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.

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	θ_e 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.

The block enables you to automatically select an optimized approximation method for the hardware board that you select in the Hardware Implementation tab of the Configuration Parameters dialog 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 hardware target.

CORDIC Approximation Method

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.

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 (FOC).

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 (FOC).

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 (FOC).

Open Model

Ports

Input

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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

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sin — Sine voltage waveform
scalar

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

Data Types: single | double | fixed point

Parameters

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Optimize for selected embedded target hardware — Optimize block for selected hardware
`off` (default) | on

Select this parameter to optimize the block automatically for the embedded target hardware you are using. If you select this parameter, the block automatically selects an approximation method (to compute the sine and cosine signals) that is optimized for your hardware target.

For example, if you select any Texas Instruments hardware target in the Hardware board parameter available in the Hardware Implementation tab of the Configuration Parameters dialog for the Simulink model containing this block, the block automatically sets the Approximation method parameter to TI IQMATH. For more information about the supported approximation methods, see the Approximation method parameter.

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:

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

Theta units — Unit of `θ_e`
`Per-unit` (default) | `Radians` | `Degrees`

Unit of the input reference voltage position.

Dependencies

To enable this parameter, 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 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 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 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 for the Simulink model containing this block.
Selecting the Optimize for selected embedded target hardware parameter.

More About

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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

SinCos Embedded Optimized