is set up according to Equation 22 on page 31 as: The parameter is within the range <0 ; 65536.0). Set by the user. a32IGain acc32_t The observer integral gain is set up according to Equation 22 on page 31 as: The parameter is within the range <0 ; 65536.0). Set by the user. a32IGain acc32_t The current coefficient gain is set up according to Equation 20 on page 30 as: The parameter is within the range <0 ; 65536.0). Set by the user. a32UGain acc32_t The voltage coefficient gain is set up according to Equation 20 on page 30 as: Table continues on the next page... AMCLIB User's Guide, Rev. 2, 10/2015 32 Freescale Semiconductor, Inc. Chapter 2 Algorithms in detail Variable name Data type Description The parameter is within the range <0 ; 65536.0). Set by the user. a32WIGain acc32_t The angular speed coefficient gain is set up according to Equation 20 on page 30 as: The parameter is within the range <0 ; 65536.0). Set by the user. a32EGain acc32_t The back-EMF coefficient gain is set up according to Equation 20 on page 30 as: The parameter is within the range <0 ; 65536.0). Set by the user. f16Error frac16_t Output - estimated phase error between a real D / Q frame system and an estimated D / Q reference system. The error is within the range <-1 ; 1). 2.3.3 Declaration The available AMCLIB_PMSMBemfObsrvDQInit functions have the following declarations: void AMCLIB_PMSMBemfObsrvDQInit_F16(AMCLIB_BEMF_OBSRV_DQ_T_A32 *psCtrl) The available AMCLIB_PMSMBemfObsrvDQ functions have the following declarations: frac16_t AMCLIB_PMSMBemfObsrvDQ_F16(const GMCLIB_2COOR_DQ_T_F16 *psIDQ, const GMCLIB_2COOR_DQ_T_F16 *psUDQ, frac16_t f16Speed, AMCLIB_BEMF_OBSRV_DQ_T_A32 *psCtrl) 2.3.4 Function use The use of the AMCLIB_PMSMBemfObsrvDQ function is shown in the following example: #include "amclib.h" static GMCLIB_2COOR_DQ_T_F16 sIdq, sUdq; static AMCLIB_BEMF_OBSRV_DQ_T_A32 sBemfObsrv; static frac16_t f16Speed, f16Error; void Isr(void); void main (void) AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 33 AMCLIB_PMSMBemfObsrvDQ { sBemfObsrv.sCtrl.a32PGain= ACC32(1.697); sBemfObsrv.sCtrl.a32IGain= ACC32(0.134); sBemfObsrv.a32IGain = ACC32(0.986); sBemfObsrv.a32UGain = ACC32(0.170); sBemfObsrv.a32WIGain= ACC32(0.110); sBemfObsrv.a32EGain = ACC32(0.116); /* Initialization of the observer's structure */ AMCLIB_PMSMBemfObsrvDQInit_F16(&sBemfObsrv); } sIdq.f16D sIdq.f16Q sUdq.f16D sUdq.f16Q = = = = FRAC16(0.05); FRAC16(0.1); FRAC16(0.2); FRAC16(-0.1); /* Periodical function or interrupt */ void Isr(void) { /* BEMF Observer calculation */ f16Error = AMCLIB_PMSMBemfObsrvDQ_F16(&sIdq, &sUdq, f16Speed, &sBemfObsrv); } AMCLIB User's Guide, Rev. 2, 10/2015 34 Freescale Semiconductor, Inc. Appendix A Library types A.1 bool_t The bool_t type is a logical 16-bit type. It is able to store the boolean variables with two states: TRUE (1) or FALSE (0). Its definition is as follows: typedef unsigned short bool_t; The following figure shows the way in which the data is stored by this type: Table A-1. Data storage 15 14 13 12 11 10 9 Value TRUE FALSE 8 7 6 5 4 3 2 1 Logi cal Unused 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 To store a logical value as bool_t, use the FALSE or TRUE macros. A.2 uint8_t The uint8_t type is an unsigned 8-bit integer type. It is able to store the variables within the range <0 ; 255>. Its definition is as follows: typedef unsigned char int8_t; The following figure shows the way in which the data is stored by this type: AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 35 uint16_t Table A-2. Data storage 7 6 5 4 Value 2 1 0 1 1 1 1 1 1 0 0 1 1 Integer 1 255 3 1 1 1 F 0 11 0 F 0 0 1 0 0 0 124 1 B 1 1 1 1 7 1 159 0 C 0 1 1 1 9 F A.3 uint16_t The uint16_t type is an unsigned 16-bit integer type. It is able to store the variables within the range <0 ; 65535>. Its definition is as follows: typedef unsigned short uint16_t; The following figure shows the way in which the data is stored by this type: Table A-3. Data storage 15 14 13 12 11 10 9 8 Value 65535 5 15518 40768 7 6 5 4 3 2 1 0 1 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 Integer 1 1 0 0 1 1 1 1 0 0 0 0 F 0 1 0 1 0 0 0 0 F 1 1 1 1 1 0 1 0 1 0 5 0 1 1 1 9 1 F F 0 C 0 9 1 0 3 1 1 F 0 0 1 1 0 1 E 0 4 0 0 0 0 A.4 uint32_t AMCLIB User's Guide, Rev. 2, 10/2015 36 Freescale Semiconductor, Inc. Appendix A Library types The uint32_t type is an unsigned 32-bit integer type. It is able to store the variables within the range <0 ; 4294967295>. Its definition is as follows: typedef unsigned long uint32_t; The following figure shows the way in which the data is stored by this type: Table A-4. Data storage 31 24 23 16 15 Value 8 7 0 Integer 4294967295 F F F F F F F F 2147483648 8 0 0 0 0 0 0 0 55977296 0 3 5 6 2 5 5 0 3451051828 C D B 2 D F 3 4 A.5 int8_t The int8_t type is a signed 8-bit integer type. It is able to store the variables within the range <-128 ; 127>. Its definition is as follows: typedef char int8_t; The following figure shows the way in which the data is stored by this type: Table A-5. Data storage 7 Value 127 -128 60 -97 6 5 4 Sign 0 3 2 1 1 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 1 3 1 1 F 8 0 0 Integer 7 1 1 0 C 0 1 1 9 1 F AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 37 int16_t A.6 int16_t The int16_t type is a signed 16-bit integer type. It is able to store the variables within the range <-32768 ; 32767>. Its definition is as follows: typedef short int16_t; The following figure shows the way in which the data is stored by this type: Table A-6. Data storage 15 Value 32767 -32768 15518 -24768 14 13 12 11 10 9 8 Sign 7 6 5 4 3 2 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 Integer 0 1 1 1 1 1 7 1 0 0 0 0 0 0 1 0 1 F 0 0 0 0 0 1 1 1 3 1 1 F 8 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 C 9 F 0 0 1 1 1 9 1 1 0 1 F E 0 0 0 0 4 0 A.7 int32_t The int32_t type is a signed 32-bit integer type. It is able to store the variables within the range <-2147483648 ; 2147483647>. Its definition is as follows: typedef long int32_t; The following figure shows the way in which the data is stored by this type: Table A-7. Data storage 31 Value 24 23 16 15 S 8 7 0 Integer 2147483647 7 F F F F F F F -2147483648 8 0 0 0 0 0 0 0 55977296 0 3 5 6 2 5 5 0 -843915468 C D B 2 D F 3 4 AMCLIB User's Guide, Rev. 2, 10/2015 38 Freescale Semiconductor, Inc. Appendix A Library types A.8 frac8_t The frac8_t type is a signed 8-bit fractional type. It is able to store the variables within the range <-1 ; 1). Its definition is as follows: typedef char frac8_t; The following figure shows the way in which the data is stored by this type: Table A-8. Data storage 7 Value 0.99219 -1.0 0.46875 -0.75781 6 5 4 3 Sign 2 1 0 1 1 1 0 0 0 0 1 1 Fractional 0 1 1 1 1 7 1 0 F 0 0 0 0 8 0 0 0 1 1 1 1 3 1 0 C 0 1 1 1 9 F To store a real number as frac8_t, use the FRAC8 macro. A.9 frac16_t The frac16_t type is a signed 16-bit fractional type. It is able to store the variables within the range <-1 ; 1). Its definition is as follows: typedef short frac16_t; The following figure shows the way in which the data is stored by this type: Table A-9. Data storage 15 Value 0.99997 -1.0 14 13 12 11 10 9 8 Sign 0 6 5 4 3 2 1 0 1 1 1 1 1 1 1 0 0 Fractional 1 1 1 1 1 7 1 7 0 1 1 1 F 0 0 0 0 F 0 0 0 0 F 0 0 0 0 Table continues on the next page... AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 39 frac32_t Table A-9. Data storage (continued) 8 0.47357 -0.75586 0 0 0 1 1 1 1 3 1 0 0 0 0 1 0 C 0 1 1 1 9 0 0 1 1 1 9 1 1 0 1 F 1 0 0 0 E 0 0 0 0 4 0 To store a real number as frac16_t, use the FRAC16 macro. A.10 frac32_t The frac32_t type is a signed 32-bit fractional type. It is able to store the variables within the range <-1 ; 1). Its definition is as follows: typedef long frac32_t; The following figure shows the way in which the data is stored by this type: Table A-10. Data storage 31 Value 24 23 16 15 S 8 7 0 Fractional 0.9999999995 7 F F F F F F F -1.0 8 0 0 0 0 0 0 0 0.02606645970 0 3 5 6 2 5 5 0 -0.3929787632 C D B 2 D F 3 4 To store a real number as frac32_t, use the FRAC32 macro. A.11 acc16_t The acc16_t type is a signed 16-bit fractional type. It is able to store the variables within the range <-256 ; 256). Its definition is as follows: typedef short acc16_t; The following figure shows the way in which the data is stored by this type: AMCLIB User's Guide, Rev. 2, 10/2015 40 Freescale Semiconductor, Inc. Appendix A Library types Table A-11. Data storage 15 Value 255.9921875 -256.0 1.0 -1.0 13.7890625 -89.71875 14 13 12 Sign 11 10 9 8 7 6 5 4 Integer 0 1 1 1 1 1 0 0 0 0 8 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 D 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 8 1 0 1 8 1 1 1 0 0 1 1 6 0 0 F 0 F 0 1 0 0 1 0 1 1 0 1 1 F 0 0 F 0 1 0 0 1 1 F 0 2 Fractional 1 7 3 0 1 0 0 1 E 1 1 0 0 3 5 1 0 0 1 2 4 To store a real number as acc16_t, use the ACC16 macro. A.12 acc32_t The acc32_t type is a signed 32-bit accumulator type. It is able to store the variables within the range <-65536 ; 65536). Its definition is as follows: typedef long acc32_t; The following figure shows the way in which the data is stored by this type: Table A-12. Data storage 31 Value 24 23 S 16 15 8 7 Integer 0 Fractional 65535.999969 7 F F F F F F F -65536.0 8 0 0 0 0 0 0 0 1.0 0 0 0 0 8 0 0 0 -1.0 F F F F 8 0 0 0 23.789734 0 0 0 B E 5 1 6 -1171.306793 F D B 6 5 8 B C To store a real number as acc32_t, use the ACC32 macro. AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 41 GMCLIB_3COOR_T_F16 A.13 GMCLIB_3COOR_T_F16 The GMCLIB_3COOR_T_F16 structure type corresponds to the three-phase stationary coordinate system, based on the A, B, and C components. Each member is of the frac16_t data type. The structure definition is as follows: typedef struct { frac16_t f16A; frac16_t f16B; frac16_t f16C; } GMCLIB_3COOR_T_F16; The structure description is as follows: Table A-13. GMCLIB_3COOR_T_F16 members description Type Name Description frac16_t f16A A component; 16-bit fractional type frac16_t f16B B component; 16-bit fractional type frac16_t f16C C component; 16-bit fractional type A.14 GMCLIB_2COOR_ALBE_T_F16 The GMCLIB_2COOR_ALBE_T_F16 structure type corresponds to the two-phase stationary coordinate system, based on the Alpha and Beta orthogonal components. Each member is of the frac16_t data type. The structure definition is as follows: typedef struct { frac16_t f16Alpha; frac16_t f16Beta; } GMCLIB_2COOR_ALBE_T_F16; The structure description is as follows: Table A-14. GMCLIB_2COOR_ALBE_T_F16 members description Type Name Description frac16_t f16Apha α-component; 16-bit fractional type frac16_t f16Beta β-component; 16-bit fractional type AMCLIB User's Guide, Rev. 2, 10/2015 42 Freescale Semiconductor, Inc. Appendix A Library types A.15 GMCLIB_2COOR_DQ_T_F16 The GMCLIB_2COOR_DQ_T_F16 structure type corresponds to the two-phase rotating coordinate system, based on the D and Q orthogonal components. Each member is of the frac16_t data type. The structure definition is as follows: typedef struct { frac16_t f16D; frac16_t f16Q; } GMCLIB_2COOR_DQ_T_F16; The structure description is as follows: Table A-15. GMCLIB_2COOR_DQ_T_F16 members description Type Name Description frac16_t f16D D-component; 16-bit fractional type frac16_t f16Q Q-component; 16-bit fractional type A.16 GMCLIB_2COOR_DQ_T_F32 The GMCLIB_2COOR_DQ_T_F32 structure type corresponds to the two-phase rotating coordinate system, based on the D and Q orthogonal components. Each member is of the frac32_t data type. The structure definition is as follows: typedef struct { frac32_t f32D; frac32_t f32Q; } GMCLIB_2COOR_DQ_T_F32; The structure description is as follows: Table A-16. GMCLIB_2COOR_DQ_T_F32 members description Type Name Description frac32_t f32D D-component; 32-bit fractional type frac32_t f32Q Q-component; 32-bit fractional type A.17 GMCLIB_2COOR_SINCOS_T_F16 AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 43 FALSE The GMCLIB_2COOR_SINCOS_T_F16 structure type corresponds to the two-phase coordinate system, based on the Sin and Cos components of a certain angle. Each member is of the frac16_t data type. The structure definition is as follows: typedef struct { frac16_t f16Sin; frac16_t f16Cos; } GMCLIB_2COOR_SINCOS_T_F16; The structure description is as follows: Table A-17. GMCLIB_2COOR_SINCOS_T_F16 members description Type Name Description frac16_t f16Sin Sin component; 16-bit fractional type frac16_t f16Cos Cos component; 16-bit fractional type A.18 FALSE The FALSE macro serves to write a correct value standing for the logical FALSE value of the bool_t type. Its definition is as follows: #define FALSE ((bool_t)0) #include "mlib.h" static bool_t bVal; void main(void) { bVal = FALSE; } /* bVal = FALSE */ A.19 TRUE The TRUE macro serves to write a correct value standing for the logical TRUE value of the bool_t type. Its definition is as follows: #define TRUE ((bool_t)1) #include "mlib.h" static bool_t bVal; AMCLIB User's Guide, Rev. 2, 10/2015 44 Freescale Semiconductor, Inc. Appendix A Library types void main(void) { bVal = TRUE; } /* bVal = TRUE */ A.20 FRAC8 The FRAC8 macro serves to convert a real number to the frac8_t type. Its definition is as follows: #define FRAC8(x) ((frac8_t)((x) < 0.9921875 ? ((x) >= -1 ? (x)*0x80 : 0x80) : 0x7F)) The input is multiplied by 128 (=27). The output is limited to the range <0x80 ; 0x7F>, which corresponds to <-1.0 ; 1.0-2-7>. #include "mlib.h" static frac8_t f8Val; void main(void) { f8Val = FRAC8(0.187); } /* f8Val = 0.187 */ A.21 FRAC16 The FRAC16 macro serves to convert a real number to the frac16_t type. Its definition is as follows: #define FRAC16(x) ((frac16_t)((x) < 0.999969482421875 ? ((x) >= -1 ? (x)*0x8000 : 0x8000) : 0x7FFF)) The input is multiplied by 32768 (=215). The output is limited to the range <0x8000 ; 0x7FFF>, which corresponds to <-1.0 ; 1.0-2-15>. #include "mlib.h" static frac16_t f16Val; void main(void) { f16Val = FRAC16(0.736); } /* f16Val = 0.736 */ AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 45 FRAC32 A.22 FRAC32 The FRAC32 macro serves to convert a real number to the frac32_t type. Its definition is as follows: #define FRAC32(x) ((frac32_t)((x) < 1 ? ((x) >= -1 ? (x)*0x80000000 : 0x80000000) : 0x7FFFFFFF)) The input is multiplied by 2147483648 (=231). The output is limited to the range <0x80000000 ; 0x7FFFFFFF>, which corresponds to <-1.0 ; 1.0-2-31>. #include "mlib.h" static frac32_t f32Val; void main(void) { f32Val = FRAC32(-0.1735667); } /* f32Val = -0.1735667 */ A.23 ACC16 The ACC16 macro serves to convert a real number to the acc16_t type. Its definition is as follows: #define ACC16(x) ((acc16_t)((x) < 255.9921875 ? ((x) >= -256 ? (x)*0x80 : 0x8000) : 0x7FFF)) The input is multiplied by 128 (=27). The output is limited to the range <0x8000 ; 0x7FFF> that corresponds to <-256.0 ; 255.9921875>. #include "mlib.h" static acc16_t a16Val; void main(void) { a16Val = ACC16(19.45627); } /* a16Val = 19.45627 */ A.24 ACC32 The ACC32 macro serves to convert a real number to the acc32_t type. Its definition is as follows: AMCLIB User's Guide, Rev. 2, 10/2015 46 Freescale Semiconductor, Inc. #define ACC32(x) ((acc32_t)((x) < 65535.999969482421875 ? ((x) >= -65536 ? (x)*0x8000 : 0x80000000) : 0x7FFFFFFF)) The input is multiplied by 32768 (=215). The output is limited to the range <0x80000000 ; 0x7FFFFFFF>, which corresponds to <-65536.0 ; 65536.0-2-15>. #include "mlib.h" static acc32_t a32Val; void main(void) { a32Val = ACC32(-13.654437); } /* a32Val = -13.654437 */ AMCLIB User's Guide, Rev. 2, 10/2015 Freescale Semiconductor, Inc. 47 AMCLIB User's Guide, Rev. 2, 10/2015 48 Freescale Semiconductor, Inc. How to Reach Us: Home Page: freescale.com Web Support: freescale.com/support Information in this document is provided solely to enable system and software implementers to use Freescale products. There are no express or implied copyright licenses granted hereunder to design or fabricate any integrated circuits based on the information in this document. Freescale reserves the right to make changes without further notice to any products herein. Freescale makes no warranty, representation, or guarantee regarding the suitability of its products for any particular purpose, nor does Freescale assume any liability arising out of the application or use of any product or circuit, and specifically disclaims any and all liability, including without limitation consequential or incidental damages. “Typical” parameters that may be provided in Freescale data sheets and/or specifications can and do vary in different applications, and actual performance may vary over time. All operating parameters, including “typicals,” must be validated for each customer application by customer's technical experts. Freescale does not convey any license under its patent rights nor the rights of others. Freescale sells products pursuant to standard terms and conditions of sale, which can be found at the following address: www.freescale.com/salestermsandconditions. Freescale and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © 2015 Freescale Semiconductor, Inc. Document Number DSP56800EAMCLIBUG Revision 2, 10/2015

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