```Reduction of Block Diagram Models
Consider the following block diagram expressed in the Laplace domain:
Reduction of Block Diagram Models
Reduction of Block Diagram Models
These block diagrams are equivalent
Transfer Function of a DC Servomotor
In the case of the DC servomotor:
Electrical Time Constant of a DC Servomotor
Consider the expression for motor armature current :
A first order system can be expressed in “standard” form as follows:
Electrical Time Constant of a DC Servomotor
In the case of the motor used in the laboratory (Pittman 9232S003), the
armature resistance is provided by the manufacturer in the datasheet as
7.38Ω and the armature inductance as 4.64 mH. This yields an electrical
time constant of 0.63 ms; a value which is also confirmed in the datasheet.
Since the maximum recommended motor voltage is 24V, the armature
current is limited by the armature resistance to a maximum of 3.25A. The
maximum motor power dissipation is therefore 78W although this power
level cannot be tolerated indefinitely.
Mechanical Time Constant of a DC Servomotor
As demonstrated previously DC servomotor can be
modeled as a second-order transfer function:
If the electrical time constant of the motor is very small, it can be
neglected and the motor can be modeled as a first-order transfer.
Mechanical Time Constant of a DC Servomotor
In the case of the motor used in the laboratory (Pittman 9232S003)
the various parameters are listed in the data sheet.
The mechanical time constant is listed in the
motor datasheet as 14.4 ms.
Mechanical Time Constant of a DC Servomotor
Given that the electrical time constant is 22.6 times smaller than the
mechanical time constant, it can be neglected in many applications and the
motor can be effectively modeled as a first-order system. The no-load response
to a 24V step input for both the second-order motor model (top) and first order
motor model (bottom) are shown below for the motor used in the lab.
```