Saturday, March 28, 2009

Servo Motion Control Tuning the PID Loop

There are two primary ways to go about selecting the PID gains.
Either the operator uses a trial and error or an analytical approach.
Using a trial and error approach relies significantly on the
operator’s own prior experience with other servo systems. The one
significant downside to this is that there is no physical insight into
what the gains mean and there is no way to know if the gains are
optimum by any definition. However, for decades this was the
approach most commonly used. In fact, it is still used
today for low performance systems usually found in process control.
To address the need for an analytical approach, Ziegler and Nichols
[1] proposed a method based on their many years of industrial
control experience. Although they originally intended their tuning
method for use in process control, their technique can be applied to
servo control. Their procedure basically boils down to these two steps.

Step 1:
Set Ki and Kd to zero. Excite the system with a step command.
Slowly increase Kp until the shaft position begins to oscillate.
At this point, record the value of Kp and set Ko equal to this value.
Record the oscillation frequency, fo.

Step 2:

Set the final PID gains using equation (6).

Loosely speaking, the proportional term affects the overall response

of the system to a position error. The integral term is needed to force
the steady state position error to zero for a constant position
command and the derivative term is needed to provide a damping
action, as the response becomes oscillatory. Unfortunately all three
parameters are inter-related so that by adjusting one parameter will
effect any of a previous parameter adjustments. As an example of
this tuning approach, we investigate the response of a Compumotor
BE342A motor with a generic servo drive and controller.

This servomotor has the following parameters:

Motor Total Inertia J = 50E-6 kgm^2
Motor Damping b = .1E-3 Nm/ (rad/sec)
Torque Constant Kt = .6 Nm/A

We begin with observing the response to a step input command with
no disturbance torque (Td = 0).

Step 1:
Fig. 2a shows the result of slowly increasing only the proportional term.
The system begins to oscillate at approximately .5 Hz (fo = .5Hz) with
Ko of approximately 5E-5 Nm/ rad.

Step 2:

Using these values, the optimum P.I .D. gains according to
Ziegler-Nichols (Z-N) are then (using equation (6)):

Kp = 3.0E-4 Nm/ rad
Ki = 3.0E-4 Nm/ (rad/sec)
Kd = 7.4E-5 Nm/ (rad/sec)

Fig. 2b shows the result of using the Ziegler Nichols gains.
The response is somewhat better than just a straight proportional gain.
As a comparison, other gains were obtained by trial and error. One set
Of additional gains is listed in Fig. 2b. Although the trial and error gains
gave a faster, less oscillatory response, there is no way of telling if a
better solution exits without further exhaustive testing.

One characteristic that is very apparent in Fig.2 is the length of
the settling time. The system using Ziegler Nichols takes about
6 seconds to finally settle making it very difficult to incorporate
into any highperformance motion control application. In contrast,
the trial and error settings gives a quicker settling time, however
no solution was found to completely remove the overshoot.

Source ( pdf )

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