**PID position loops**

**Theory**

The velocity loop is the most basic servo control loop. However,

since a velocity loop cannot ensure that the machine stays in

position over long periods of time, most applications require

position control. There are two common configurations used for

position control: the cascaded position-velocity loop, as discussed

last month, and the PID position controller, as shown below.

Block diagram of PID position loop

The position loop compares a position command to a position

feedback signal, and calculates the position error, PE. In a PID

controller, current command is generated with three gains: PE is

scaled by the proportional gain (KPP), the integral of PE is scaled by

the integral gain (KPI), and the derivative of PE is scaled by the

derivative gain (KPD).

**More ( pdf )**

http://apps.danahermotion.com/support/troubleshooting/

PDF_Resources/2000-08%20PID%20pos%20loops.pdf

**Servo Motion Control - PID Control**

The basic components of a typical servo motion system are

depicted in Fig.1 using standard LaPlace notation. In this figure,

the servo drive closes a current loop and is modeled simply as

a linear transfer function G(s). Of course the servo drive will

have peak current limits, so this linear model is not entirely

accurate, however it does provide a reasonable representation

for our analysis. In their most basic form, servo drives receive

a voltage command that represents a desired motor current.

Motor shaft torque, T is related to motor current, I by the torque

constant, Kt. Equation (1) shows this relationship.

For the purposes of this discussion the transfer function of

the current regulator or really the torque regulator can be

approximated as unity for the relatively lower motion frequencies

we are interested in and therefore we make the following

approximation shown in (2).

depicted in Fig.1 using standard LaPlace notation. In this figure,

the servo drive closes a current loop and is modeled simply as

a linear transfer function G(s). Of course the servo drive will

have peak current limits, so this linear model is not entirely

accurate, however it does provide a reasonable representation

for our analysis. In their most basic form, servo drives receive

a voltage command that represents a desired motor current.

Motor shaft torque, T is related to motor current, I by the torque

constant, Kt. Equation (1) shows this relationship.

For the purposes of this discussion the transfer function of

the current regulator or really the torque regulator can be

approximated as unity for the relatively lower motion frequencies

we are interested in and therefore we make the following

approximation shown in (2).

The servomotor is modeled as a lump inertia, J, a viscous damping

term, b, and a torque constant, Kt. The lump inertia term is

comprised of both the servomotor and load inertia. I t is also

assumed that the load is rigidly coupled such that the torsional

rigidity moves the natural mechanical resonance point well

out beyond the servo controller’s bandwidth. This assumption

allows us to model the total system inertia as the sum of the

motor and load inertia for the frequencies we can control.

Somewhat more complicated models are needed if coupler

dynamics are incorporated.

The actual motor position, q(s) is usually measured by either an

encoder or resolver coupled directly to the motor shaft. Again the

underlying assumption is that the feedback device is rigidly

mounted such that its mechanical resonant frequencies can be

safely ignored. External shaft torque disturbances, Td are added

to the torque generated by the motor's current to give the torque

available to accelerate the total inertia, J.

term, b, and a torque constant, Kt. The lump inertia term is

comprised of both the servomotor and load inertia. I t is also

assumed that the load is rigidly coupled such that the torsional

rigidity moves the natural mechanical resonance point well

out beyond the servo controller’s bandwidth. This assumption

allows us to model the total system inertia as the sum of the

motor and load inertia for the frequencies we can control.

Somewhat more complicated models are needed if coupler

dynamics are incorporated.

The actual motor position, q(s) is usually measured by either an

encoder or resolver coupled directly to the motor shaft. Again the

underlying assumption is that the feedback device is rigidly

mounted such that its mechanical resonant frequencies can be

safely ignored. External shaft torque disturbances, Td are added

to the torque generated by the motor's current to give the torque

available to accelerate the total inertia, J.

Around the servo drive and motor block is the servo controller that

closes the position loop. A basic servo controller generally contains

both a trajectory generator and a PID controller. The trajectory

generator typically provides only position setpoint commands labeled

in Fig.1 as q* (s). The PID controller operates on the position error

and outputs a torque command that is sometimes scaled by an

estimate of the motor's torque constant, ˆt K . I f the motor's torque

constant is not known, the PID gains are simply re-scaled accordingly.

Because the exact value of the motor's torque constant is generally

not known, the symbol "^ " is used to indicate it is an estimated value

in the controller. In general, equation (3) holds with sufficient accuracy

so that the output of the servo controller (usually + / - 10 volts) will

command the correct amount of current for a desired torque.

closes the position loop. A basic servo controller generally contains

both a trajectory generator and a PID controller. The trajectory

generator typically provides only position setpoint commands labeled

in Fig.1 as q* (s). The PID controller operates on the position error

and outputs a torque command that is sometimes scaled by an

estimate of the motor's torque constant, ˆt K . I f the motor's torque

constant is not known, the PID gains are simply re-scaled accordingly.

Because the exact value of the motor's torque constant is generally

not known, the symbol "^ " is used to indicate it is an estimated value

in the controller. In general, equation (3) holds with sufficient accuracy

so that the output of the servo controller (usually + / - 10 volts) will

command the correct amount of current for a desired torque.

There are three gains to adjust in the PID controller, Kp, Ki and Kd.

These gains all act on the position error defined in (4). Note the

superscript "* " refers to a commanded value.

These gains all act on the position error defined in (4). Note the

superscript "* " refers to a commanded value.