Re: Challenge for best Feedforward/Feedback control

On Nov 25, 4:26 am, "JCH" <ja...@xxxxxxxxxxxxxxxxxxx> wrote:
"Peter Nachtwey" <pnacht...@xxxxxxxxxxx> schrieb im Newsbeitragnews:IO-dnYJV6LUNT9XanZ2dnUVZ_gednZ2d@xxxxxxxxxxxxxx

Self-regulating process
tau*y'(t)+w*y(t)=K*u(t)+C

w*y(t)=0 in any ODE causes no-self-regulation.

The data set in Page 2http://home.arcor.de/janch/janch/_control/20071123-pd2(pid)z1z2/
is a 'real' no-self-regulating process.

Page 1 still looks the same to me. What is all this PD2(PID) stuff?
Only a simple PID is required.
Page 2 and 3, Figure 2 is still wrong because the control output v2 is
proportional to the process value v1 or position.
Page 4. You are not representing the disturbance response
accurately. You tuning values make the closed loop transfer function
under damped so the process value should over shoot the target value
but your graphs don't show this.


I think it is clear that in a context of ODEs in control theory time t is
the independant variable. That's why I left t out.

You can't leave out time in a general case. If you want to ID
temperature systems with dead time then you need to write the
differential equation like this:
tau*y'(t)+w*y(t)=K*u(t-deadtime)+C
One must find the best combination of tau, K, deadtime, and C that
will minimize the error between the actual and estimated data. All
this first just a simple FOPDT estimation. The good news is that once
this is done, one can go to www.controlguru.com to find the equations
that calculate the PI controller gains.

The control function, u(t),must change during system identification.
A simple step will not do for five reasons.

1. To get the best estimates for K and C u(t) must change between two
levels so there is plenty of time where the system reaches or almost
reaches a steady state. With only a single step it is impossible to
calcuate K and C which is kind of like an offset and scale.

2. To get the best estimates for tau and dead time one needs plent of
rise and fall time. It is hard to detect the correct dead time
unless there are plenty of places where one can see the phase
relationship between the signal and the response. Horizontal flat
lines will not do.

3. On a position system with limits the motor or actuator will
eventually hit something.

4. When tuning a motor in torque mode the motor will accelerate
proportionaly to the control signal. The motor will spin up to very
high speed and if there is a physical stop then there will be an
accident. Even setting the control output to 0 is not enough because
the motor will coast until it hits something. One must output a
short pulse in the positive direction and then an equal pulse in the
negative direction to stop the motor. If done right the motor will
not move very far.

5. u(t) can be a very complicated function. It can be a motion
profile with polynomial ramps where t is required to index into the
polynomial to calculate position, velociy and acceleration and these
are then mulitplied by feed forwards gains and summed to generate the
control signal.

You can see that the control function, u(t), is very important.
Don't ignore this.

Peter Nachtwey
.

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