# 9: Proportional-Integral-Derivative (PID) Control

- Page ID
- 22411

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

- 9.2: P, I, D, PI, PD, and PID control
- A variety of process controls are used to manipulate processes, however the most simple and often most effective is the PID controller. The controller attempts to correct the error between a measured process variable and desired setpoint by calculating the difference and then performing a corrective action to adjust the process accordingly. A PID controller controls a process through three parameters: Proportional (P), Integral (I), and Derivative (D).

- 9.3: PID Tuning via Classical Methods
- When a mathematical model of a system is available, the parameters of the controller can be explicitly determined. However, when a mathematical model is unavailable, the parameters must be determined experimentally. Controller tuning is the process of determining the controller parameters which produce the desired output. Controller tuning allows for optimization of a process and minimizes the error between the variable of the process and its set point.

- 9.5: PID tuning via Optimization
- Tuning a controller is a method used to modify the effect a process change will have on the piece of equipment being controlled. The goal of tuning a system is to construct the most robust process possible. The method chosen for tuning a system varies depending on the parameter being measured, the sensitivity of the materials, the scale of the process, and many other variables unique to each process. This chapter discusses the basics of tuning a controller using predictive methods.

- 9.6: PID Downsides and Solutions
- A proportional-integral-derivative (PID) controller is one of the most common algorithms used for control systems. It is widely used because the algorithm does not involve higher order mathematics, but still contains many variables. The amount of variables that are used allows the user to easily adjust the system to the desired settings. The algorithm for the PID uses a feedback loop to correct the difference between some measured value and the setpoint.