Smaller than mechanical time constant
nrmature control DC server motor is a single time constant feedback control mechanism as la =0

Electrical Time-Constant of an Armature-Controlled DC Servomotor

The electrical time-constant of an armature-controlled DC servomotor refers to the time it takes for the motor's armature winding to reach approximately 63.2% of its final value when subjected to a step change in voltage. This time-constant is an important parameter that characterizes the dynamic response of the motor.

Relationship with Mechanical Time-Constant

The mechanical time-constant of a DC servomotor, on the other hand, refers to the time it takes for the motor's mechanical system to reach approximately 63.2% of its final value when subjected to a step change in torque. It characterizes the inertia and mechanical damping of the motor.

The electrical and mechanical time-constants are related because the armature current, which is directly affected by the electrical time-constant, generates the torque that drives the mechanical system. Therefore, the electrical time-constant influences the speed at which the mechanical system responds to changes in the armature current.

Explanation of the Correct Answer

The correct answer, option 'B', states that the electrical time-constant of an armature-controlled DC servomotor is smaller than the mechanical time-constant. This is generally true for most DC servomotors, and here's why:

1. Electrical Processes: The armature-controlled DC servomotor operates based on electrical processes. The electrical time-constant is primarily determined by the resistance and inductance of the armature winding. These electrical components have relatively fast response times compared to the mechanical system.

2. Mechanical Processes: The mechanical processes in a DC servomotor, such as the inertia and damping, are inherently slower compared to the electrical processes. The mechanical time-constant depends on the moment of inertia of the motor's rotor, the frictional forces, and the mechanical load connected to the motor.

3. Armature Inductance: The inductance of the armature winding introduces a delay in the response of the motor's armature current to changes in the applied voltage. This delay contributes to the smaller electrical time-constant compared to the mechanical time-constant.

4. Feedback Control: In armature-controlled DC servomotors, a feedback control system is typically employed to regulate the motor's speed or position. This control system further influences the time-constants by adjusting the voltage applied to the motor based on the feedback signal. The feedback control loop can be designed to compensate for the differences in time-constants and improve overall performance.

In summary, the electrical time-constant of an armature-controlled DC servomotor is generally smaller than the mechanical time-constant due to the faster response of the electrical components compared to the mechanical system. This difference in time-constants is important to consider when designing and analyzing the dynamic behavior of DC servomotors.