Lectures & Excercises

Transcription

1 TLTE.3120 Computer Simulation in Communication and Systems (5 ECTS) Lecture Timo Mantere Professor, Embedded systems University of Vaasa timan@uva.fi Lectures & Excercises Lectures Wednesdays in Technobotnia class TF4104 Week 38 Thursday Ends week 44 Exercises Thursdays TF4104 Week 38 Thursday Ends week 45 Participating is not obligatory Due duties in Seinäjoki some classes might have to be rescheduled 1

2 Lecture 1 Information about Course arrangements & schedule What is Matlab What is Simulink What is Simulation Basics of modelling Course Website Follow the page continuously every piece of course material will be added there Lectures Exercises Homeworks Important announcements Course results (announcement is ed over Oodi, when results are available) 2

3 General Credits: 5 ECTS Prerequisites: one can take this course without prior knowledge of Matlab or Simulink Passing the course Passing the mandatory exercises, homeworks and final exam 50% Final homework ( Project ) 50% Final examination 0% Homeworks 0% Class exercises Grading Usual 1-5 or failed Based on points collected from mandatory exercises, homeworks and final exam Course Contents Getting started with MATLAB and SIMULINK Writing simple programs with Matlab Design simple models with Simulink Matlab and Simulink toolboxes Matlab as a part of the simulation environment Use of Matlab in Control and in Communications Possibly other simulation environments (Labview, Comsol, etc.) are briefly reviewed Combining Matlab and C (Optional, if course time is sufficient) 3

4 Matlab-Imitating Freeware/Shareware Policy The use of any kind of Matlab-imitating freeware/shareware such as Octave etc. is NOT allowed in this course The use of any other licensed mathematical software, such as Maple, Mathematica or Mathcad etc., is NOT allowed in this course Exercises or homeworks solved by using some other software than Matlab & Simulink are automatically ignored We have an up-to-date Matlab license in the University of Vaasa, and the computer classes in Technobothnia are available Why Matlab? It is not a toy The most common program for mathematical computation and simulations in professional use A huge amount of toolboxes Compatibility the program is de facto standard in professional and in research use File exchange Huge amount of Matlab-software including additional toolboxes available (one must be careful, though) 4

5 What is Matlab? MATLAB (short for matrix laboratory) is a company run by the company MathWorks It is computer software meant for numerical computations, it contains also it s own programming language. MATLAB provides opportunities for easy and efficient handling of matrices, functions, and visualization of data, implementation of algorithms, creation of user interfaces and interaction with the programs created with other languages. In addition to the basic configuration of the software, there is available a number of additional tools (toolboxes), which allows specific areas of functionality, for example, or the possibility of symbolic computation. What is Simulink? Simulink is a additional program for MATLAB that can be used to model, analyze and simulate dynamic systems in various technical areas. Systems can be linear or non-linear and can be time dependent. The time dependence can be discrete, continuous, or a mixed type. Simulink is a graphical user interface that allows the model to be created using block diagrams, which consist of blocks and signal lines. Simulink block diagrams may contain a variety of mathematical operations, MATLAB code and the inputs and outputs. Block diagrams are hierarchical, allowing both top-down and a bottom-up approach, when the model is created. 5

6 What is Simulink? Common Simulink toolboxes include e.g. Communication System Toolbox Control System toolbox DSP System Toolbox Fuzzy logic toolbox Neural Network Toolbox 3D Animation Toolbox System Identification Toolbox Etc. Learn Matlab by yourself There are Matlab training courses offered by Mathworks demy_ %2Bstudent 6

7 Matlab Many Matlab codes and Simulink systems are created all around the world and many have given their codes and models for the free use of others via Matlab file exchange (and other webpages) Matlab examples are available in Matlab tutorial videos Simulation Simulation or simulating is an imitation of reality. The reality is the world around you. Man simulate reality in their own world of imagination. An important and growing area of simulation is computer simulation. Computer simulations are used by building an artificial reality in the computer that tries to mimic the real reality, as far as it can. The simulation of the reality include, child play, many games and playing, imagination and the simulation of reality in physical or other models and their calculation (solar eclipses, exsosolar planet finding models etc.). In humans and mammals, a significant imitation of reality is a game. Simulation is often cheaper than the reality (flight simulator training), safer than the real situations (for a nuclear power plant simulator, playing war, a war game), and is often the only way to get information (atmosphere simulator to the greenhouse effect). 7

8 The basics of modeling Modeling of the systems may have started a long time ago, at least from the Isaac Newton s differential equations which he used to model physical systems Usually computer simulations require coal to which the simulation aims or physical reality that the simulation tries to mimic Typically we need to think about To what the model is used for The profitability of the modeling Users of the model What is modelled and calculated and how accurately How detailed model is needed 15 The basics of modeling Usage of the model Model can be used for several purposes, e.g. to predict the system behavior (weather, economy, population growth, climate change etc.) Basic process model uses are To improve the existing systems Changing how the system is used Improve control system To design a new process To design a new manufacturing system or equipment 16 8

9 The basics of modeling Profitability of the model In industry the profitability of the modeling and simulation have to be justified Often simulation results are abstract and the company lead requires proofs that simulation brings economic benefits and cost savings Simulation is often used for decreasing the bugs in the system in advance Profits of the model may include Direct benefits To increase the knowledge about the process Better control increases output Teaching the users to use system with the help of simulator 17 The basics of modeling The users of the model In industry models are used by designers and development managers Simulations could be used to introduce the idea for management And for teaching staff how to use a new system To introduce the system to the customers 18 9

10 The basics of modeling How detailed model is needed? If we try to define the values for different components in the system we may need very accurate model E.g. fluid flow systems, building structure strenght etc. (often static models) When planning control systems models may be less accurate, but dynamic. Models may contain transfer functions and state models and differential equations Control systems usually require feedback loops 19 The basics of modeling Modeling project consist of Preplanning Delimit, time table, resources, experiments Selecting the variables What model is used for, theory, measurements needed Designing the model structure Linear, nonlinear, real-time, state model, discrete, continuous Designing the test plan (scenarios) Doing the experiments Analyzing the results To improve the model and testing 20 10

11 Numeric calculus Matlab is an Numerical calculation system Numerical analysis is the branch of mathematics that seeks to find the approximate solution of mathematical problems that can not or need not be solved accurately. Numerical methods are often applied in the needs of physics, for example, to solve the differential equations. Numerical methods such as equations, numerical solving of function, approximation and numerical integration. An example of numerical analysis methods is forking which aims to find a continuous function zeros. Forking algorithm is as follows: Select number interval within which to examine the function, and that the end points of the function has a different sign values. (* if search zeros) Shortening of the interval at either end, so that the function gets a head to tail values of the endpoints of the interval. Repeat until the desired accuracy is achieved. Numerical and Symbolic Computation Example: Numerical computation: π sin = x e dx = Symbolic computation: π 1 sin = 4 2 Symbolic computation computation in closed form by using mathematical symbols values of the variables are irrelevant (no rounding errors) great influence in development of mathematical theories programs supporting symbolic calculus can handle algebraic expressions and calculate e.g. integrals and derivatives using symbols 1 0 x e dx = e 1 11

12 Numerical and Symbolic Calculus Numerical calculus: e.g. pocket calculator: results are always approximate values depending on the calculator s internal computation accuracy risk: is the computation accuracy sufficient? numerical methods are efficient in solving complex problems it s not even possible to solve all problems in closed form - numerical calculus is needed (sometimes iterative) many integrals are difficult to solve in symbolic form whereas numerical method would be more straightforward and faster therefore many practical applications (mathematical modeling, simulation) usually exploit numerical calculus Numerical and Symbolic Calculus The development of computer programs started at 1970 s the first programs were developed for numerical calculus due to limited computing power In the beginning it was difficult to use these programs operation based on programming e.g. Fortran (calculation of derivative using parable interpolation) Due to increased computing power graphical features and user-friendliness have become more popular subroutine deriv1(h, y, dy, n) integer n real h, hp, y(n), dy(n) hp = 0.5 / h C endpoints dy(1) = hp * (-3*y(1) + 4*y(2) - y(3)) dy(n) = hp * (y(n-2) - 4*y(n-1) + 3 y(n)) C midpoints do i = 2,n-1 dy(i) = hp * (y(i+1) - y(i-1)) end do return end 12

13 Numerical and Symbolic Calculus It may not be possible to use numerical calculus program in real time computation in some process to be controlled reason: program intended for numerical computation is not efficient enough in real time solution (if needed): implementation using C-programming language programs are efficient in development because some of the needed functions are already programmed Symbolic calculus: Mathematica Maple MathCad Numerical calculus: Matlab Excel Octave MATRIXx Some programs intended for symbolic calculus also support numerical calculus and vice versa 13