3.1.9.1.50.1.4 Tuning Concept in Brief
For tuning the cascaded structure, we should first focus on the inner (velocity) loop. As it is the inner
controlling loop, it should be faster than the outer position loop. However, if all parameters of the outer
position controller are set to 0, the inner loop will be disconnected from the user position commands. As a
result, we can increase the K_p of both position and velocity controllers with a ratio of 10 (K_p_velocity` = 10 *
K_p_position`). Once the real position started to follow the reference position, we can stop increasing the
K_p_position, and only focus on increasing K_p_velocity. At this stage, we can increase (sharpen) the velocity
controller as much as possible. As a rule of thumb, increase K_p_velocity until you get close to the instability
margin (at this margin, you will feel a vibration effect and some acoustic noise which is caused by controller
sharpness). Now, you can reduce K_p_velocity to 90% of its value to increase the stability margin, and remove
vibration noise. Once the velocity controller (the inner controlling loop) is tuned, it is time to tune the position
controller (the outer controlling loop). To tune the position controller loop, we should start with the P part of
its PID controller. Increase K_p_position until the entire position control gets close to instability margin. At this
state, you will feel a vibration (or acoustic noise) which is because of too sharpened position control. At this
step, reduce K_p_position to its 90% to increase the stability margin and remove the vibration/acoustic noise.
So far, the proportional parts of both inner velocity loop and outer position loop are tuned, and we can focus
on integrator part of the outer position or inner velocity loop (depends on chosen structure of controller).
Increasing the integrator constant will remove the steady state error, but at the same time, it adds some
overshoot at step responses. As a rule of thumb, you can increase K_i step by step until the following two
conditions are met at the same time:
the steady-state error is eliminated in a short enough period of time
the overshoot is in its acceptable range
In the following section, the explained tuning concept is divided in separate systematic steps.
3.1.9.1.50.1.5 Tuning Steps
Step 1. Set the PID constants of both controllers equal to 0. By default, the integral limit of the velocity
controller should be set to motor maximum torque and the integral limit of position controller should be
set to motor maximum velocity. From this step forth, the step response of position controller should
always be evaluated.
Step 2. In this step, the K_p constant of the velocity controller should be tuned. Increase the K_p of both
position and velocity controllers with a ratio of 10 (K_p_velocity = 10 * K_p_position). Once the real position
starts to follow the reference position, stop increasing the K_p_position and only focus on increasing the
K_p_velocity. Increase (sharpen) the velocity controller as much as possible. As a rule of thumb, increase
K_p_velocity until you get close to the instability margin (at this margin, you will feel a vibration effect and
some acoustic noise which is because of controller sharpness). Now, you can reduce K_p_velocity to 90% of
its value to increase the stability margin, and remove vibration noise.
Step 3. Now that the velocity controller is tuned, it is time to tune the parameters of the PID position
controller. Start with K_p_position, and increase it until you again get close to the instability margin, and
then reduce K_p_position` to its 90%. So far, the proportional parts of both inner velocity loop and outer
position loop are tuned.
Step 4. In this step, increase K_i to eliminate the steady state error. As a suggestion start with K_i equal to
0.01, and in each step, increase it with a factor of 2. Increase K_i step by step until the following two
conditions are met at the same time:
the steady-state error is eliminated in a short enough period of time
the overshoot is in its acceptable range
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