Question

The Ziegler-Nichols open-loop tuning method allows you to use the delay time L and the time constant to calculate the gain, integral time and derivative time. The transfer function of a PID controller is: $G_{PID}(s) = \frac{U(s)}{E(s)} = K_P \left[ 1 + \frac{1}{T_I s} + T_d s \right]$ (1) Based on this method, we have the following transfer function of a PID controller: $G(PID) = 25 \left[ 4 + \frac{1}{x s} + 2s \right]$ (2) Table 10-1 Ziegler-Nichols Tuning Rule Based on Step Response of Plant (First Method) Type of Controller $K_P$ $T_I$ $T_d$ P $\frac{T}{L}$ $\infty$ 0 PI $0.9 \frac{T}{L}$ $\frac{L}{0.3}$ 0 PID $1.2 \frac{T}{L}$ $2L$ $0.5L$ 1) Use the table to find the values of T and 2) Find the transfer functions of the P, and PI controllers 3) Find the value of x is the given equation (2)

          The Ziegler-Nichols open-loop tuning method allows you to use the delay time L and the time
constant to calculate the gain, integral time and derivative time. The transfer function of a PID
controller is:
$G_{PID}(s) = \frac{U(s)}{E(s)} = K_P \left[ 1 + \frac{1}{T_I s} + T_d s \right]$ (1)
Based on this method, we have the following transfer function of a PID controller:
$G(PID) = 25 \left[ 4 + \frac{1}{x s} + 2s \right]$ (2)
Table 10-1
Ziegler-Nichols Tuning Rule Based on Step
Response of Plant (First Method)
Type of
Controller
$K_P$
$T_I$
$T_d$
P
$\frac{T}{L}$
$\infty$
0
PI
$0.9 \frac{T}{L}$
$\frac{L}{0.3}$ 
0
PID
$1.2 \frac{T}{L}$
$2L$
$0.5L$
1) Use the table to find the values of T and
2) Find the transfer functions of the P, and PI controllers
3) Find the value of x is the given equation (2)

The Ziegler-Nichols open-loop tuning method allows you to use the delay time L and the time
constant to calculate the gain, integral time and derivative time. The transfer function of a PID
controller is:
GPID(s) = (U(s))/(E(s)) = KP [ 1 + (1)/(TI s) + Td s ] (1)
Based on this method, we have the following transfer function of a PID controller:
G(PID) = 25 [ 4 + (1)/(x s) + 2s ] (2)
Table 10-1
Ziegler-Nichols Tuning Rule Based on Step
Response of Plant (First Method)
Type of
Controller
KP
TI
Td
P
(T)/(L)
∞
0
PI
0.9 (T)/(L)
(L)/(0.3)
0
PID
1.2 (T)/(L)
2L
0.5L
1) Use the table to find the values of T and
2) Find the transfer functions of the P, and PI controllers
3) Find the value of x is the given equation (2)

Added by Juan Manuel R.

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