bdsim 0.6

Simulate dynamic systems expressed in block diagram form using Python.

• GitHub repository: https://github.com/petercorke/bdsim
• Examples and details: https://github.com/petercorke/bdsim/wiki
• Documentation: https://petercorke.github.io/bdsim
• Dependencies: numpy, scipy, matplotlib, spatialmath, ffmpeg (if rendering animations as a movie)

Block diagram simulation

This Python package enables modelling and simulation of dynamic systems conceptualized in block diagram form, but represented in terms of Python class and method calls. Unlike Simulink or LabView we write Python code rather than drawing boxes and wires. Wires can communicate any Python type such as scalars, lists, numpy arrays, other objects, and even functions.

We first sketch the dynamic system we want to simulate as a block diagram, for example this simple first-order system

which we can express concisely with bdsim as (see bdsim/examples/eg1.py

     1	#!/usr/bin/env python3
     2	
     3	import bdsim.simulation as sim
     4	
     5	bd = sim.Simulation()
     6	
     7	# define the blocks
     8	demand = bd.STEP(T=1, pos=(0,0), name='demand')
     9	sum = bd.SUM('+-', pos=(1,0))
    10	gain = bd.GAIN(10, pos=(1.5,0))
    11	plant = bd.LTI_SISO(0.5, [2, 1], name='plant', pos=(3,0))
    12	scope = bd.SCOPE(styles=['k', 'r--'], pos=(4,0))
    13	
    14	# connect the blocks
    15	bd.connect(demand, sum[0], scope[1])
    16	bd.connect(plant, sum[1])
    17	bd.connect(sum, gain)
    18	bd.connect(gain, plant)
    19	bd.connect(plant, scope[0])
    20	
    21	bd.compile()   # check the diagram
    22	bd.report()    # list all blocks and wires
    23	
    24	bd.run(5)  # simulate for 5s
    25	
    26	bd.dotfile('bd1.dot')  # output a graphviz dot file
    27	bd.savefig('pdf')      # save all figures as pdf
    28	
    29	bd.done()

which is just 18 lines of code.

The red block annotations in the diagram are the names of blocks, and have become names of instances of object that represent those blocks. The blocks can also have names which are used in diagnostics and as labels in plots.

In bdsim all wires are point to point, a one-to-many connection is implemented by many wires.

Ports are designated using Python indexing and slicing notation, for example sum[0]. Whether it is an input or output port depends on context. Blocks are connected by connect(from, to_1, to_2, ...) so an index on the first argument refers to an output port, while on the second (or subsequent) arguments refers to an input port. If a port has only a single port then no index is required.

A bundle of wires can be denoted using slice notation, for example block[2:4] refers to ports 2 and 3. When connecting slices of ports the number of wires in each slice must be consistent. You could even do a cross over by connecting block1[2:4] to block2[5:2:-1].

Line 22 shows a report, in tabular form, showing all the blocks and wires in the diagram.

Blocks::

  id  name                  nin    nout    nstate  
----  ------------------  -----  ------  --------  
0     source.step.demand  0      1       0         
1     function.sum.b1     2      1       0         
2     function.gain.b2    1      1       0         
3     transfer.LTI.plant  1      1       1         
4     sink.scope.b4       2      0       0         

Wires::

  id  from    to      description                     type     
----  ------  ------  ------------------------------  -------  
0       0[0]    1[0]  step.demand[0] --> sum.b1[0]    int      
1       0[0]    4[1]  step.demand[0] --> scope.b4[1]  int      
2       3[0]    1[1]  LTI.plant[0] --> sum.b1[1]      float64  
3       1[0]    2[0]  sum.b1[0] --> gain.b2[0]        float64  
4       2[0]    3[0]  gain.b2[0] --> LTI.plant[0]     float64  
5       3[0]    4[0]  LTI.plant[0] --> scope.b4[0]    float64  

Line 24 runs the simulation for 5 seconds

s.run(5)

using the default variable-step RK45 solver and saves output values at least every 0.1s. The scope block pops up a graph

Line 27 causes the graphs in all displayed figures to be saved in the specified format, in this case the file would be called scope.b4.pdf.

Line 28 blocks the script until all figure windows are closed, or the script is killed with SIGINT.

To save the results is achieved by

out = s.run(5, dt=0.1)

The result out is effectively a structure with elements

• t the time vector: ndarray, shape=(M,)
• x is the state vector: ndarray, shape=(M,N)
• xnames is a list of the names of the states corresponding to columns of x, eg. "plant.x0"

Line 26 attempts to produce something like a real block diagram by generating produce a Graphviz .dot file. Using dot we can generate a graphic

% dot -Tpng -o demo.png demo.dot 

or neato

% neato -Tpng -o demo.png demo.dot

While this is topologically correct, it's not quite the way we would expect the diagram to be drawn. dot ignores the pos options on the blocks while neato respects them, but is prone to drawing all the lines on top of each other.

Sources are shown as 3D boxes, sinks as folders, functions as boxes (apart from gains which are triangles and summing junctions which are points), and transfer functions as connectors (look's like a gate). To create a decent looking plot you need to manually place the blocks using the pos argument to place them. Unit spacing in the x- and y-directions is generally sufficient.

Other examples

In the folder bdsim/examples you can find a couple of runnable examples:

• eg1.py the example given above
• waveform.py two signal generators connected to two scopes

Examples from Chapter four of Robotics, Vision & Control (2017):

• rvc4_2.py Fig 4.2 - a car-like vehicle with bicycle kinematics driven by a rectangular pulse steering signal
• rvc4_4.py Fig 4.4 - a car-like vehicle driving to a point

• rvc4_6.py Fig 4.6 - a car-like vehicle driving to/along a line

• rvc4_11.py Fig 4.11 a car-like vehicle driving to a pose

Figs 4.8 (pure pursuit) and Fig 4.21 (quadrotor control) are yet to be done.

Limitations

There are lots! The biggest is that bdsim is based on a very standard variable-step integrator from the scipy library. For discontinuous inputs (step, square wave, triangle wave, piecewise constant) the transitions get missed. This also makes it inaccurate to simulate hybrid discrete-continuous time systems. We really need a better integrator.