P, PI, PID Implementation in two-op-Amps

I have a question that I need some help with.

I have derived using Ziegler-Nichols the values of controllers with values

P Controller P=4.95

PI Controller P=3.75, I=0.2

PID Controller P=30, I=1.8, D=19.575

I know need to impement these into a corresponding two-op-amp unsing the formulas attached.

I am struggling to understand how this can be calulated to give the values of R1, R2, R3, R4, C1, C2 etc with only the solution known to the equations.

Answer 1

[Joel Van Sickel]

hello Steven,

there are two pieces. 1st, you need to write your PID controller in form A(Bs+1)(Cs+1)/s. This gives you A = R1*C1 and B = R2*C2. (you could also expand the design equation you have if you don't want to factor your equation to solve for B and C)

https://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=ControlPID

Now, the design equations you have shared provide more variables than equations, so you need to arbitrarily assign some values before other values can be determined. For instance, you can just set both your capacitor values to 10 uF. This will determine what R1 and R2 are, which in term will tell you what ratio R3 and R4 must be. I think you'll then need to pick a value for R3 or R4 to get the final value.

if you have the symbolic toolbox, you can use matlab to do this analytically, or you can do the math by hand.

Regards,

Joel