SinCos Embedded Optimized

Implement sine and cosine functions

Since R2024b

• 

Libraries:
Motor Control Blockset / Controls / Math Transforms

Description

The SinCos Embedded Optimized block implements sine and cosine functions using the specified position or phase input signal, based on the selected approximation method. The block also allows you to implement sine and cosine functions using optimized computations according to the target hardware, without the need to specify the approximation method.

The block supports CORDIC, TI IQMATH, and lookup-based approximation methods to compute the sine and cosine signals. The following table lists the supported data types, θ_e input units, as well as use cases for each approximation method.

Approximation Method	Data Types Supported	θe Input Units Supported	When to Use This Method
None	Floating point	Per-unit (0 to 1) Radians (0 to 2π) Degrees (0 to 360)	You want to use the default Taylor series algorithm.
CORDIC	Floating point and fixed point	Radians (-π to π)	You want a fast, approximate iterative calculation.
Lookup	Floating point and fixed point	Per-unit (0 to 1) Radians (0 to 2π) Degrees (0 to 360)	You want a fast, approximate lookup table implementation.
Texas Instruments® IQMATH	Fixed point (TI IQMATH does not support 16-bit fixed point data type)	Per-unit (0 to 1)	You cannot manually select this value. The block automatically selects this value, when you optimize the block for a Texas Instruments hardware.

If you choose the optimization option, the block selects an optimized approximation method for the hardware board that you select in the Hardware Implementation tab of the Configuration Parameters dialog box for the Simulink^® model containing this block.

For example, the block automatically selects the Texas Instruments IQ math approximation method, if you select any Texas Instruments (TI) hardware target.

CORDIC Approximation Method

CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations. For more information, see CORDIC. The block input has further requirements.

For more information about selecting the CORDIC approximation method, see Approximation method.

This table summarizes what happens for an invalid input.

Block Usage	Effect of Invalid Input
Simulation modes	An error appears.
Generated code	Undefined behavior occurs. Avoid relying on undefined behavior for generated code.

Lookup Approximation Method

The block supports the lookup table approach. This approach results in optimized code-execution when used with the model settings and configuration adopted by the examples shipped in Motor Control Blockset™. You can specify the number of lookup table points in the Number of data points for lookup table parameter.

This figure shows the input position along with the sine and cosine output signals that the block generates using the lookup approximation method:

For more information about selecting the lookup approximation method, see Approximation method.

Use Optimization

For the option Optimized for selected angle units and data type, the block applies the approximation method based on the values specified for target platform, Theta data type, and Theta units, as shown in this table:

Required input			Approximation method applied
Target platform (based on selection for the Hardware board parameter)	Theta data type	Theta units
Texas Instruments (TI)	Floating point	Rad / Per-unit / Deg	None
	Fixed-point	Per-unit	TI IQMATH
STM32TM	Floating point	Rad / Per-unit / Deg	None
	Fixed-point	Rad / Per-unit / Deg	Lookup
ARM® Cortex®	Floating point	Rad / Per-unit / Deg	None
	Fixed-point	Rad / Per-unit / Deg	Lookup
Other targets	Floating point	Rad / Per-unit / Deg	Lookup
	Fixed-point	Rad / Per-unit / Deg	Lookup

For the option Best possible optimization, the block applies the approximation method, theta data type, and theta units, based on the target platform, as shown this table:

Required input	Read-only parameters that are applied
Target platform (based on selection for the Hardware board parameter)	Approximation method	Theta data type	Theta input
TI	None	Floating point	Rad / Per-unit / Deg
STM32	None	Floating point	Rad / Per-unit / Deg
ARM Cortex	None	Floating point	Rad / Per-unit / Deg
Others	Lookup	Floating point or Fixed-point	Rad / Per-unit / Deg

Examples

Field-Oriented Control of Induction Motor Using Speed Sensor

Implements the field-oriented control (FOC) technique to control the speed of a three-phase AC induction motor (ACIM). The FOC algorithm requires rotor speed feedback, which is obtained in this example by using a quadrature encoder sensor. For details about FOC, see Field-Oriented Control.

• Open Model

Field-Weakening Control (with MTPA) of PMSM

Implements the field-oriented control (FOC) technique to control the torque and speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a quadrature encoder sensor. For details about FOC, see Field-Oriented Control.

• Open Model

Field-Oriented Control of PMSM Using Hall Sensor

Implements the field-oriented control (FOC) technique to control the speed of a three-phase permanent magnet synchronous motor (PMSM). The FOC algorithm requires rotor position feedback, which is obtained by a Hall sensor. For details about FOC, see Field-Oriented Control.

• Open Model

Ports

Input

θ_e — Reference voltage position

scalar

Position or phase value of the reference voltage signal specified as scalar in either per-unit, radians, or degrees.

Data Types: single | double | fixed point

Output

sin — Sine voltage waveform

scalar

Sine waveform output with a frequency that is identical to the position or phase signal (θe) frequency.

Data Types: single | double | fixed point

cos — Cosine voltage waveform

scalar

Cosine waveform output with a frequency that is identical to the position or phase signal (θe) frequency.

Data Types: single | double | fixed point

Parameters

Adjust computation for selected target — Choose between applying an approximation method or applying an optimized computation

Disabled (default) | Optimized for selected angle units and data type | Best possible optimization

Use this parameter to choose between applying an approximation method (by disabling automatic computation adjustment) or applying optimized computation.

• Disabled — specify the Approximation method and the values for other related parameters

• Optimized for selected angle units and data type — the block applies the approximation method that is optimized for execution time based on the selected hardware, by using the values specified for Theta data type and Theta units

• Best possible optimization — the block applies the approximation method that is optimized for execution time based on the selected hardware.

Approximation method — Approximation method for computing sine and cosine signals

Lookup (default) | None | CORDIC | TI IQMATH

Specify the type of approximation for computing the sine and cosine output signals. You can select one of these values.

• None — Select this value if you do not want to use any approximation.

• CORDIC — Select this value if you want to use the CORDIC approximation method.

• Lookup — Select this value if you want to use the lookup approximation method.

• TI IQMATH — Block selects this value if you are using a Texas Instruments hardware target.

Dependencies

You cannot manually select the value TI IQMATH. The block automatically selects this value, when both these two conditions are satisfied:

• You select any Texas Instruments hardware target in the Hardware board parameter available in the Hardware Implementation tab of the Configuration Parameters dialog box for the Simulink model containing this block.

  

• You select the Optimize for selected angle units and data type option for Adjust computation for selected target parameter.

Theta units — Unit of θe

Per-unit (default) | Radians | Degrees

Unit of the input reference voltage position.

Dependencies

To enable this parameter, set the Adjust computation for selected target parameter to Disabled, and set the Approximation method parameter to either None or Lookup.

Number of data points for lookup table — Size of lookup table array

1024 (default) | scalar

Size of the lookup table array. This parameter accepts a value between 125 and 4095.

Note

Based on the value you enter in this parameter, the block uses a value nearest to (125*n)+2. The block performs this approximation to optimize the computation in the hardware.

Dependencies

To enable this parameter, set the Adjust computation for selected target parameter to Disabled, and set the Approximation method parameter to Lookup.

Table data type — Data type of lookup table array

Inherit: Inherit via input (default) | double | single | fixdt(1,16,0) | <data type expression>

Data type for the lookup table array, specified as:

• Inherit: Inherit via input

• double

• single

• fixdt(1,16,0)

• <data type expression>

For more information on setting data types, see Control Data Types of Signals.

Dependencies

To enable this parameter, set the Adjust computation for selected target parameter to Disabled, and set the Approximation method parameter to Lookup.

Number of iterations — Number of iterations for CORDIC algorithm

11 (default) | positive integer, less than or equal to word length of fixed-point input

Specify the number of iterations to perform the CORDIC algorithm. The default value is 11.

• When the block input uses a floating-point data type, the number of iterations can be a positive integer.

• When the block input is a fixed-point data type, the number of iterations cannot exceed the word length.

  For example, if the block input is fixdt(1,16,15), the word length is 16. In this case, the number of iterations cannot exceed 16.

Dependencies

To enable this parameter, set the Adjust computation for selected target parameter to Disabled, and set the Approximation method parameter to CORDIC.

Theta data type — Data type of lookup table array

fixdt([],16,0) (default) | double | single | <data type expression>

Data type for the lookup table array, specified as:

• double

• single

• fixdt([],16,0)

• <data type expression>

For more information on setting data types, see Control Data Types of Signals.

Dependencies

To enable this parameter, configure the block to use the TI IQMATH approximation method by:

• Selecting any Texas Instruments hardware target in the Hardware board parameter available in the Hardware Implementation tab of the Configuration Parameters dialog box for the Simulink model containing this block.

• Selecting the Optimize for selected angle units and data type option for Adjust computation for selected target parameter.

More About

CORDIC

CORDIC is an acronym for coordinate rotation digital computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see References). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

Increasing the number of CORDIC iterations can produce more accurate results, but doing so increases the expense of the computation and adds latency.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced in R2024b