Solutions. Discretization HANS-PETTER HALVORSEN,

Transcription

1 Telemark University College Department of Electrical Engineering, Information Technology and Cybernetics Solutions HANS-PETTER HALVORSEN, Discretization Faculty of Technology, Postboks 203, Kjølnes ring 56, N-3901 Porsgrunn, Norway. Tel: Fax:

2 Table of Contents Table of Contents... ii 1 Introduction to Discretization Discrete Low-pass Filter Discrete PI Controller ii

3 1 Introduction to Discretization Task 1: Formula Node in LabVIEW A Formula Node in LabVIEW evaluates mathematical formulas and expressions similar to C on the block diagram. In this way you may use existing C code directly inside your LabVIEW code. It is also useful when you have complex mathematical expressions. Create a simple SubVI where you use the Formula Node to calculate a (slope) and b (intercept) in the equation when you have two points and. The Procedure is as follows: Step 1: Create a New VI (File New VI) (Blank VI) Step 2: Give the VI a Name (Linear Scaling.vi) Step 3: Create your Front Panel with your necessary Controls and Indicators. Example: Step 4: Switch to your Block Diagram (Ctrl+E). 3

4 4 Introduction to Discretization Step 5: Add the Formula Node to you Block Diagram: Step 6: Add Inputs and Outputs: Step 7: Create your C-code inside your Formula Node. The formula for finding the slope (a) and intercept (b) is as follows: The Block Diagram could look something like this:

5 5 Introduction to Discretization Step 8: Create the Input and Output Connectors. Right-click on the little icon in the upper right corner and select Show Connector. Step 9: Create an Icon using the Icon Editor. Right-click on the little icon in the upper right corner and select Edit Icon. Step 10: Create a new VI that you use to test your Sub VI. [End of Task] Solutions: LabVIEW program: Block Diagram: Front Panel:

6 6 Introduction to Discretization Testing the SubVI: Block Diagram: Front Panel:

7 7 Introduction to Discretization

8 2 Discrete Low-pass Filter Task 2: Discrete Low-pass Filter Create the discrete low-pass filter algorithm using pen and paper. Create a discrete low-pass filter in LabVIEW using the Formula Node in LabVIEW. Create a SubVI of the code. You will use this subvi in your project later. The user needs to be able to set the time constant of the filter T f from the outside, i.e., it should be an input to the SubVI. The simulation Time-step T s needs also to be set from the outside. Before you start implementing your SubVI, define the necessary inputs and outputs of the VI using pen and paper. Create a nice Icon for the SubVI using the Icon Editor. Create also a Help text for the SubVI which is visible when using Ctrl+H, see example above. In the Help text you should describe your VI and what it does and document the discrete algorithm you are using. The inputs and outputs should also be documented. [End of Task] Solutions: LabVIEW Program: Block Diagram: 8

9 9 Discrete Low-pass Filter Front Panel: Task 3: Testing

10 10 Discrete Low-pass Filter Make sure your filter works! Plot the input and the output of the filter in LabVIEW. Check that the filter works correct under static conditions, i.e., when all signals have constant values. Check by simulations that the filter actually has the time-constant as set on the Front panel. Describe and explain your results. Add random noise on the filter input. Analyze the results. You may, e.g., use the Uniform White Noise PtByPt.vi. [End of Task] Solutions: We test the filter: Block Diagram

11 11 Discrete Low-pass Filter Front Panel: As you can see this gives a good results. The filter take away the noise from the signal.

12 3 Discrete PI Controller Task 4: Discrete PI Controller Create the discrete PI Controller algorithm using pen and paper. Create a discrete PI controller in LabVIEW using the Formula Node. Create a SubVI of the code. You will use this subvi in your project later. Before you start implementing your SubVI, define the inputs and outputs of the VI using pen and paper. Create a nice Icon for the SubVI using the Icon Editor. Create also a Help text for the SubVI which is visible when using Ctrl+H. In the Help text you should describe your VI and what it does and document the discrete algorithm you are using. The inputs and outputs should also be documented. [End of Task] Solutions: Block Diagram: 12

13 13 Discrete PI Controller Front Panel:

14 14 Discrete PI Controller Task 5: Simulation Implement your PI controller and Low-pass filter in a simulation. You may, e.g., use the example General PID Simulator.vi as a base for your simulation. Use the NI Example Finder (Help Find Examples ) in order to find the VI in LabVIEW. Note! You will need the LabVIEW PID and Fuzzy Logic Toolkit in order to fulfill this Task. Run the example and see how it is implemented and how it works. Save the VI with a new name and replace the controller used in the example with the controller you created in the previous task.

15 15 Discrete PI Controller Find proper PID Parameters. Explain how you found them. Add your Low-pass filter to the system. Plot both the ordinary the process output (Process Value, PV) and your filtered output. What is your value and how did you found it? [End of Task] Solutions: Block Diagram: Front Panel:

16 16 Discrete PI Controller With Noise and Low-pass filter: Block Diagram:

17 17 Discrete PI Controller Task 6: Integrator Anti Windup Implement Integrator anti windup to your PI Controller. Describe how you do it. Test your PI controller with Integrator anti windup on the simulated process from the previous task. [End of Task] Solutions:

18 Telemark University College Faculty of Technology Kjølnes Ring 56 N-3914 Porsgrunn, Norway Hans-Petter Halvorsen, M.Sc. Telemark University College Department of Electrical Engineering, Information Technology and Cybernetics Phone: Blog: Room: B-237a

19 19 Discrete PI Controller