Resolver-to-Digital Converter

Resolver-to-digital converter

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Simscape / Electrical / Control / Observers

Description

The Resolver-to-Digital Converter block models a transducer that converts the angular position or velocity of a rotating shaft to an electrical signal. Resolver-to-digital converters are commonly used in harsh, rugged environments, such as in fully electric vehicles.

The converted signal is proportional to the sine or cosine of the shaft angle.

A resolver sensor has one rotor winding with the exciter sine wave that is AC-coupled to two stator windings. The stator windings, a sine coil and a cosine coil, are mechanically positioned 90-degrees out-of-phase. As the rotor spins, the rotor position angle changes with respect to the stator windings. The resulting amplitude-modulated signals must then be gained, demodulated and post processed to extract angle and velocity information ([1] and [2]).

Equations

The block uses a phase-locked loop (PLL) to extract the angle and the velocity of the rotating shaft. The error voltage used by the PI controller is obtained as:

$V_{e} = V_{y} V_{p} \cos (N θ) - V_{x} V_{p} \sin (N θ),$

where:

V_p is the excitation voltage.
V_x is the x voltage for the secondary winding of the resolver.
V_y is the y voltage for the secondary winding of the resolver.
N is the number of pole pairs for the resolver.
θ is the angle.

Therefore, the velocity is obtained as:

$ω = K_{p} V_{e} + K_{i} \int V_{e},$

and the angle is computed from the velocity using:

$\frac{d θ}{d t} = ω .$

Examples

Three-Phase PMSM Traction Drive

Three-Phase PMSM Traction Drive

Control the rotor speed in a permanent magnet synchronous machine (PMSM) based electrical-traction drive. A high-voltage battery feeds the FEM-Parameterized PMSM block through a controlled three-phase converter. A Rotational Friction block provides the load. The position and speed information are obtained by using a high-fidelity resolver. The PMSM controller subsystem includes a cascade control structure which has an outer speed-control loop and two inner current-control loops. During the 0.25 seconds simulation, the rotor speed demand is ramped-up from 0 to 1000 rpm.

Open Model

Ports

Input

Vp — Voltage phase angle
scalar

Simulink signal that corresponds to the voltage phase angle.

Data Types: single | double

Vx — `x`-axis voltage
scalar

Simulink signal that corresponds to the x-axis voltage.

Data Types: single | double

Vy — `y`-axis voltage
scalar

Simulink signal that corresponds to the y-axis voltage.

Data Types: single | double

Output

Velocity — Rotational velocity
scalar

Simulink signal that corresponds to the rotational velocity.

Data Types: single | double

Angle — Rotational angle
scalar

Simulink signal that corresponds to the rotational angle.

Data Types: single | double

Parameters

Number of pole pairs — Pole pairs in the attached machine
`4` (default) | positive scalar integer

Number of pole pairs in the attached machine.

Phase-looked loop proportional gain — PLL proportional gain
`15` (default) | positive scalar

Proportional gain for the phase-locked loop filter. This value determines how aggressively the PLL tracks and locks to the phase angle. Increase this value to more closely track step changes in the phase angle.

Phase-looked loop integral gain — PLL integral gain
`2.5e5` (default) | positive scalar

Integral gain for the phase-locked loop filter. Increase this value to increase the rate at which steady-state error is eliminated in the phase angle. This value also determines how aggressively the PLL tracks and locks to the phase.

Initial position (rad) — Initial phase angle
`0` `rad` (default) | scalar

Initial estimate of the phase angle. If the input signal is a vector, use scalar parameters or use vector parameters that are the same size as the input signal.

Sample time (-1 for inherited) — Block sample time
`-1` (default) | 0 | positive scalar

Time between consecutive block executions. During execution, the block produces outputs and, if appropriate, updates its internal state. For more information, see What Is Sample Time? and Specify Sample Time.

For inherited discrete-time operation, specify -1. For discrete-time operation, specify a positive integer. For continuous-time operation, specify 0.

Note

If this block is in a masked subsystem, or another variant subsystem that allows you to switch between continuous operation or discrete operation, promote the sample time parameter to ensure correct switching between the continuous and discrete implementations of the block. For more information, see Promote Block Parameters on a Mask.

References

[1] Santanu Sarma, V.K. Agrawal, Subramanya Udupa. Software-Based Resolver-to-Digital Conversion Using a DSP. IEEE Transactions on Industrial Electronics, 55, 371-379. February 2008. (https://www.researchgate.net/publication/3219673_Software-Based_Resolver-to-Digital_Conversion_Using_a_DSP)

[2] Ankur Verma, Anand Chellamuthu. Design considerations for resolver-to-digital converters in electric vehicles. Texas Instruments, Analog Applications Journal. 2016.

Extended Capabilities

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

Version History

Introduced in R2019b

See Also

Sinusoidal Measurement (PLL) | Sinusoidal Measurement (PLL, Three-Phase)