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.

$ pip install simupy

$ git clone https://github.com/simupy/simupy.git
$ pip install -e simupy