PID tuning on SLC 5/05

[drbitboy]

Originally Posted by Robb B

Here's a typical pressure cycle.

The valve is not opening (i.e. passing flow) until CV% is around 24%; that is effectively a reset windup neither visible to, nor affected by, the anti-windup reset algorithm built in to the PID.

Try adding a constant feedforward (Control Word 6; N16:5 in your configuration) of ~3900 once the vent valve closes and/or the PID is switched to Automatic (.AM=0).
_

[Robb B]

Originally Posted by drbitboy

The valve is not opening (i.e. passing flow) until CV% is around 24%; that is effectively a reset windup neither visible to, nor affected by, the anti-windup reset algorithm in the PID.

Try adding a constant feedforward (Control Word 6; N16:5 in your configuration) of ~3900 once the vent valve closes and/or the PID is switched to Automatic (.AM=0).

I was considering something like this, in combination with your post #24, keeping the PID in manual until around 75% of the setpoint, then moving the CV to 25% and switching to automatic mode. I probably won't get a chance to test this for several days, it depends on when pressure cycles happen and I need to be present if I'm testing.

[drbitboy]

Originally Posted by Robb B

I was considering something like this, in combination with your post #24, keeping the PID in manual until around 75% of the setpoint, then moving the CV to 25% and switching to automatic mode. I probably won't get a chance to test this for several days, it depends on when pressure cycles happen and I need to be present if I'm testing.

Fuggedabout Post #24; I was still woefully ignorant of the process.

You do not have to be in manual first and then, at 75% of setpoint, (i) move the CV% to 25% and (2) switch to auto.

That valve is closed when the CV+feedback* is between 0 and 24%**. Closed. Shut. Not open. Zero flow. That valve's controllable range is 24% to (maybe) 100% in CV%, or ~3900 to 16383 in CV. Spending any time between 0% and 24% is a waste of time and the primary reason for the overshoot***.

So you can put it in Auto like you do now and write 3900 into Control Word 6 whenever it is in Auto e.g.

XIC N16:0/1 CLR N16:6

XIO N16:0/1 MOV 3900 N16:6

If you do that, the valve, and the PV, will react more or less immediately when the PV crosses the SP.

* the feedforward value in Control Word 6 is an INT in the range -16383 to +16383; a CV% of 24% open is ~3900 on that scale.

** 24% is my calibrated eyeball's estimate from the trend, it may be 23% or 25%

*** Note that, at 165PSI setpoint, the pressure is rising slower because of lower pump flow into the system (centrifugal pump curve => increased head => less flow), and that slower rise in pressure is why it overshoots less i.e. it only rises 5PSI before CV reaches ~3900 and the valve actually first opens.

[drbitboy]

@Peter Nachtwey did an interesting study for a valve that was not only non-linear, it was more or less stochastic; I forget if it was a sticky valve.

This situation is far simpler than that ...

[drbitboy]

What is the timescale on that trend plot?


Is it two minutes per division?

[MaxK]

Originally Posted by Robb B

The 125psi target might (will!) change in the future, I'd like to design the system to respond better to any future setpoints that might be implemented.

Below you can see a diagram of your system
kleak - system leakage coefficient (~sqrt(system pressure))
kpump - pump efficiency reduction factor
kvalve - coefficient of increase in the capacity of the control valve (~sqrt(system pressure))

You can define controller gains using system transfer function

G(s) = (k/s)*exp(-deadtime*s) / (1 + k/s*exp(-deadtime*s) * (kleak + kpump + kvalve * (kp + ki/s)))

I also gave a diagram from the Pump to the system output. Transfer function from the Pump to the system output is:

G(s) = k / (T*s+1)

T = 1 / (k*(kleak + kpump)
k = 1 / (kleak + kpump)

If we express the deadband as deadtime, then the transfer function from the controller output to the system output is:

G(s) = k * exp(-DeadTime*s) / (T*s+1)

T = 1 / (k*(kleak + kpump)
k = kvalve / (kleak + kpump)

The more pressure, the more kleak, kpump, kvalve, i.e. decreases T (for both TFs), the gain from the pump to the system outlet decreases more than CO to SO gain. That is why the control is more effective at high pressure.


If we find CO to SO transfer function coefficients (using the curves from your post #41):

G(s) = 0.91 * exp(-60*s) / (36*s+1)

60/36 = 1,6667 – it is NOT good

In other words your ACTUAL PROBLEM IS A CONTROL VALVE DEADBAND

The most efficient solution would be make control valve position=24% (or what the actual deadband) to controller output=0 as drbitboy wrote.
This case you'll get easiest to control first order lag plant
G(s) = 0.91/ (36*s+1)

I think it would be safer to set the control valve position to 0 at the end of the cycle.

[drbitboy]

Originally Posted by MaxK

...

Wow, noice.

I was going to say the pump curve was available in the trend plot, (positive dPressure/dt as a function of Pressure while the valve is closed; dPressure/dt is a proxy for pump flow dVolume/dt from rearranging the bulk modulus formula K = dP / (dV/V₀), to first order anyway).

And a similar approach for the valve would model negative dPressure/dt as a function of Pressure and CV% e.g. dPressure/dt = √P / (C (76/(CV%-24) + R) whenever CV% > 24, and zero otherwise (valve is closed).

Adding those positive and negative dPressure/dt values yields a dynamic model of the pressure of the vessel as a function of CV%. Of course there are a lot of things not modeled (head from storage tank, non-linear valve characteristic, leakage, etc.).

[drbitboy]

@Robb B, I am curious about the end of the cycle, starting around 2:57 PM on the trend.

It looks like some other drain has been opened, or maybe the PID CV was disconnected from the control valve, because the pressure drops steeply. The PID is still trying to control so it closes (CV drops to zero).

The setpoint is also being ramped down in steps, which seems superfluous if the control (of the?) valve is bypassed, but each step down in SP gives a positive kick to the CV - was there some Derivative action in place during that trend i.e. T_d was non-zero?

[Robb B]

Originally Posted by drbitboy

@Robb B, I am curious about the end of the cycle, starting around 2:57 PM on the trend.

It looks like some other drain has been opened, or maybe the PID CV was disconnected from the control valve, because the pressure drops steeply. The PID is still trying to control so it closes (CV drops to zero).

The setpoint is also being ramped down in steps, which seems superfluous if the control (of the?) valve is bypassed, but each step down in SP gives a positive kick to the CV - was there some Derivative action in place during that trend i.e. T_d was non-zero?

Yeah, that's part of the bleed-off stage, it takes the pressure down in steps, hence the valve and pressure responses. It uses the same PID control, no different values. I assume the CV responds since the setpoint lowered, but the math quickly determines that it's still a negative error.

[drbitboy]

Originally Posted by Robb B

Yeah, that's part of the bleed-off stage, it takes the pressure down in steps, hence the valve and pressure responses. It uses the same PID control, no different values. I assume the CV responds since the setpoint lowered, but the math quickly determines that it's still a negative error.

The setpoint, not the pressure, comes down in steps.

I'm guessing the pump is stopped, which is the real reason the pressure drops (backflow through the pump?) like a stone.

The control valve is trying to respond to the drop in pressure but not actually modulating anything at that point; the lowering of the setpoint is interesting but meaningless. The CV kicks at each setpoint drop are momentary; they could be caused by a non-zero T_d, but K_c could also be the cause if T_d was 0.

Btw, instead of feed forward/bias, another way to bump the CV to 24% or so might be to put ~3900 in the Output Minimum, word 12 of the Control Block (N16:12).

[Robb B]

Originally Posted by drbitboy

The setpoint, not the pressure, comes down in steps.

I'm guessing the pump is stopped, which is the real reason the pressure drops (backflow through the pump?) like a stone.

The control valve is trying to respond to the drop in pressure but not actually modulating anything at that point; the lowering of the setpoint is interesting but meaningless. The CV kicks at each setpoint drop are momentary; they could be caused by a non-zero T_d, but K_c could also be the cause if T_d was 0.

Btw, instead of feed forward/bias, another way to bump the CV to 24% or so might be to put ~3900 in the Output Minimum, word 12 of the Control Block (N16:12).

Setpoint comes down in steps, part of the bleed off cycle.

I tried using the MOV 3900 to word 6, and it shows in the PID setup box, but didn't have any effect on the Output percentage, ie: it didn't jump the output to ~24% even after crossing the setpoint.

I tried tuning the PID using the suggested method in rockwells help manual on the PID instruction. I got oscillation around Kc of 25 so I halved that, then the oscillation period was about 20 seconds, so Ti is 0.3, and derivative should be 1/8 of the Ti, which came out to 0.0375 so I went with 0.04 because of limited decimals. Response at setpoint is very smooth, but I haven't had a chance to test it against the initial ramping time.

[drbitboy]

Originally Posted by Robb B

Setpoint comes down in steps, part of the bleed off cycle.

But that does nothing, because the pressure has already dropped, and the controller is trying to raise the pressure by closing the valve. Presumably another bleed valve has been opened, and if that is the case, then the code that ramps down the setpoint serves no purpose.

Originally Posted by Robb B

I tried using the MOV 3900 to word 6, and it shows in the PID setup box, but didn't have any effect on the Output percentage, ie: it didn't jump the output to ~24% even after crossing the setpoint.

Huh. Maybe 3900 needs to be in word 12 (Output Minimum, CVL) instead, or as well, because without that, any feed forward bias in Word 6 is eventually overridden (negated) by the accumulation of reset (T_i) bias, and the CV output ends up at 0 anyway. What values are in Words 17 and 18 when Word 12 is 0 and Word 6 is 3900, and what values are in Words 17 and 18 when Words 12 and 6 are both 0?

[drbitboy]

off course you could, as an alternative, apply the bias external to the PID, i.e. leave the PID as is (Word 6 = 0 = Word 12), and add 3900 to the PID CV output (ADD N9:5 2900 Nx:y) after the PID whenever .EN is 1 and .AM is 0, and send that result (Nx:y) to your valve output.

[MaxK]

Originally Posted by Robb B

I tried tuning the PID using the suggested method in rockwells help manual on the PID instruction. I got oscillation around Kc of 25 so I halved that, then the oscillation period was about 20 seconds, so Ti is 0.3, and derivative should be 1/8 of the Ti, which came out to 0.0375 so I went with 0.04 because of limited decimals. Response at setpoint is very smooth, but I haven't had a chance to test it against the initial ramping time.

Can you show the curves system setpoint change response and disturbance rejecting (when pressure overcome setpoint) response?

If setpoint changes then changes system pressure, i.e. changes system model (model acts some kind like spring).
When it is rejecting disturbance it is possible to “hold” pressure, i.e. “freez” model.

In summary, I think it makes sense to try more aggressive controller settings for disturbance rejecting . More aggressive controll will allow:
1. Faster overcome the deadband of the control valve
2. Stabilize the pressure in the system faster and prevent the system model from changing.

Curve below illustrated my idea

[drbitboy]

Originally Posted by drbitboy

... Maybe 3900 needs to be in word 12 (Output Minimum, CVL) instead ...

From the SLC instruction set manual about PID (here):

Anti-reset windup is a feature that prevents the integral term from becoming
excessive when the output (CO) reaches a limit. When the sum of the PID and
bias terms in the output (CO) reaches the [output] limit, the instruction stops
calculating the integral sum until the output (CO) comes back in range.

So the proposed lower limit ~3900 should be put into the Output Minimum - CVL at Word 12 (N16:12) to ensure the valve opens sooner. This may also change the tuning.

The feed forward/bias in Word 6 is meant for process disturbances, i.e. time-dependent bias.