| algebra |
A branch of math that uses known quantities to find unknown quantities. Algebra can be used for functions involving regular shapes and straight lines. |
| calculus |
A type of mathematics that measures changes in one quantity in relation to another. Calculus is used for functions involving curves. |
| closed-loop system |
A type of control system that automatically changes the output based on the difference between the feedback signal to the input signal. |
| continuous function |
A function that can be compared to a bridge that connects a road on both sides. Just as a bridge allows you to drive along the road with no interruptions, obstacles, or detours, a continuous function allows you to draw a line or a curve without lifting your pencil. |
| coordinate |
A number that indicates a location in 2- or 3-dimensional space. Two-dimensional graphs use x- and y-coordinates. |
| delta |
A mathematical operator used to indicate a change in a value. It is represented by the Greek letter Δ. |
| dependent variable |
A value that is typically the output of a function. |
| derivative |
The rate of change. |
| difference quotient |
The ratio of the change in y-values over the change in x-values. The difference quotient is simply a more complex variation of the formula for slope. |
| differentiation |
The process of determining the rate of change of a curve. |
| discontinuous function |
A function that has a break, hole, or jump in the graph. |
| error |
The difference between the setpoint and the process variable. When errors are detected, the controller sends instructions to the control system to adjust the output to compensate. |
| function |
A relationship between two things in which the value of one thing depends on the value of the other. Functions can be represented by graphs. |
| graph |
A two-dimensional representation of a function on an x- and y-axis. |
| independent variable |
A value that is typically used as input for a function. |
| input |
The value or independent variable entered into a function. |
| integral |
A small part of a larger whole. |
| integration |
The process of summing up small areas under a curve to determine the total area. |
| limit |
A value that you would expect the function to go to, or a value that gets extremely close to the value you want to reach. |
| line |
A set of two or more points that extend endlessly in two directions. A line is the quickest way to get from one point to another. |
| linear equation |
An equation of the form y = ax + b, where a and b can be any real number. Linear equations are a way to represent lines. |
| negative slope |
When a line goes down and to the right. |
| output |
The end result or dependent variable of a function. |
| PID control |
One of the most common types of process control. Proportional, integral, derivative control adjusts system outputs when there is a difference between the setpoint and process variable. |
| point |
A dot that indicates a definite position or location. A point has no width, depth, or length. |
| positive slope |
When a line goes up and to the right |
| process variable |
The actual value detected by a sensor as a process is taking place. |
| rise |
The vertical movement of a line. |
| run |
The horizontal movement of a line. |
| secant line |
A line that intersects the graph at two points. |
| setpoint |
A preset value such as a specific temperature, speed, or flow rate that the control system is supposed to reach. |
| slope |
A measure of the slant or steepness of a line. |
| substitution method |
The simplest method for evaluating limits. In the substitution method, you replace x with another value. |
| summing junction |
The part of a PID control system in which the SP and PV are compared to each other. The difference between the SP and PV is called error. |
| tangent line |
A line that touches the graph only once. |