ME422 Mechanical Control Systems Matlab/Simulink Hints and Tips

Transcription

1 Cal Poly San Luis Obispo Mechanical Engineering ME Mechanical Control Systems Matlab/Simulink Hints and Tips Ridgely/Owen, last update Jan Building A Model The way in which we construct models for analyzing control systems is slightly different from that in which you may have built models for other classes such as ME6. In Controls, we use the Simulink block diagram form to represent most or all of the mathematics in our system instead of placing large portions of our code inside s-function blocks. We do this because hiding our code inside s-functions makes it more difficult to visualize, modify, and debug our simulations; also, it is important to be able to view and record signals inside the simulation as well as the inputs and outputs. Building the model from many simple blocks allows us to quickly view what s happening anywhere in the model. An Example Below is shown a simple example model. This model represents the dynamic equation ẋ =.5x(t) + u(t). The variable x is the state of the system; it could be the velocity of a vehicle for example. The input to the system, which is some function of time, is u(t). Here, u(t) is a step input. The step input is a time-varying value which changes from one specified value to another at a specified time. In this example the input changes from to at a simulation time of one second. The number.5 is the feedback gain of the system; for reasons you will soon learn, it must be negative for the system to behave. Note how the number.5 is combined with a negative sign on the summing block to create a gain of.5. x dot Step Input u(t) x dot s Integrator x Scope.5 Feedback simout To Workspace Model Components The system inputs come from the Sources set. You will use step inputs and constants frequently. Double-click on each to set its parameters; for example, a step input has a beginning value, and ending value, and the time at which it changes from one to the other. Common Math Operations include addition and multiplication. Addition is accomplished using summation blocks. Double-clicking on a block allows you to change

2 the number of inputs and their polarity. For example, the control string +-- creates a block which implements the function output = a b c. (The vertical bar controls the positions of the inputs on the summing block.) Multiplication comes in two flavors, gain and general. Gains are multiplication by a constant, as the gain.5 in the example. (Note that the gain block was flipped left-to-right with <Ctrl-I> so that the signal can travel in the correct direction across the page.) General multiplication refers to simply multiplying two numbers together and is much less commonly used in ME, which focuses on linear systems that cannot contain multiplication by non-constant numbers. Dynamic systems involve integration, which comes from the Continuous set. The integrator is shown using its Laplace transform designation, /s. To view and save your output data from Simulink, use Sinks. Two are shown. The oscilloscope ( Scope ) allows you to create graphs of system data quickly. Note how a multiplexer (or Mux, the solid bar) is used to combine two signals before they go into the scope. This causes the scope to plot two data on one graph axis. If you want two separate graphs with one plot each, double-click on the scope and set it to use inputs. Oscilloscope graphs can be printed, but the formatting and labels cannot be modified sufficiently to create good graphs for lab reports. Therefore, we use the To Workspace block to save simulation output in a variable called simout. This actually causes two variables to be created called tout and simout. The use of these variables is discussed below. Important note: Double-click on the To Workspace block and change its save format to Array before running your simulation. This is necessary to get output data in easy-to-use matrix form. If you need to save more than one signal from a test (such as position and velocity), there are two ways to do this. First you can use a multiplexer to combine multiple channels of data into a single array before saving the data. You could also use two or more to-workspace blocks, each with a different variable name. Choose whichever method you prefer. Running the Simulation Before running your simulation, you should adjust the simulation settings in the dialog box from menu item Simulation Simulation parameters... Three settings will be important here: Set the stop time so that the significant behavior of the system is clearly shown. If dynamic behavior is still happening at the end of the simulation, you should set a longer time; if all the action takes place over at the left side of the plot and the graph shows mostly straight lines after the fun stuff has died out, shorten it. Adjust the relative tolerance. The default value of is too imprecise for most ME work. Change it to 9. Go to the Workspace I/O index tab and un-check the box which limits data

3 points to last. This is needed to ensure that all your data is saved and can be plotted. Plotting Simulink Data In order to get the best looking graphs, we save our data to the Matlab workspace, where it shows up in variables called tout and simout. The first contains simulated times. These times are controlled by the part of Simulink which solves differential equations and may not be equally spaced. The second variable, simout, is an array of data; each of its columns contains values of one variable. The expression simout(:,) refers to all the data in column number of the array; simout(:,) refers to the second column, and so on. If you used multiple to-workspace blocks, you may have several more output variables; in this demonstration, we have used a multiplexer to combine two signals and save them with one to-workspace block. This data can be plotted using a script similar to the following: subplot (,, ); plot (tout, simout(:,)); title ( Derivative of X ); xlabel ( ); ylabel ( Value [units/sec] ); axis ([ -..]); subplot (,, ); plot (tout, simout(:,), -- ); title ( Value of X ); xlabel ( ); ylabel ( Value [units] ); axis ([ - 5]); % rows, one column, first graph % Default line type is solid % You must have graph title % and axis labels % This adjusts the axis scales % rows, one column, second graph % The -- means dashed line Derivative of X Value [units/sec] Value of X Value [units]

4 Note that you can vary the number of curves on one plot and the number of plots on one page. If we had wanted to plot two curves on one axis, we would have used a command like the following: plot (tout, simout(:,), tout, simout(:,), -- ); For your plotting needs, you may want to read the Matlab help pages on the following commands: plot, title, xlabel, ylabel, subplot, hold, and grid. Plotting Experimental and Simulation Data Together Oscilloscope Data For some experiments, you will need to plot data from the oscilloscope on the same graph axes as data from your simulation. This is most easily done by measuring data from an oscilloscope printout and entering it into Matlab by hand. The process might seem tedious, but for only or points it doesn t take long. First take your measurement, using proper triggering procedure (see the Triggering a Scope handout for the proper procedure), and print out the oscilloscope screen. Then measure the coordinates of data points by hand on the screen. Usually you should measure about points; sometimes you will want to measure more closely spaced points near an interesting feature on the graph and fewer points elsewhere. Now enter the coordinates of these points in Matlab as vectors one vector for time coordinates and one for each measured quantity. Note that an easy way to create a vector containing evenly spaced values in Matlab is to issue a command such as t = [:.5:]. This creates a vector of evenly spaced values,.5 apart, running from to. t = [ ]; x = [ ]; plot (tout, simout(:,), t, x, o ); title ( System Performance Test ); xlabel ( ); ylabel ( Speed [knots] ); System Performance Test Speed [knots] The formatting code o is what causes the experimental data to show up as little circles;. makes dots and + makes small plus signs. LabView Data The plotting of data from a LabView program works in much the same way as does plotting of hand data, except you need to load your experimental data from a file. This is done with the load command as follows:

5 data = load ( mydata.txt ); plot (tout, simout (:,), data(:,), data(:,), + ); title ( LabView Experiment Results ); xlabel ( ); ylabel ( Potential [volts] ); LabView Experiment Results Potential [volts] The data file mydata.txt is assumed to contain time in the first column and system output in the second column (and any subsequent columns if more data is saved). This format is used by the LabView programs in the controls lab.