Controls Glossary

control effort

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

control input

The input of a plant used for the purpose of controlling it

control law

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


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


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


Reference minus an output or state.


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


An input to the plant (hence the name) that can be used to change the plant’s state.

  • 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 input to the system.


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


A set of mathematical equations that reflects some aspect of a physical system’s 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.


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


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


The system or collection of actuators being controlled.

process variable

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


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

rise time

The time a system takes to initially reach the reference after applying a step input.


The term used to describe the reference of a PID controller.

settling time

The time a system takes to settle at the reference after a step input is applied.


A characteristic of a system (e.g., velocity) that can be used to determine the system’s 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 system’s state is often represented by the variable \(\mathbf{x}\), a column vector with one entry per state.

steady-state error

Error after system reaches equilibrium.

step input

A system input 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 system to a step input.


A term encompassing a plant and it’s interaction with a controller and observer, which is treated as a single entity. Mathematically speaking, a system maps inputs to outputs through a linear combination of states.

system identification

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

system response

The behavior of a system over time for a given input.


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


\(\hat{\mathbf{x}}\), or x-hat: the estimated state of a system, as estimated by an observer.