# What is the point of using this derived PID controller?

Previously, I answer for this PID controller that I want to understand completly.

This is used for control the opening $$U_n$$ of a valve let gas pass and reach a certain pressure (SetPoint).

There is current error, and Tsample and 2 Tsample before. Aditionally, there is a variable that store the current change in the error respect the last , and the same Tsample before. Finally a variable that store the variation of the change of the error.

$$e_{n-2}=e_{n-1}$$ $$e_{n-1}=e_n$$ $$e_n=SetPoint-ProcessValue$$

$$P_n=e_n-e_{n-1}$$ $$P_{n-1}=e_{n-1}-e_{n-2}$$

$$Q_{n}=P_n-P_{n-1}=(e_n-e_{n-1})-(e_{n-1}-e_{n-2})$$

And the calculation of control signal, where $$dP_n$$ is the proportional part, $$dI_n$$ is the integral part, $$dD_n$$ is derivative part, $$K_p$$ is global gain, $$R_p$$ is proportional gain, $$T_i$$ integral time, $$T_d$$ derivative time, and $$dU_n$$ is the PID output:

$$dP_n=R_p*P_n$$ $$dI_n=T_i*e_n$$ $$dD_{n-1}=dD_{n}$$ $$dD_n=(Q_{n}*T_d+dD_{n-1})/2$$ $$dU_n=K_p*(dP_n+dI_n+dD_n)$$

After that, it calculate the direction of the correction, where PC (positive correction) is a variable with TRUE value if $$dU_n>0$$ and FALSE value if $$dU_n<0$$ and NC (negative correction) is TRUE if $$dU_n<0$$ and FALSE if $$dU_n>0$$.

If PC=TRUE then $$U_n$$=$$U_{n-1}$$+$$dU_n$$

If NC=TRUE then $$U_n$$=$$U_{n-1}$$-$$dU_n$$

In the post whose link I attached at the beginning of the query, Tim Wescott answered me that the step where $$U_n=U_{n−1}±dU_n$$ is a numerical integration.

He said that this is an ordinary PID controller, with a numerical derivative of every step.

What is the point of using this derived PID controller?

• In your original question, the if-then clauses are different -- there they depend on some (presumably preset) variable PC. Here, they depend on the sign of $dU_n$. This is a significant difference. Please clarify! Nov 25, 2022 at 16:33
• @TimWescott I just edited, please I await your response. From already thank you very much. Dec 2, 2022 at 11:51