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From: Susan on 5 Apr 2010 14:34
I'm not sure if I've made a MATLAB mistake or maybe misunderstood something in the control theory. I was hoping to verify my MATLAB code

The following TF is a closed loop TF with unity feedback and PID values using Ziegler-Nichols (ZN) first method. I've not tuned the PID any further. I'm plotting this TF using step(TF, t) where t is time.

Transfer function of closed loop Plot with ZN PID values:
1.4 s^3 + 49.48 s^2 + 4.371 s
---------------------------------------------
0.005597 s^4 + 5.816 s^3 + 51.84 s^2 + 6.58 s

The plot is what I'd expect but the problem arises when I increase Kp or Kd. An increase in Kp results in a plot that appears has more damping. Increasing Kd results in a plot with more oscillations. So the opposite result as expected.

here is some of my code in case it's helpful
Control_Kp_Ki_Kd=tf([Kd Kp Ki],[1 0]);
Plant:
s
------------------------------------------
0.005597 s^3 + 4.416 s^2 + 2.359 s + 2.209

sys_CL_Kp_Ki_Kd=feedback(Control_Kp_Ki_Kd*Plant,1);
step(sys_CL_Kp_Ki_Kd,'m-',t);

Can anyone explain this result, or have I made a mistake?
From: Susan on 6 Apr 2010 14:18
I also plotted the same Plant but without the S in the numerator

Plant No S


1
-------------------------------------------------------
0.005597 s^3 + 4.416 s^2 + 2.359 s + 2.209

In both TFs the input was a unit step and the Ziegler Nichols PID values were the same. The plant above without an S in the numerator responds as expected to an increase in Kp and Kd. Increasing Kp increases the oscillations and an increase in Kd increases damping as is expected.

Why is it that an S in the numerator results in a system in which Kp behaves like Kd and Kd like Kp?
From: Susan on 6 Apr 2010 14:19
I also plotted the same Plant but without the S in the numerator

Plant No S


1
-------------------------------------------------------
0.005597 s^3 + 4.416 s^2 + 2.359 s + 2.209

In both TFs the input was a unit step and the Ziegler Nichols PID values were the same. The plant above without an S in the numerator responds as expected to an increase in Kp and Kd. Increasing Kp increases the oscillations and an increase in Kd increases damping as is expected.

Why is it that an S in the numerator results in a system in which Kp behaves like Kd and Kd like Kp?
From: Jacob Mueller on 6 Apr 2010 16:46
Was the TF closed loop with unity feedback in both cases?
From: Susan on 7 Apr 2010 01:05
Please if anyone has any ideas it would help. I'm really stuck on this.

The closed loop of Plant with no "S" in the numerator (PID control in feedforward and unity feedback):
1.4 s^2 + 98.97 s + 4.371
------------------------------------------------------
0.005597 s^4 + 4.416 s^3 + 3.759 s^2 + 101.2 s + 4.371

The closed loop of Plant with "S" in the numerator (PID control in feedforward and unity feedback):

1.4 s^3 + 98.97 s^2 + 4.371 s
---------------------------------------------
0.005597 s^4 + 5.816 s^3 + 101.3 s^2 + 6.58 s
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