Return time derivative of operand
der(x)
x.der
The equations section may contain der operator,
which returns the time derivative of its operand:
der(x) = x.der = =
der operator takes any numerical expression
as its argument:
der applied to expressions that
are continuous returns their time derivative
der applied to time argument
returns 1
der applied to expressions that
are parametric or constant returns 0
der applied to countable operands returns 0. For example,
der(a<b) returns 0 even if a and
b are variables.
The return unit of der is the unit of its
operand divided by seconds.
You can nest der operators to specify higher
order derivatives. For example, der(der(x))is the
second order time derivative of x.
The following restrictions apply:
You cannot form nonlinear expressions of the output
from der. For example, der(x)*der(x) would
produce an error because this is no longer a linearly implicit system.
For a component to compile, the number of differential equations should equal the number of differential variables.
This example shows implementation for a simple dynamic system:
The Simscape™ file looks as follows:
component MyDynamicSystem
variables
x = 0;
end
equations
x.der == (1 - x)*{ 1, '1/s' }; % x' = 1 - x
end
end
The reason you need to multiply by { 1, '1/s' } is
that (1-x) is unitless, while the left-hand side
(x.der) has the units of 1/s. Both sides of the
equation statement must have the same units.