Autoclave Temperature Control Setup
The problem asks for the proportional gain ($K_p$) of a controller used for autoclave temperature regulation.
- Temperature Range Span: $130\degree C - 60\degree C = 70\degree C$
- Proportional Band (PB): $25\%$
Proportional Gain Formula
The proportional gain ($K_p$) is inversely related to the proportional band (PB) when PB is expressed as a percentage of the total control range. The formula is:
$K_p = \frac{100}{\text{PB percentage}}$
Gain Calculation Steps
Using the provided proportional band percentage:
- Substitute the PB value into the formula:
$K_p = \frac{100}{25\%}$
- Calculate the result:
$K_p = 4$
Final Proportional Gain Value
The calculated proportional gain ($K_p$) is 4.
Important Questions from Proportional Derivative and Integral Control
Which of the following statements are CORRECT for a controller?
P. In a proportional controller, a control action is proportional to the error
Q. In an integral controller, a control action is proportional to the derivative of the error
R. There is no “offset” in the response of the closed-loop first-order process with a proportional controller
S. There is no "offset" in the response of the closed-loop first-order process with a proportional-integral controller
- Which one of the following statements is CORRECT about proportional controllers?
- The transfer function of a Proportional-Integral (PI) controller $G_c(s)$ is given by $$G_c(s) = K_c \left(1 + \frac{1}{\tau_I s}\right)$$ where $K_c$ is the controller gain, $\tau_I$ is the controller integral time constant and $s$ is the Laplace variable. The role of the integral component of the controller is to ____________.
