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##### From Essentials of Mechatronics

8.1   DIFFERENTIAL EQUATIONS

8.1.1   Breaking Down the State Equations

In Section 6.6, we saw how a system could be described by a matrix state
equation of the form

in which there are several simultaneous first-order equations.

We have looked at an example where

and we could consider applying feedback

to get

In matrix form these equations are

We can eliminate v from the two equations to get the “conventional” form of
a single second-order differential equation

or

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DC Motors
DC motors are most commonly used in variable speed and torque applications. They include brushless and gear motors, as well as servomotors.
AC Motors
AC motors include single, multiphase, universal, induction, synchronous, and gear motors. They also include servomotors.
Stepper Motors (Rotary)
Stepper motors use a magnetic field to move a rotor in small angular steps or fractions of steps. They provide precise positioning and ease of use, especially in low acceleration or static load applications.
Linear Motors
Linear motors generate force only in the direction of travel. They are capable of extremely high speeds, quick acceleration, and accurate positioning.
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AC servomotors are responsive, high-acceleration motors typically constructed as permanent magnet synchronous motors.

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