An Introduction to Xcos

Transcription

1 A. B. Raju Ph.D Professor and Head, Electrical and Electronics Engineering Department, B. V. B. College of Engineering and Technology, HUBLI , KARNATAKA 28 th September 2010

2 Outline of Presentation 1 Ordinary Differential Equations 2 Why Scilab/Xcos? 3 How do I construct dynamic models? 4 More examples

3 Ordinary Differential Equations These equations are of great importance in Science and Engineering Many physical laws and relations appear mathematically in the form of differential equations A physical law involving a rate of change of function, such as velocity or acceleration it leads to a differential equation

4 Example (1): Experiments show that a radioactive substance decomposes at a rate proportional to the amount present. Starting with a given amount of substance, say, 2 gms, at a certain time, say, t=0, what can be said about the amount available at a later time? dy dt = ky where k is a constant, whose value depends on the radioactive substance.

5 Example (2): The tank shown below contains 200 gal of water in which 40 lb of salt are dissolved. Five gal of water, each containing 2 lb of dissolved salt, run into the tank per minute, and the mixture, kept uniform by stirring, run out at the same rate. Find the amount of salt y(t) in the tank at any time t. dy dt = inflow rate outflow rate = y

6 Example (3): A body slides on a surface, it experiences friction force F. Experiments show that F = µ N. Assume that the body weighs 45 nt (about 10 lb), µ = 0.20, α = 30 0, the slide is 10 mtr long, initial velocity is zero. Find the velocity of the body at the end of the slide. s(t) W α y N W v(t) Ν F (W/g )*a x Equating horizontal and vertical forces, we get N = W cos α F = µn = µw cos α 0 = W sin α µw cos α W g dx dt

7 Example (4): Find the transfer function, X(s)/F(s) for the system given below. x(t) K M f(t) D Equating horizontal forces, we get f(t) = M d2 x(t) dt 2 + D dx(t) dt + Kx(t)

8 Example (5): RL circuit R V + i L The corresponding differential equation is given by: di dt = 1 (V ir) L

9 How do I solve such differential equations? 1 Get all the data required for the solution (viz., all constants, initial conditions, time-step etc)

10 How do I solve such differential equations? 1 Get all the data required for the solution (viz., all constants, initial conditions, time-step etc) 2 Select a suitable numerical integration algorithm among many available methods

11 How do I solve such differential equations? 1 Get all the data required for the solution (viz., all constants, initial conditions, time-step etc) 2 Select a suitable numerical integration algorithm among many available methods 3 Write a program to implement selected algorithm using any programing languages (viz., C, C++, Fortran, Scilab, Matlab etc)

12 How do I solve such differential equations? 1 Get all the data required for the solution (viz., all constants, initial conditions, time-step etc) 2 Select a suitable numerical integration algorithm among many available methods 3 Write a program to implement selected algorithm using any programing languages (viz., C, C++, Fortran, Scilab, Matlab etc) 4 Collect data required for visualization

13 How do I solve such differential equations? 1 Get all the data required for the solution (viz., all constants, initial conditions, time-step etc) 2 Select a suitable numerical integration algorithm among many available methods 3 Write a program to implement selected algorithm using any programing languages (viz., C, C++, Fortran, Scilab, Matlab etc) 4 Collect data required for visualization 5 Interpret results so obtained

14 Let us see the implementation of aforementioned steps in action: Run rlckt1.sce from Scilab

15 Why Scilab/Xcos? 1 Xos/Scicos: Scilab connected object simulator visual editor

16 Why Scilab/Xcos? 1 Xos/Scicos: Scilab connected object simulator visual editor 2 Scilab package for modelling and simulation of dynamic systems

17 Why Scilab/Xcos? 1 Xos/Scicos: Scilab connected object simulator visual editor 2 Scilab package for modelling and simulation of dynamic systems 3 Dynamic systems can include continuous or discrete sub-systems

18 Why Scilab/Xcos? 1 Xos/Scicos: Scilab connected object simulator visual editor 2 Scilab package for modelling and simulation of dynamic systems 3 Dynamic systems can include continuous or discrete sub-systems 4 It has a friendly GUI for editing models by interconnecting Xcos blocks

19 How do I construct dynamic models? 1 Starting Xcos with an empty diagram

20 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes

21 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes 3 Copying blocks of interest from the palettes into the diagram

22 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes 3 Copying blocks of interest from the palettes into the diagram 4 Setting parameters of the blocks to desired values

23 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes 3 Copying blocks of interest from the palettes into the diagram 4 Setting parameters of the blocks to desired values 5 Connecting the blocks input and output ports

24 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes 3 Copying blocks of interest from the palettes into the diagram 4 Setting parameters of the blocks to desired values 5 Connecting the blocks input and output ports 6 Compiling and simulating the diagram

25 How do I construct dynamic models? 1 Starting Xcos with an empty diagram 2 Opening one or more palettes 3 Copying blocks of interest from the palettes into the diagram 4 Setting parameters of the blocks to desired values 5 Connecting the blocks input and output ports 6 Compiling and simulating the diagram 7 Renaming and saving the diagram

26 Xcos implementation RL circuit will be

27 Xcos response of this circuit for R=10Ω, L=100mH and a step input voltage of 50 V is applied 6 Graphic Current (A) Time (s)

28 RLC circuit with step input voltage i V + R L V c C The corresponding differential equations are given by: di dt dv c dt = 1 L (V ir v c) = i C

29 Xcos block diagram is

30 Xcos response for R=2Ω, L=100mH, C=1000µF and a step input voltage of 50 V is applied 5 4 Graphic 1 3 Current (A) Time (s) 100 Graphic 2 80 Voltage (V) Time (s)

31 A Variable Frequency Oscillator d 2 y 1 dt 2 = ω2 y 1 Converting this equation into two first-order differential equations y 2 = ( ) 1 dy1 ω dt dy 2 dt = ωy 1

32 y y Xcos implementation isod Graphic Time (s) Graphic Time (s)

33 Separately excited/permanent magnet dc motor Motor parameters: Rated power = 2 kw Rated armature voltage = 125 V Rated armature current = 16 A Rated speed = 1750 rpm R a = 0.24 Ω, L a = 18 mh, K a φ = , J = 0.5 kgm 2, T l = ω 2 m DC Motor defining equations are: V a = di a R a i a + L a dt + K aφω K a φi a = J dω dt + Bω + T l

34

35 Xcos response is 400 Graphic 1 Speed (rps) Current (A) Time (s) Graphic Time (s)

36 DC motor closed loop speed control system

37 Xcos response is Current (A) Graphic Time (s) 150 Graphic y Time (s)

38 Thank You Any Questions?