# 7. Glossary¶

- 2nd order low pass filter¶
A second order low pass filter is an input-output block that computes

\[\begin{split}\dot x(t) = \begin{pmatrix} r & 0 \\ -r & r \end{pmatrix} \, x(t) + \begin{pmatrix} -r \\ 0 \end{pmatrix} \, u(t)\end{split}\]and

\[y(t) = (0, \, 1) \, x(t),\]where \(r\) is a positive real number. This causes the input signal \(u(\cdot)\) to be converted to an output signal \(y(\cdot)\) that is differentiable in time. See the plot of a filtered step response.

- compressible flow¶
The opposite of incompressible flow.

- incompressible flow¶
In fluid mechanics, incompressible flow refers to flow where the mass density is constant within a fluid volume that moves with the fluid.

- iterative solver¶
An iterative solver is a numerical solver that iterates until the approximate solution satisfies a convergence test. Examples include Newton solvers for nonlinear systems of equations, and ordinary differential equation solvers with adaptive time step length.

- numerical noise¶
In numerical solutions, numerical noise refers to fast but small changes in variables whose magnitude is typically smaller than the solver tolerance.

- regularization¶
By regularization, we mean approximating a non-differentiable function by another function that is differentiable and has continuous and bounded derivatives, i.e., a function that is continuously differentiable. Continuous differentiability is a necessary condition for Newton-based solvers to solve nonlinear equations.

- state variables¶
State variables are variables whose time rate of change is defined by a differential equation.

- thermo-fluid system¶
Thermo-fluid systems are systems that compute combined mass and energy flow, such as a heat exchanger in which heat is added to the medium that flows through it.

For a control valve, the valve authority \(N\) is defined as

\[N = \frac{\Delta p_v(1)}{\Delta p_v(1) + \Delta p_0},\]where \(\Delta p_v(1)\) is the pressure drop across the fully open valve, and \(\Delta p_v(1) + \Delta p_0\) is the pressure drop across the whole flow leg whose mass flow rate is controlled by the valve. Valves should be designed such that \(N\) is around 0.5, but not higher.