## Servo Types

No matter what is dealt with in life, it seems that it must be named and classified-servos are no exception. Servos are classified into three types: type 0, type 1, and type 2. This column will be devoted to discussing these three types plus the advantages and disadvantages of each.

Basically, the type number refers to the number of integrators in the servo loop. A type 1 servo is the most popular having 1 integrator (the motor) in the loop. In order to explain advantages and disadvantages, it is necessary to refer to servo basics. The block diagram and response formula, as discussed on page 39 of the September/October 1990 issue of Motion Control, is shown below for your convenience.

Once A is well defined, one can predict accurately how well the output follows the input (F/C) or how much error will be experienced (E/C).

If the input command were a ramp in position (constant velocity), the error would increase as the position increases, so the output ramp would have a different slope (velocity).

The conclusion is that a type 0 system does not accurately follow steps in position nor constant velocity commands (position ramps).

In the steady state condition, the error (E) must approach 0 since the gain (A) approaches ∞. The result of a 1.00" step command would be a final output of 1.00" and an error of 0".

If the input command is a ramp in position (constant velocity), the output will be a ramp in position of precisely the same value (velocity), but lagged in position. This is true because a motor or integrator puts out a position ramp (or velocity) with a constant error (voltage) applied to it. In the steady state (after acceleration is over) the actual position (F) will lag the command (C) by the error (E), but the velocities (ramp slope) of C and F will be identical.

There are two major advantages of a type 1 system over type 0. The steady state error at rest is 0 and it responds precisely to constant velocity input commands (position ramps).

If one considers the condition when a position ramp (constant velocity) is commanded, there are two logical inferences that can be made. The second integrator (the motor) must have a constant input to provide a velocity output. This means that the first integrator needs to supply a constant signal to the second integrator, thus the input to the first integrator must be 0. If the input to the first integrator is 0, then there is no position error in this system in the constant velocity mode. This is exactly the case and explains why so much effort has gone into developing type 2 systems.

In addition to no position error at rest, a type 2 system has the additional feature of no position error with a steady state ramp input in position (after the acceleration is complete.)

If zero position error is important under steady state positional ramping (constant velocity) conditions, then the PID approximation of a type 2 system is the answer. Don't complicate the design if you don't need it, though.

An example of the need for zero position error would be in master/slave applications where the slave is expected to stay in precise position synchronism with the master even though an operator may choose to change the "speed" of the master.

So much for this class in classifying servos.

Also, let me know if there are any motion control questions that you want me to address. I want this column to serve the user, so I need your feedback to know if it is doing that. It has been suggested that a series of articles on programming techniques from different vendors would be helpful-would it?

Basically, the type number refers to the number of integrators in the servo loop. A type 1 servo is the most popular having 1 integrator (the motor) in the loop. In order to explain advantages and disadvantages, it is necessary to refer to servo basics. The block diagram and response formula, as discussed on page 39 of the September/October 1990 issue of Motion Control, is shown below for your convenience.

Once A is well defined, one can predict accurately how well the output follows the input (F/C) or how much error will be experienced (E/C).

#### Type 0

A type 0 servo has no integrator (motor) as part of the amplifier (A). A is simply a proportional term and is treated strictly as a numeric value independent of frequency. As an example, consider a type 0 servo with a gain (A) of 99. According to the above equations, F/C = 99/100 = .99 and E/C = 1/100 = .01. Giving this type 0 servo a 1.00" step command would result in actual motion on the output of .99" and an error of .01". This would be the steady state or rest position of the servo.If the input command were a ramp in position (constant velocity), the error would increase as the position increases, so the output ramp would have a different slope (velocity).

The conclusion is that a type 0 system does not accurately follow steps in position nor constant velocity commands (position ramps).

#### Type 1

A type 1 servo has an integrator (motor) as part of the amplifier, so the A term takes the form ; as discussed in previous columns. As the frequency (ω) increases, the gain decreases. As the frequency decreases, the gain increases and approaches <∞> when ω approaches 0.In the steady state condition, the error (E) must approach 0 since the gain (A) approaches ∞. The result of a 1.00" step command would be a final output of 1.00" and an error of 0".

If the input command is a ramp in position (constant velocity), the output will be a ramp in position of precisely the same value (velocity), but lagged in position. This is true because a motor or integrator puts out a position ramp (or velocity) with a constant error (voltage) applied to it. In the steady state (after acceleration is over) the actual position (F) will lag the command (C) by the error (E), but the velocities (ramp slope) of C and F will be identical.

There are two major advantages of a type 1 system over type 0. The steady state error at rest is 0 and it responds precisely to constant velocity input commands (position ramps).

#### Type 2

A type 2 servo has two integrators (usually one motor and one "software" integrator) as part of the amplifier. The A term takes the form . Since the A term approaches ∞ as ω approaches 0, there will be no error (E) when the system is at rest. In this respect, it is similar to the type 1 servo.If one considers the condition when a position ramp (constant velocity) is commanded, there are two logical inferences that can be made. The second integrator (the motor) must have a constant input to provide a velocity output. This means that the first integrator needs to supply a constant signal to the second integrator, thus the input to the first integrator must be 0. If the input to the first integrator is 0, then there is no position error in this system in the constant velocity mode. This is exactly the case and explains why so much effort has gone into developing type 2 systems.

In addition to no position error at rest, a type 2 system has the additional feature of no position error with a steady state ramp input in position (after the acceleration is complete.)

#### Final Comments

It would appear that one should simply use a type 2 servo. Needless to say, it isn't that easy. A type 2 servo is inherently unstable. One must use compensation techniques to make it a type 2 servo which converts to a type 1 near bandwidth frequencies where stability is determined. The February column on PID described just such a technique to give the low frequency benefits of a type 2 servo, yet achieve stability.If zero position error is important under steady state positional ramping (constant velocity) conditions, then the PID approximation of a type 2 system is the answer. Don't complicate the design if you don't need it, though.

An example of the need for zero position error would be in master/slave applications where the slave is expected to stay in precise position synchronism with the master even though an operator may choose to change the "speed" of the master.

So much for this class in classifying servos.

Also, let me know if there are any motion control questions that you want me to address. I want this column to serve the user, so I need your feedback to know if it is doing that. It has been suggested that a series of articles on programming techniques from different vendors would be helpful-would it?

*This article originally appeared in Motion Control Magazine, April 1991.*