Hands-on Lab. LabVIEW Simulation Tool Kit

Transcription

1 Hands-on Lab LabVIEW Simulation Tool Kit The LabVIEW Simulation Tool Kit features a comprehensive suite of tools to test designs. This lab provides a primer to implementing a simulation. This will be useful in verifying one s models and forecasting performance in real-world implementations. Concept 1: Integrating a square wave yields a triangular one (see Figure below - left). This front panel and accompanying block diagram (Figure below right) serve to underscore simulation loops, waveform graphs and integrators. Square wave (left) and integration (right) Block diagram of simulation Step 1: Create a Simulation Loop Start with the Block Diagram. From the Programming palette, select Control Design & Simulation Simulation Simulation Loop. Click and place in your block diagram. All simulations require elements to be placed inside this loop. Next, configure the loop for a 5 second run time as follows. Click on the loop and then right click. Select Configure Simulation Parameters (see Figure 1-1A). In the pop-up box, change the Final Time (s) to be 5 seconds. Next, choose Runge-Kutta 3 as the ODE Solver (see Figure 1-1B) Figure 1-1A: Simulation Loop and Configuration Figure 1-1B: Simulation Parameters 1

2 Step 2: Add an integrator and initial conditions From the block diagram Programming palette, select Control Design & Simulation Simulation Continuous Linear Systems Integrator (see Figure 1-2A). Place the integrator inside the simulation loop. Next, set the integrator s initial conditions as follows. Right click on the integrator and select Configuration. In the pop-up box (Figure 1-2B) see the Parameter Source pull down menu. Select Terminal. Figure 1-2A: Select an Integrator Figure 1-2B: Integrator initial conditions This enables one to enter an initial condition for the integrator. For this exercise, set the initial condition to zero as follows. Create a numeric constant with a value of zero and wire it to the integrator as shown in Figure 1-2C. Figure 1-2C: Integrator s terminal wired for initial conditions 2

3 Step 3: Add Signal Generation and Waveform Display From the block diagram Programming palette, select Control Design & Simulation Simulation Signal Generation Signal Generator and drag into the simulation loop (see Figure 1-3A). Right click on the signal generator element and select Configuration. In the resulting pop-up box, select a square wave (see Figure 1-3B). Set a 1 Hz signal. ` Figure 1-3A: Select a Signal Generator Figure 1-3B: Configure 1 Hz square wave Next, add a Waveform Chart as follows. From the Programming palette, select Control Design & Simulation Simulation Graph Utilities SimTime Waveform and drag into the simulation loop (see Figure 1-3C). Wire the integrator output into the waveform generator. Add another waveform generator and wire it to the signal generator. Label these two waveform generators as Output and Input Signal respectively. Save as labviewsimulationsquarewaveintegration.vi Figure 1-3C: Signal Generator and Waveform Chart wired up 3

4 Step 4: Front Panel setup In the Front Panel, arrange the wave displays side by side (Figure 1-4A). Right click the Input Signal wave display and select Properties. Click the Scales tab and check off the Autoscale box (Figure 1-4B). Repeat this process for the Output Signal wave display. Save all and execute. The results should match those in Figure 1-4C) Figure 1-4A: Front panel with displays Figure 1-4B: Select Autoscale Figure 1-4C: Integrating a square wave (left) results in a saw tooth wave (right) 4

5 Exercise 1: In LabVIEW create programs for the following: 1.1. Add two integrators (both with zero initial conditions) that operate on a sine wave. Display the input and 2 outputs (one for each integrator) Display a saw tooth wave and its derivative (should be a square wave). Concept 2: Simulate a 2 nd order damped system The equation of motion for a damped compound pendulum (Free Body Diagram sketched above) can be derived as: && θ c ml gd sin J θ = & J θ Experience tells that such a system will oscillate (a pendulum is a 2 nd order system) but eventually stop (due to damping). The figures below illustrate this through LabVIEW simulation. Exponentially decaying sinusoid Block diagram simulation with 2 integrators 5

6 Step 1: Create a Simulation Loop In the block diagram set up a Simulation Loop with 2 integrators (with initial conditions set for Terminals see Concept 1 Step 2 if needed) and a waveform display. In the front panel, add to numeric controls labeled theta initial and theta dot initial. Let the initial theta be (i.e. 60 degrees) and initial theta dot be zero. Wire these elements in the block diagram to the integrators. The result should look like Figure 2-1A and 2-1B Figure 2-1A: Front Panel Figure 2-1B: Block diagram with 2 integrators Step 2: Implement the equations of motion The Free Body Diagram sketch shows parameter values. Given a damping coefficient c = then one has c J = = ml gd = = J Consequently, these values are used to populate the block diagram as shown in Figure 2-2A. The sine element is entered as follows. Click Express Arithmetic & Comparison Math Trigonometric Sine. Figure 2-2A: Implementing equations of motion 6

7 Step 3: Configure Simulation Loop and add Summation Set the Simulation Loop to run 30 seconds with Runge-Kutta 3 ODE Solver (recall Concept 1, Step 1 if needed). Complete the equation of motion by adding the signals. Place the Summation element as shown in Figure 2-3A, click Control Design & Simulation Simulation - Signal Arithmetic Summation. Right click on the Summation element and choose Configuration. Click on the minus sign to change it into a plus one. Complete the wire diagram as shown in Figure 2-3B. Save program as labviewsimulationdampedpendulum.vi Figure 2-3A: Complete the equations of motion Figure 2-3B: Summation element In the Front Panel, configure the waveform display Scale to be Autoscale. Save and execute the program should yield results shown in Figure 2-3C. Figure 2-3C: Simulating the 2 nd order damped compound pendulum reveals an exponentially decaying sinusoid. The initial condition for theta was set for 60 degrees (or radians). 7

8 Exercise 2: 2-1: The damping ratio and natural frequency for 2 nd order systems can be calculated using logarithmic decrement. Recall that if a and b are the heights of subsequent peaks, as shown in the figure below: Calculate the damping ratio ζ and natural frequency ωn for the Concept 2 simulation 8