simulink c: advanced features

Mechlab, Brno University of Technology (R. Grepl, [email protected])

Simulink C: Advanced features

Robert GreplInstitute of Solid Mechanics, Mechatronics and Biomechanics

Faculty of Mechanical Engineering, Brno University of Technology

2008-2016

Simulating Dynamic Systems

After the click on “Run”, Simulink does following: [Simulink docs]

Model Compilation– Evaluates the model's block parameter expressions to determine their

values.

– Determines signal attributes, e.g., name, data type, numeric type, and dimensionality.

– A process called attribute propagation is used to determine unspecified attributes.

– Performs block reduction optimizations.

– Flattens the model hierarchy by replacing virtual subsystems with the blocks that they contain.

– Determines the block sorted order.

– Determines the sample times of all blocks in the model whose sample times you did not explicitly specify.

www.mechlab.czISMMB, Faculty of Mechanical Engineering, Brno University of Technology

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Simulating Dynamic Systems

Link Phase– In this phase, the Simulink engine allocates memory, creates method

execution lists(the most efficient order in which to invoke a model's block methods to compute its outputs).

Simulation Loop Phase– Loop Initialization phase – occurs once at the start of the loop.

– Loop Iteration phase – repeated once per time step from the simulation start time to the simulation stop time.

1. Computes the model's outputs.

2. Computes the model's states - the Simulink engine computes a model's states by invoking a solver.

3. Optionally checks for discontinuities in the continuous states of blocks – Zero-Crossing Detection.

4. Computes the time for the next time step.


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Solver

Solver = algorithm for computing model states. How to compute model states? This depends on the type of the dynamical system.

Discrete-Time System – described by difference equation(s)

– solution = evaluation of an equation

– Solver in Simulink: Fixed-Step / discrete

Continuous-Time System – described by ordinary differential equations = ODE

– solution = numerical integration.

– Solvers in Simulink: Fixed-Step / ode1, ode2, ode3,ode4, ode5,ode8, ode14xVariable-Step / ode45, ode23, ode113, ode15s, ode23s, ode23t, ode23tb


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Solvers – ode1 = Euler

initial value problem:

Euler approximation of solution:


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0( ) ( ( ), ), ( 0)y t f y t t y t y

1 ( , )n n n ny y hf y t

Solvers

What means “Fixed step” and “Variable step”?

types of solvers– fixed step

– variable stepThe variable-step solvers in the Simulink product dynamically vary the step size during the simulation. Each of these solvers increases or reduces the step size using its local error control to achieve the tolerances that you specify. Computing the step size at each time step adds to the computational overhead but can reduce the total number of steps, and the simulation time required to maintain a specified level of accuracy. [Simulink help – Choose a Solver]


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How solver determines the time step?

Experiment: solver: ode45

model: sine input, integrator.

1. t_sim = 10 -> number of steps = 51

2. t_sim = 110 -> number of steps = 51


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How to get number of steps?1. Set “Save data to

workspace”in Scope.2. length(ScopeData.time)


What is happening if the time of simulation further increase?


8-100 0 100 200 300 400 5000

20

40

60

80

100

120

140

160

180

200

time of simulation

nr.

of

ste

ps



Experiment #2: Minimalistic model

Warning: The model 'example_minimalistic_model' does not have continuous states, hence Simulink is using the solver 'VariableStepDiscrete' instead of solver 'ode45'.


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Experiment #3:


10

-100 0 100 200 300 400 5000

20

40

60

time of simulation

nr.

of

ste

ps



Now, let’s study the length of time step.Experiment #4:

o model = mechanical oscillator

o stiffnes k will be changed and the length of time step plot.


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0 5 10 15 200.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

k = 0.01

2

10

25

100



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Nonlinear model

k = 10

b = 2

How the step size is changed using different solvers?

0 5 10 15 20-1

-0.5

0

0.5

1

0 5 10 15 200

0.1

0.2

0.3

0.4

0.5

t [s]

ste

p s

ize

ode45

ode15s

ode23

ode45

ode15s

ode23

{SL07}


Sample Times

Discrete sample time[positive_num offset]

Continuous sample time [0 0]

Fixed-in-Minor steps [0 1]Simulink does not execute the block at the minor time steps; updates occur only at the major time steps. This process eliminates unnecessary computations of blocks whose output cannot change between major steps. [help]

% [0 offset] : Continuous sample time

%

%

% [-1, 0] : Inherited sample time

% [-2, 0] : Variable sample time

block.SampleTimes = [0 0];


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Run simulation programmatically – command sim

command sim:simOut = sim('model', 'ParameterName1',Value1,...)

simOut = sim('pendulum','StopTime', '15')

How to plot results? ScopeData = simOut.get('ScopeData')

plot(ScopeData.time, ScopeData.signals.values,'b-o')

simOut.who – lists variables available in the output object

Alternatively, you can say:simOut = sim('model', ConfigSet)

where ConfigSet includes all parameters. How to get ConfigSet:configSet = getActiveConfigSet('pendulum')

– This may be useful, the several sets can be stored, ...


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{SL07}


Run simulation programmatically – sim old-fashioned

Backwards Compatible Syntax[T,X,Y] =sim('model',Timespan, Options, UT)

options = simset('Refine',2)

[T,X,Y] = sim('pendulum',[0 15], options)

plot(T,X(:,1),'k-o')


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Run simulation programmatically – sim_set

Alternative – start, stop, pause, continue simulation usingsim_set

set_param('my_pendulum','SimulationCommand','start')

get_param('my_pendulum','SimulationStatus')

set_param('my_pendulum','SimulationCommand','pause')

set_param('my_pendulum','SimulationCommand','WriteDataLogs')

set_param('my_pendulum','SimulationCommand','stop')


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{SL08}


Control and Display the Sorted Order


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Custom Blocks

Custom block types:

SubSystem

Fcn

Interpretted MATLAB Function

MATLAB Function

Level-2 MATLAB S-Function

C MEX S-Function


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S-functions

How S-Functions works? -> How Simulink works? Dynamical system:

output is calculated based on states and input

states are discrete and continuous:


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An S-function comprises a set of S-function callback methods that perform tasks required at

each simulation stage.

S-function template msfuntmpl_basic

Template for s-function consists of these functions:function my_sfcn(block)

setup(block);

function setup(block)

function DoPostPropSetup(block)

function InitializeConditions(block)

function Start(block)

function Outputs(block)

function Update(block)

function Derivatives(block)

function Terminate(block)


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S-function – Major and minor steps

What is Minor step:Some continuous solvers subdivide the simulation time span into major and minor time steps, where a minor time step represents a subdivision of the major time step. The solver produces a result at each major time step. It uses results at the minor time steps to improve the accuracy of the result at the major time step. [help]


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S-function – How to animate simulation results

model penddemo, s-function pendan.m

Some tricks...:– The handle to Figure (properties, lines, ...) is stored in ‘UserData’ of

the S-function Simulink block. To acces Figure, say: Fig = get_param(gcbh,'UserData');

– Use line + set(hline,'XData',x,...) instead of plot(...)


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{SL10}


Optimizing Graphics Performance

Set automatic-mode properties to manual whenever possible to prevent MATLAB from performing unnecessary operations.

Modify existing objects instead of creating new ones.

Use low-level core objects when creating objects repeatedly.

Do not recreate legends or other annotations in a program loop; add these after you finish modifying the graph.

Set the text Interpreter property to none if you are not using TeX characters.

Try various renderers and erase modes. MATLAB might not have auto-selected the fastest renderer for your application.


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www.mechlab.czInstitute of Solid Mechanics, Mechatronics and Biomechanics

Faculty of Mechanical EngineeringBrno University of Technology

Contakt: assoc. prof. Robert Grepl, [email protected], tel.: +420 5114 288

simulink c: advanced features

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