# Controls Glossary¶

control effort

A term describing how much force, pressure, etc. an actuator is exerting.

control input

The input of a used for the purpose of controlling it

control law

A mathematical formula that generates to drive a to a desired , given the current . A common example is the control law $$\mathbf{u} = \mathbf{K(r - x)}$$

controller

Used in position or negative feedback with a to bring about a desired by driving the difference between a signal and the to zero.

dynamics

A branch of physics concerned with the motion of bodies under the action of forces. In modern control, systems evolve according to their dynamics.

error

minus an or .

gain

A proportional value that relates the magnitude of an input signal to the magnitude of an output signal. In the signal-dimensional case, gain can be thought of as the proportional term of a PID controller. A gain greater than one would amplify an input signal, while a gain less than one would dampen an input signal. A negative gain would negate the input signal.

hidden state

A that cannot be directly measured, but whose can be related to other states.

input

An input to the (hence the name) that can be used to change the .

• Ex. A flywheel will have 1 input: the voltage of the motor driving it.

• Ex. A drivetrain might have 2 inputs: the voltages of the left and right motors.

Inputs are often represented by the variable $$\mathbf{u}$$, a column vector with one entry per to the .

measurement

Measurements are that are measured from a , or physical system, using sensors.

model

A set of mathematical equations that reflects some aspect of a physical behavior.

moment of inertia

A measurement of a rotating body’s resistance to angular acceleration or deceleration. Angular moment of inertia can be thought of as angular mass. See also: Moment of inertia.

observer

In control theory, a system that provides an estimate of the internal of a given real from measurements of the and of the real . WPILib includes a Kalman Filter class for observing linear systems, and ExtendedKalmanFilter and UnscentedKalmanFilter classes for nonlinear systems.

output

Measurements from sensors. There can be more measurements then states. These outputs are used in the “correct” step of Kalman Filters.

• Ex. A flywheel might have 1 from a encoder that measures it’s velocity.

• Ex. A drivetrain might use solvePNP and V-SLAM to find it’s x/y/heading position on the field. It’s fine that there are 6 measurements (solvePNP x/y/heading and V-SLAM x/y/heading) and 3 states (robot x/y/heading).

Outputs of a are often represented using the variable $$\mathbf{y}$$, a column vector with one entry per (or thing we can measure). For example, if our had states for velocity and acceleration but our sensor could only measure velocity, our, our vector would only include the 's velocity.

plant

The or collection of actuators being controlled.

process variable

The term used to describe the output of a in the context of PID control.

reference

The desired state. This value is used as the reference point for a controller’s error calculation.

rise time

The time a takes to initially reach the after applying a .

setpoint

The term used to describe the of a PID controller.

settling time

The time a takes to settle at the after a is applied.

state

A characteristic of a (e.g., velocity) that can be used to determine the future behavior. In state-space notation, the state of a system is written as a column vector describing it’s position in state-space.

• Ex. A drivetrain system might have the states $$\begin{bmatrix}x \\ y \\ \theta \end{bmatrix}$$ to describe it’s position on the field.

• Ex. An elevator system might have the states $$\begin{bmatrix} \text{position} \\ \text{velocity} \end{bmatrix}$$ to describe its current height and velocity.

A state is often represented by the variable $$\mathbf{x}$$, a column vector with one entry per .

after reaches equilibrium.

step input

A that is $$0$$ for $$t < 0$$ and a constant greater than $$0$$ for $$t \geq 0$$. A step input that is $$1$$ for $$t \geq 0$$ is called a unit step input.

step response

The response of a to a .

system

A term encompassing a and it’s interaction with a and , which is treated as a single entity. Mathematically speaking, a maps to through a linear combination of .

system identification

The process of capturing a in a mathematical model using measured data. The characterization toolsuite uses system identification to find kS, kV and kA terms.

system response

The behavior of a over time for a given .

x-dot

$$\dot{\mathbf{x}}$$, or x-dot: the derivative of the vector $$\mathbf{x}$$. If the had just a velocity , then $$\dot{\mathbf{x}}$$ would represent the 's acceleration.

x-hat

$$\hat{\mathbf{x}}$$, or x-hat: the estimated of a system, as estimated by an .