pathsim.blocks.differentiator module

class pathsim.blocks.differentiator.Differentiator(f_max=100.0)

Bases: Block

Differentiates the input signal (SISO) using a first order transfer function with a pole at the origin which implements a high pass filter.

\[H_\mathrm{diff}(s) = \frac{s}{1 + s / f_\mathrm{max}}\]

The approximation holds for signals up to a frequency of approximately f_max.

Note

Depending on ‘f_max’, the resulting system might become stiff or ill conditioned! As a practical choice set f_max to 3x the highest expected signal frequency.

Example

The block is initialized like this:

#cutoff at 1kHz
D = Differentiator(f_max=1e3)

Parameters:

f_max (float) – highest expected signal frequency

op_dyn

internal dynamic operator for ODE component

Type:

DynamicOperator

op_alg

internal algebraic operator

Type:

DynamicOperator

set_solver(Solver, **solver_args)

set the internal numerical integrator

Parameters:

• Solver (Solver) – numerical integration solver class

• solver_args (dict) – parameters for solver initialization

update(t)

update system equation fixed point loop

Parameters:

t (float) – evaluation time

Returns:

error – absolute error to previous iteration for convergence control

Return type:

float

solve(t, dt)

advance solution of implicit update equation

Parameters:

• t (float) – evaluation time

• dt (float) – integration timestep

Returns:

error – solver residual norm

Return type:

float

step(t, dt)

compute update step with integration engine

Parameters:

• t (float) – evaluation time

• dt (float) – integration timestep

Returns:

• success (bool) – step was successful

• error (float) – local truncation error from adaptive integrators

• scale (float) – timestep rescale from adaptive integrators