Motor Mechanical Controlled

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Description

The Motor Mechanical Controlled component is a DC motor model designed for scenarios where the mechanical dynamics are solved externally. The user provides the motor speed and load torque as inputs, and the motor calculates the resulting electrical characteristics, including current draw, voltage drop, and back-EMF. This approach is useful when the motor is coupled to an external physics solver or when the mechanical behavior is predetermined.

This component inherits from Motor Base, which provides the common electrical modeling including armature resistance, armature inductance (via companion model), and back-EMF calculations.

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Example Use Cases

• External Physics Coupling: Interface with external dynamics solvers where mechanical motion is computed separately from the electrical system.
• Hardware-in-the-Loop Testing: Simulate the electrical impact of a motor when speed profiles are provided from external sources or test equipment.
• Predefined Motion Profiles: Analyze power consumption for motors following known speed trajectories.

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Module Implementation

Speed and Torque Inputs

The motor accepts two primary inputs from the external solver:

• Speed Input ($\omega$): The rotational speed of the motor shaft in rad/s.
• Load Torque (${\tau }_L$): The mechanical load torque applied to the motor shaft in Nm.

A convenience property is also available for specifying speed in RPM:

$${\omega }_{\mathrm{RPM}}=\omega \cdot \frac{60}{2\pi }$$

Back-EMF Calculation

The back-EMF voltage is computed based on the externally provided speed input:

$$V_{\mathrm{EMF}}=K_e\cdot \omega$$

where $K_e$ is the back-EMF constant (V/(rad/s)).

Armature Current

The armature current is determined by the motor’s electrical circuit, accounting for the applied voltage, back-EMF, and armature resistance:

$$I_a=\frac{V-V_{\mathrm{EMF}}}{R_a}$$

where $V$ is the terminal voltage, $V_{\mathrm{EMF}}$ is the back-EMF, and $R_a$ is the armature resistance. For transient behavior, the armature inductance is incorporated using a companion circuit model.

Electromagnetic Torque

The electromagnetic torque produced by the motor is:

$${\tau }_e=K_t\cdot I_a$$

where $K_t$ is the torque constant (Nm/A). For an ideal DC motor, $K_t=K_e$.

Shaft Torque

The shaft torque available after accounting for viscous friction losses is:

$${\tau }_s={\tau }_e-B\cdot \omega$$

where $B$ is the viscous friction coefficient.

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Assumptions/Limitations

• The mechanical dynamics are not solved internally; the motor relies entirely on externally provided speed and load torque values.
• The electrical time constant of the armature inductance is modeled using a companion circuit approach for numerical stability.
• Friction is modeled as a simple viscous term; Coulomb or static friction effects are not included.