A framework for modeling and simulating dynamical systems.

SimuPy is a framework for simulating interconnected dynamical system models and provides an open source, python-based tool that can be used in model- and system- based design and simulation workflows. Dynamical system models can be specified as an object with the interface described in the API Documentation. Models can also be constructed using symbolic expressions, as in

from sympy.physics.mechanics import dynamicsymbols from sympy.tensor.array import Array from simupy.systems.symbolic import DynamicalSystem x = x1, x2, x3 = Array(dynamicsymbols('x1:4')) u = dynamicsymbols('u') sys = DynamicalSystem(Array([-x1+x2-x3, -x1*x2-x2+u, -x1+u]), x, u)

which will automatically create callable functions for the state equations,
output equations, and jacobians. By default, the code generator uses a wrapper
for `sympy.lambdify`. You can change it by passing the system initialization
arguments `code_generator` (the function) and additional keyword arguments
to the generator in a dictionary `code_generator_args`. You can change the
defaults for future systems by changing the module variables

import simupy.systems.symbolic simupy.systems.symbolic.DEFAULT_CODE_GENERATOR = your_code_generator_function simupy.systems.symbolic.DEFAULT_CODE_GENERATOR_ARGS = {'extra_arg': value}

A number of helper classes/functions exist to simplify the construction of models. For example, a linear feedback controller can be defined as

from simupy.systems import LTISystem ctrl = LTISystem([[1.73992128, 0.99212953, -2.98819041]])

The gains in the example come from the infinite horizon LQR based on the system linearized about the origin. A block diagram of the system under feedback control can be constructed

from simupy.block_diagram import BlockDiagram BD = BlockDiagram(sys, ctrl) BD.connect(sys, ctrl) # connect the current state to the feedback controller BD.connect(ctrl, sys) # connect the controlled input to the system

Initial conditions for systems with non-zero dimensional state can be defined
(it defaults to zeros of the appropriate dimension) and the interconnected
systems can be simulated with the `BlockDiagram`’s `simulate` method,

sys.initial_condition = [5, -3, 1] res = BD.simulate(10)

which uses `scipy.integrate.ode` as the default solver for the initial-valued
problem. The results are an instance of the `SimulationResult` class, with
array attributes `t`, `x`, `y`, and `e`, holding time, state, output,
and event values for each integrator time step. The first axis indexes the time
step. For `x`, `y`, and `e`, the second axis indexes the individual
signal components, ordered first by the order each system was added to the
block diagram then according to the system state and output specification. The
simulation defaults to the `dopri5` solver with dense output, but a different
`integrator_class` and `integrator_options` options can be used as long as
it supports a subset of the `scipy.integrate.ode` API. The default values
used for future simulations can be changed following the pattern for the
symbolic code generator options.

A number of utilities for constructing and manipulating systems and the simulation results are also included:

`process_vector_args`and`lambdify_with_vector_args`from`simupy.utils.symbolic`are helpers for code generation using`sympy.lambdify``simupy.utils.callable_from_trajectory`is a simple wrapper for making polynomial spline interpolators using`scipy.interpolate.splprep``simupy.matrices`includes tools for constructing (vector) systems using matrix expressions and re-wrapping the results into matrix form`simupy.systems.SystemFromCallable`is a helper for converting a function to a state-less system (typically a controller) to simulate`MemorylessSystem`and`LTISystem`are subclasses to more quickly create these types of systems`SwitchedSystem`is used to construct systems with discontinuities, defined by zero-crossings of the`event_equation_function`output.

The examples subdirectory includes a number of worked problems. The documentation and docstrings are also available for reference.

## Installation

SimuPy is `pip` installable

$ pip install simupy

SimuPy has been tested locally against

but tests on Travis may run with newer versions. Much of the functionality works without SymPy, so installation does not require it. The examples use matplotlib to visualize the results. Testing uses pytest. The documents are built with Sphinx == 1.6.3.

## Contributing

- To discuss problems or feature requests, file an issue. For bugs, please include as much information as possible, including operating system, python version, and version of all dependencies.
- To contribute, make a pull request. Contributions should include tests for any new features/bug fixes and follow best practices including PEP8, etc.

## Release History

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