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Servomotor - Model brushless motor with closed-loop torque control

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Actuators & Drivers

Description

The Servomotor block represents a brushless motor with closed-loop torque control. This block abstracts the torque-speed behavior of the combined motor and motor driver in order to support system-level simulation where simulation speed is important.

The block allows for the range of torques and speeds that the torque-speed envelope defines. You specify this data in the block dialog box as a set of speed data points and corresponding maximum torque values. The following figure shows a typical torque-speed envelope for a servomotor.

Specify the torque-speed envelope for the forward-direction motoring region (Quadrant 1) only. This region is typically the only one specified by manufacturers. The Servomotor block implements this torque-speed envelope regardless of motor direction or power flow direction, interpreting the x-axis as the absolute value of speed and the y-axis as the absolute value of torque.

The block models the electrical losses as the sum of three terms:

A supply series resistance.
A torque-independent electrical loss, .
A torque-dependent electrical loss , where is the torque and is a constant.

The block produces a positive torque acting from the mechanical C to R ports.

Basic Assumptions and Limitations

This model is based on the following assumptions:

The motor driver tracks a torque demand with a time constant Tc.
Motor speed fluctuations due to mechanical load do not affect the motor torque tracking.

Dialog Box and Parameters

Electrical Torque Tab

Vector of rotational speeds

Rotational speeds for permissible steady-state operation. The default value is [ 0 3.75e+03 7.5e+03 8e+03 ] rpm. To avoid poor performance due to an infinite slope in the torque-speed curve, specify a vector of rotational speeds that does not contain duplicate consecutive values.

Vector of maximum torque values

Maximum torque values for permissible steady-state operation. These values correspond to the speeds in the Vector of rotational speeds in RPM parameter and define the torque-speed envelope for the motor. The default value is [ 0.09 0.08 0.07 0 ] Nm.

Torque Control time constant, Tc

Time constant with which the motor driver tracks a torque demand. The default value is 0.02 s.

Motor and driver overall efficiency (percent)

The block defines overall efficiency as

where:

represents the Torque at which efficiency is measured
represents the Speed at which efficiency is measured
represents the Torque-independent electrical losses
represents the torque-dependent electrical losses.

At initialization, the block solves the efficiency equation for . The block neglects losses associated with the rotor damping.

Speed at which efficiency is measured

Speed that the block uses to calculate torque-dependent electrical losses. The default value is 3.75e+03 rpm.

Torque at which efficiency is measured

Torque that the block uses to calculate torque-dependent electrical losses. The default value is 0.08 Nm.

Torque-independent electrical losses

Fixed electrical loss associated with the driver when the motor current and torque are zero. The default value is zero.

Supply series resistance

The equivalent resistance used in series with the DC supply to model electrical losses that are proportional to the driver supply current. The block assumes that the DC supply current is approximately constant under constant load conditions. The default value is 0 Ω.

Mechanical Tab

Rotor inertia: Rotor resistance to change in motor motion. The default value is 5e-06 kg*m². The value can be zero.
Rotor damping: Rotor damping. The default value is 1e-05 N*m/(rad/s). The value can be zero.
Initial rotor speed: Rotor speed at the start of the simulation. The default value is 0 rpm.