20-sim Tutorial

Modelling and experimenting with 20-sim



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voorkant.png
voorkantplot.png

Modelling in 20-sim

20-sim is a program in which you can make a model of a physical system and simulate that model. There are
a few different ways to make a model of a system. In this manual only 1 method is shown.

The physical system

The system we are going to model in this guide is a simple mass-spring-damper system as shown in figure
1. The system is a mass M hanging from a spring and damper. The mass is pulled down by gravity.

mass_spring_damper.png
figure 1: Mass-spring-damper system


Modelling method: Iconic

The first and for most people the easiest method, is the iconic diagram method in 20-sim. With this method
it is possible to model the system like you were making a sketched diagram. So a mass is simply a mass-icon,
a damper is a damper icon and a force actuator is a force icon. These icons have to be connected to
each other so that forces and velocities can 'flow' between the elements of the model.

Open 20-sim, the program starts with a list in the Library on the left and an empty screen on the right. Now
we have to select the components we want to use and place them on the worksheet:
Library → Iconic Diagrams → Mechanical → Translation → Components
From the mechanical iconic diagrams, we have selected the translational diagrams. Here we can select the
mass, a damper and a spring, and also important, a fixed world. Drag these icons onto the worksheet.

Drag a mass, spring, damper and fixed world onto worksheet. Also drag a Force
from Library → Iconic Diagrams → Mechanical → Translational → Actuators → Force
In figure 2 you can see what it should look like.
When all components are on the worksheet, you have to connect them. To do this, you have to enable the
connection mode in 20-sim. This can be toggled by pressing the space-bar on your keyboard, or by selecting
the connection mode button in 20-sim.

Press space-bar to enable the connection mode. Then click on the force and on
the mass, to connect these two components. Also connect the mass to the spring
and damper, and connect the spring and damper to the fixed world.
After connecting the blocks, press space-bar again to enable selection mode.

20simMassspringdamper.png
figure 2: Components for a mass-spring-damper model


In figure 3 you can see how you can connect these blocks. The mass and spring have two connection ports, a
high port and a low port. These ports determine the internal direction of forces. It is best to select them in
such a way that 'the wires do not cross'. So like in figure 3, connect the mass to the filled dark green ports
(high) and the fixed world to the light, open, ports (low).

portselect.png
figure 3: The high port (Spring.p_high) is the filled green port, the other port is the low port.


Now we have a model with different connected components, but we haven't put in the right parameters yet.
Each component in 20-sim has its own default parameters, but for our model it is necessary to adapt these
parameters. By double-clicking a component, you can edit the internals of this component. This means that
you can change the behavior, by altering the equations in the component, or you can change the
parameters of a component. So if we want to set the following parameters:
  • Mass: m=1 Kg
  • Spring stiffness: k= 15 N/m
  • Damping constant: d=3 N.s/m
  • Force (gravity): F=-9.8 N
We have to double click each component and change these parameters. When you want to go back to the
worksheet, you have to press the 'Go up' button (red dot with green triangle above it). By pressing the go
down button, you can edit a selected component (same as double clicking).

Select 'Force' block and press 'Go Down' or double click. Then set:
real F = -9.8 {N}; . Press 'Go up'.

Repeat this for all components and set the right values. Make sure that you only edit the value, not the rest
of the text in the block.
We now have a complete model of the physical system.

Simulating in 20-sim

Now that we have a model of the system, we can simulate it and see if it behaves like expected. 20-sim has a
designated simulator, in which all simulations are performed. In the simulator you can set simulation
properties like simulation time, integration method and plotting properties. It is also possible to change
parameters of the model in this simulator.

Simulating the model

Start the simulator by pressing the simulator icon (graph icon in the top bar in 20-sim). In here you can
change parameters of the model by clicking on the 'parameters' button (red triangles). You can also set the
simulation properties by clicking on the 'Run' button (blue triangle with pencil). For now we leave these
settings to default and concentrate on the plotting properties. These are available from the 'Plot' button
(graph with pencil). In this plot dialogue you have to select which properties the simulator has to plot. We
are interested in the position x of the mass.

Click on the 'Plot' button (graph with pencil), and click on 'add curve'. Now
you can select a property to plot. Choose the mass in the left column, and then
the x, from the right column, see figure 4. Exit these dialogues by clicking OK.

In the simulator you can see that the position x has appeared as a legend item in the plot-window. We are all
set to perform a simulation, so press the 'Run Simulation' button (blue play button). In figure 5 you can see
what this should look like.

plotten1.png
figure 4: Select the position x of the mass


plot2.png
figure 5: The graph of position x of the mass



20-sim and transfer functions

In the previous part we have made a model of a system in iconic diagrams and simulated in time domain. In
control engineering we are almost always more interested in the frequency domain than time domain, so
we also have to make a frequency domain model of this system.

Making a transfer function in 20-sim

We are going to make a transfer function of this system by hand and put it into 20-sim. First you have to
derive this transfer function by hand. For this system this is easy and results in:



In 20-sim you have to select the 'LinearSystem' block from the signal toolbox, and fill in the numerator and
denominator.

Select: Library → Signal → Transfer Functions → LinearSystem and drag it into
the worksheet. Leave the old model in place for reference. See figure 6
TF1.png
figure 6: The linear system block and the iconic model on the same worksheet


Double click the LinearSystem block or press 'Go Down'. In this window, make
sure that the 'Transfer Function' is selected as System Description. Press
'Edit' and change the numerator to 1, and the denominator to 1 3 15. See figure
7. Close this window by clicking OK.

TFeditor.png
figure 7: Edit the transfer function via its numerator and denominator



Now the transfer function is in the Linear System Editor. And it can be analyzed in different ways. By
clicking on the different plot options (Bode, Nyquist, Pole Zero, Step and Nichols), you can see that
particular plot.
Inspect the bode, pole zero and step plot.
If you close the Linear System Editor, it asks if you want to update the graph, press yes to get a small
representation of the transfer function in the block.


Controllers in 20-sim

Now we have a model of the system and have some simulation results, we want to design and implement a
controller. There are a lot of different ways of designing and implementing controllers, and in this manual
only two ways are shown. The first method is to design and implement the controller in time domain and
tune the controller by looking at its time domain responses.

Time domain controller design and implementation

In this part we again take the mass-spring-damper model, but assume that there is no gravity. So we can
remove the static gravitational force. We also assume that we have an actuator that can generate a force on
the mass. The position of the mass can be measured with a position sensor.

Open the mass-spring-damper model and remove the force. Add a Force actuator:
Library → Iconic Diagrams → Mechanical → Translation → Actuators → Force
Actuator. Also add an absolute position sensor: Library → Iconic Diagrams →
Mechanical → Translation → Sensors → PositioSensor-Absolute. Connect the force
actuator and the position sensor to the mass.
We now have a model with actuator and sensor. We can add a reference signal and a simple PD controller
from the library. Also a plus-minus block is needed to subtract the sensor signal from the reference signal to
produce the error signal for the controller.

Library → Signal → Sources → SignalGenerator-Step. Library → Signal → Block
Diagram → PlusMinus. And the controller: Library → Signal → Control → PID
Control → Continuous → ControllerWizard.
Connect all the blocks in the right order, so connect the sensor output to the minus of the plusminus block.
Connect the reference (Step) to the plus side of the plusminus block, and connect the output of the
plusminus block to the input of the controller wizard. Connect the controller to the force actuator. Your
model should look like figure 8.

controller1.png
figure 8: Model with controller


With this controller wizard you can implement a lot of different controllers and filters. From the
ControllerWizard, you can go directly to the Linear System Editor to analyze your controller in frequency
domain with bode plots and pole zero plots, and in time domain with a step response. So this is a very
useful tool.

We are going to implement a PD controller, so open the Controller Wizard and select the PD controller from
the list. Leave the parameters at their default values and run a simulation of the controlled system.

Open ControllerWizard and select 'PD Controller'. Close the window by clicking
OK and update the graph if it ask you to. Now open the simulator (press
simulator button). Now press the plot button to set the plot properties. Select
the property you want to plot (x-position of mass), and simulate this model (Run
simulation from the Simulator).
You should see a plot of the x-position of the mass versus the time. Now we can investigate the effect of the
different PD parameters on the behavior of this feedback controlled system. Within the simulator you can
change parameters and run a second simulation. The results of the first simulation are also shown, so you
can compare the results.

In the simulator, click on the 'parameters' icon (2 red triangles) and locate
the ControllerWizard in the left screen. When you click on the ControllerWizard,
you should see the 3 parameters of this controller. Change the Kp value from 1
to 15. Click OK to close this dialogue. Run another simulation and inspect the
result. It should look like figure 9
If you would like to clear the plot screen, you can use the reset button (rewind, two blue triangles pointing
left).

PD1.png
figure 9: Two plots of the controlled system



Linearisation of the model

In the previous section we analyzed the system and controller in time-domain, we looked at the time
response of the system as result of a step function. Now we want to analyze the system in frequency domain
and also analyze the controller this way.

The first thing we need to do, is to make a frequency domain description (e.g. a transfer function) of the
system. We already did this manually (see 3.1), but now we let 20-sim do this for us.

There are different ways to do this, like: Tools frequency domain toolbox model → → linearization, and then
select an input and output. The other option is directly from the simulator, where you can define multiple
frequency responses, and select later which of them you would like to simulate.

From the simulator, choose Properties → Frequency Response. In this menu, you
can define an input and output probe. These probes define the input and output
of your desired transfer function. As input probe, choose the force of the force
actuator (ForceActuator\F), and as output choose the position of the mass
(Mass\x). Add this response by clicking on Add Frequency response, you can
change some settings here but that is not necessary now. Click OK to close this
window. In the simulator, you can choose which response you want to see by
clicking Simulation → Frequency Response, and then select one from the list.
A bode diagram should pop-up which describes the frequency domain behavior of the system. Also the
Linear System Editor should appear in which a transfer function is shown. You should notice that this
transfer function does not match the one we derived earlier. This is because 20-sim makes small mistakes
when linearizing a model. You can see that in the numerator as well as in the denominator, an extra s
appears. These s'es cancel each other out, so they don't have an effect on the behavior, but it is better when
this transfer function is just correct.
Click on Edit → Reduce system, and accept the default tolerance.
Now the correct transfer function should appear. Now you have this transfer function in the Linear System
Editor, you can analyze the system in frequency domain (Bode, Nyquist, Pole Zero) or time domain (Step).

Implementation of controller in frequency domain
Since we have a transfer function of the system, we can use that to design a controller. We could do that the
same way as in section 4.1, but we want to use a more sophisticated method. In 20-sim you can use the so
called 'Controlled Linear System' block. This is a tool which combines a transfer function of the plant
(model of the system), a transfer function of the controller with the power of the Linear System Editor. So
you can design a controller and see the effect of this controller on the behaviour of the system from the
same window. If you want to make the most use out of this tool, it is best if you already have a transfer
function of your model. Luckily we made this transfer function it the previous section, so we can use that
one. To do this, copy the transfer function to the clipboard.

In the Linear System Editor, make sure you have the Transfer function selected
as system description, and click on Edit → Copy.
If you had already closed this Linear System Editor, you can repeat section 4.2 or calculate it by hand.
We don't need the iconic model anymore, so we open a new model.
File → New → Graphical Model
In this new model, we are going to use the ControlledLinearSystem tool. In this tool, we can define our
plant (transfer function of the model), by pasting the, just copied, transfer function.

Library → Signal → Control → Controlled Linear Systems → ControlledLinearSystem,
and place this block onto the worksheet. Double click this block to open it.
Make sure that 'Plant (P)' is selected as subsystem, and click on Edit → Paste.

The transfer function of the plant should be shown in the window. You can also put in this transfer function
manually, by using the edit button.

Like in the Linear System Editor, it is now possible to show the bode plot, pole-zero and Nyquist plot for
this plant. Also a step response can be shown. These plots are the plots of the selected Sub-System (top left in
figure 10), so if you select the controller C, than the plot is for the controller. On the left side of this Sub
system window, are the real sub-systems. On the right there are the loop-transfers. So the loop transfer (L) is
the open loop transfer of the controller and plant. The Sensitivity (S) is the sensitivity function. The
Complementary Sensitivity (T) is the closed loop response.

So if you would like to design a controller for this system (Plant), these plots are very useful!

Now we are going to implement a controller in this editor. We have to select the Compensator/Controller
(C) as sub-system, and we can edit it's transfer function with the 'edit' button. It is also possible to use the
Filter editor, in which you can choose a controller and set the parameters, exactly the same as the Controller
Design Wizard in 4.1.

Select the Compensator (C) as subsystem and click on Filter. In this Filter
Editor, select the PD Controller and set the parameters to Kp=15, Kd=1 and Fd=1.
Now use the 'Linear System Editor' button to place this PD Controller into the
Controller block of the Controller Design Editor (yes). Click on OK to close
this window and do not save the model. Now the transfer function of the PD
controller is shown in the Controller Design Editor.



controllerdesigneditor.png
figure 10: The controller design editor, with plant transfer function



We can look at the open loop response of the system by selecting the Loop Transfer (L) as subsystem and
show the bode plot. If we want to see a step response of the closed loop feedback system, we can select the
Complementary Sensitivity (T) and plot the step response (figure 11).

stepresponse1.png
figure 11: Step response of the closed loop system