Causal Block Diagram Assignment [15%]

General Information

• The due date is Wednesday 1 October 2008, before 23:55.
  
  
• Submissions must be done via WebCT. Beware that WebCT's clock may differ slightly from yours. As described on the Assignments page, all results must be uploaded to WebCT and accessible from links in the index.html file. There is no need to upload AToM³.
  
  
• The assignment must be made in groups of maximum 2 people. It is understood that all partners will understand the complete assignment (and will be able to answer questions about it). Clearly identify who did what.
  
  
• Grading will be done based on correctness and completeness of the solution. Do not forget to document your requirements, assumptions, design, implementation and modelling and simulation results in detail !
  
  
• Extensions, if given, will involve extending not only the alotted time, but also the assignment !
  
  

The assignment [10% of course grade]

Implement the missing functions of the simulator (atom3/Formalisms/CausalBlockDiagram/ST_CBD/ST_Simulator.py) to accomplish the following requirements:

1. [10%] The construction of the dependency graph;
2. [10%] Given an algebraic loop, detection of whether it is linear;
3. [10%] Given a linear algebraic loop, construct input for a linear solver; the format of the input should be:

   ///////////////////////////////////////////////////////////////////////////
   // Input for the solver is of the form: [M1, M2], where
   // 
   //      [[ C11, C12, C13 ],
   // M1 =  [ C21, C22, C23 ],
   //       [ C31, C32, C33 ]]
   //
   // M2 =  [ C1,  C2,  C3 ]
   //
   // represents the following linear equation system:
   // {
   //   C11*x + C12*y + C13*z = C1
   //   C21*z + C22*y + C23*z = C2 
   //   C31*z + C32*y + C33*z = C3
   // }
   // where x, y, and x are signals (block outputs) inside a strong component.
   ///////////////////////////////////////////////////////////////////////////
   

4. [10%] For each of the blocks, write the computation they need to perform. You need to implement all algebraic blocks, the test block, as well as the timeDelay blocks (delay, derivative, and integrator).

[50% -- 5% per item] Test all aspects of your simulator:

1. Simple algebraic models without loop, one for each algebraic block;
2. A non-trivial algebraic model without loop to test sorting;
3. An algebraic model with a non-linear loop;
4. An algebraic model with a linear loop ;
5. An algebraic model with at least two linear loops, and computation in between;
6. A simple Delay block model;
7. A Derivative model using delay block. Test using simple linear input. Use the same test to check the hard-coded version.
8. An Integrator model using delay block. Test using simple constant input. Use the same test to check the hard-coded version.
9. A Circle Test model using hard-coded and modelled Integrators.
10. Plot error (wrt. analytical solution) as a function of stepsize (comparing sin(t) using a Generic block with the approximate value obtained by solving x''=-x).

For the last 10%: optimizations.

Download

• atom3.tgz AToM³ with the Causal Block Diagrams formalism and a starting-point implementation of the simulator.

Tutorial

An old tutorial is available here.