How do you calculate the transfer function of a DC motor?

How do you calculate the transfer function of a DC motor?

Transfer Function of Armature Controlled DC Motor:

1. Let Ra = Armature resistance,
2. La = Armature inductance.
3. Ia = Armature current.
4. Va = Armature voltage.
5. eb = Back emf.
6. Kt = Torque constant.
7. Kb= Back emf constant.

How do you find the coefficient of viscous friction?

The ratio of the shearing stress to the velocity gradient is a measure of the viscosity of the fluid and is called the coefficient of viscosity η, or η=Fx/Av.

How do you find the damping coefficient of a DC motor?

Short-circuit damping When the terminals of the motor are shorted together, you get a viscous damping torque T opposing the shaft angular velocity ω, satisfying the equation T = −Bω, where B > 0. The damping B can be calculated from the torque constant and terminal resistance.

What is the transfer function of a motor?

The transfer function from the input voltage to the resulting motor torque is found by combining equations (1.2) and (1.3). So, a step input in field voltage results in an exponential rise in the motor torque.

Is viscosity a friction?

Viscosity is a measure of a fluid’s resistance to flow. It describes the internal friction of a moving fluid. A fluidwith large viscosity resists motion because its molecular makeup gives it a lot of internal friction.

What is Coulomb and viscous friction?

Description. The Coulomb and Viscous Friction block models Coulomb (static) and viscous (dynamic) friction. The block models a discontinuity at zero and a linear gain otherwise. The output is a scalar, vector, or matrix depending on the dimensions of Gain and Offset .

What is the speed regulation of a DC motor?

Definition: The speed regulation of a DC Motor is defined as the change in speed from no load to full load. It is expressed as a fraction or a percentage of the full load speed.

What is the transfer function of a DC motor?

Armature Controlled DC Motor Transfer Functions is controlled through the armature voltage a V . o The motor torque increases linearly with the armature current. K is a constant that depends on a given motor.

Which DC motor will not be preferred for machine tools?

DC Differentially compound motor: It has low starting torque and has a constant speed, but the dangerously high speed at no load under the circumstances it is seldom used.

When does viscous friction occur in a motor?

A viscous friction occurs in the cases when there is an oil between the contact surfaces, which reduces friction coefficient f. This coefficient is lower than Coulomb friction coefficient fC. Viscous friction is represented as a linear function of velocity 2.4.

How is the friction of a DC motor measured?

At first the paper deals with basic friction models. In the next section the DC motor mathematical model is stated. The DC motor friction identification is based on basic Newton´s motion equation of motor. The friction course by means of Matlab and measuring card is measured.

How to calculate the motor speed in MATLAB?

For this example, we will assume that the input of the system is the voltage source () applied to the motor’s armature, while the output is the rotational speed of the shaft . The rotor and shaft are assumed to be rigid. We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity.

How is the rotational speed of a motor calculated?

The electric equivalent circuit of the armature and the free-body diagram of the rotor are shown in the following figure. For this example, we will assume that the input of the system is the voltage source () applied to the motor’s armature, while the output is the rotational speed of the shaft .

What are the design requirements for a unit step command in DC motor speed those requirements meet the control system output?

In summary, for a unit step command in motor speed, the control system’s output should meet the following requirements.

• Settling time less than 2 seconds.
• Overshoot less than 5%
• Steady-state error less than 1%

How is the state of a DC motor derived?

State-space representation is a mathematical model of a physical system as set of input, output and state variables related by first order differential equations. A state model ofthe DC motor is derived by defining the three states : The position of the motor shaft, the velocity of the motor shaft and armature current.

What is the DC motor speed in steady state?

First consider that our uncompensated motor rotates at 0.1 rad/sec in steady state for an input voltage of 1 Volt (this is demonstrated in the DC Motor Speed: System Analysis page where the system’s open-loop response is simulated).

How is the torque of a DC motor calculated?

We further assume a viscous friction model, that is, the friction torque is proportional to shaft angular velocity. The physical parameters for our example are: In general, the torque generated by a DC motor is proportional to the armature current and the strength of the magnetic field.

How is the rotational speed of a motor assumed?

The electric equivalent circuit of the armature and the free-body diagram of the rotor are shown in the following figure. For this example, we will assume that the input of the system is the voltage source () applied to the motor’s armature, while the output is the rotational speed of the shaft . The rotor and shaft are assumed to be rigid.