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Tutorial Contents
In the first tutorial, I have briefly explained the usage of Xcos for a control system design and its benefits. In this tutorial, I will be talking about simulating state space model of mass-damper-spring system with the powerful toolbox Xcos. Firstly, I will derive the state space model of mass-damper-spring system. It can be showed as;
Figure 1: Mass-Spring-Damper System
This system is a very common problem to solve. Governing equation of the system is a second order ordinary differential equation. From the Newton's second law of motion it can be derived as;
Figure 2: Forces on the mass
When we apply Newton's second law of motion to the Figure [2];
Now I will talk about the Xcos blocks that we will use for simulation. Firstly the state space block which is named in Xcos Palette as CLSS open the Palette and check for continuous time systems;
Figure 3: Xcos Palette Browser
We need to provide A, B, C, D matrices, which are obtained from the mathematical model itself, to this block from the workspace of the Scilab. When I use this block, I will explain how we are gonna do it. This block takes the system inputs and outputs the system outpus. In our case, the input will be Force and the output will be displacement.
Second block is called Clock and in Xcos Palette Browser it is named as CLOCK_c. When we open the Palette Browser;
Figure 4: Xcos Palette Browser
This block continuously gives time of the simulation as output. For drawing purposes we will need this block.
Third block and Fourth blocks are commonly used blocks in simulations. They are called Step Input and Scope blocks and in Xcos they are named as STEP_FUNCTION, CSCOPE. In the Palette Browser they can be found from;
Figure 5: Xcos Palette Browser
Step function block is used for generating step input at a specified simulation time. Since we need input for the simulation we will use this block for continuous force generation. Cscope block draws a 2-D plot and input determines the y axis and the red input is the time input and it determines the x axis of this plot.
Building System in Xcos
Firstly, I will set up the state-space system and simulate it. In order to do this initially we need A, B, C, D matrices defined in the Scilab Workspace. It can be done as;
Figure 6: Scilab Console
They can be set up by typing in Scilab Console and they will appear in Variable Browser. All the variables defined in the Variable Browser can be used in Xcos with same name. Now open the CLSS in Xcos and type variable names;
Figure 7: CLSS block input parameters
When double clicked on this block a window will open as shown in Figure [7]. In this window, we will write variable names defined in Variable Browser initially. Moreover, it asks for initial states. For this simulation since we have two variable which are displacement and velocity I have initialize them as 0.
After that we will use step input block to give force input to the system. When we double click on this block a window will pop up which is;
Figure 8: Step Function Block
In this block, Step Time determines the time when output of this block jumps from Initial Value to Final Value. Since I will apply 0 force until first second and after that constant 1 Newton force no need to change any parameter in this block. Now our system will look like;
Figure 9: Block Diagram for State Space
Now what will this system do is that, state space block takes the input coming from the step function and determines the variable dots and integrates them and generates outputs as variables we want to determine and send to the scope block. Before running the system we need to configure the simulation.
Figure 10: Simulation Setup
From this parameters simulation time can be set. Set Final Integration Time to 15 in order to set simulation time to 15 seconds.
When we run the Xcos, the scope block gives us;
Figure 10: State Space Results to a Given 1 Newton Force
Results are as we expected the system starts from zero and oscillates. One way of modelling and simulating in Xcos a dynamic system is that. Other way of doing this is using integrating block and more complicated way which will be showed in the next tutorial. I hope this tutorial will be helpful for you guys :)
Xcos Program
[- Xcos Code] https://drive.google.com/open?id=12AJG2XdGVL2Gka3T7EjQfzPB5u9JCeTY
Curriculum
[ Tutorial-1] Simple Control System Design with XCOS - Scilab Tutorial
References
