Simulink. Simulink is a software package to be run from Matlab, and it is used for simulating, modeling and analyzing dynamical systems. It is possible to work with linear and nonlinear systems, modeled in continuous time, sampled time or a mixture of them. Simulink uses graphical user interface for building up models to be simulated [7]. A library of blocks is included in Simulink and the click-and-drag mouse operations make it possible to build complete models. The block library consists of e.g. sinks, sources, linear and nonlinear components and connectors. It is also possible to write own functions, so called S- functions [8], in C code or in Matlab code. To build up a model in Simulink you choose suitable blocks and connect them with graphical connections. When a complete model is built it is possible to simulate it. Settings in Simulink can be changed in Simulinks menus or by entering commands in Matlab’s command window. The Matlab command for change settings in Simulink is set_param [7]. With different parameters for this function it is possible to control Simulink from Matlab workspace. Examples of settings can be the simulation time and if you want an ongoing simulation you choose inf in the time window. Parameters in Simulink may also be changed during the simulation. By using scopes and other display blocks, you can see the results while running the simulation. The results can be sent to a file. After the simulation you can load the file in Matlab workspace e.g. for plotting and analyzing. S-function (system function) is a block for extended functions in Simulink. An S-function is a computer language description of a dynamic system. The S-function is written in C or Matlab. To use the S-function in Simulink it has to be compiled as an MEX-file (Matlab Executable file). S-functions written in C are divided in three major parts, one to be executed in the initial part, one to be executed during running simulation and one to be executed in the termination part of the simulation. In the initial part of the S-function you declare start performance, number of inputs and outputs and the sample time for the block. In the next part of the S- function the runtime performance is declared. At last all terminations are implemented [8].
Simulink. This is a widely used tool for simulation based on control law diagrams [20]. A popular solver uses a variable-step policy based on change rate of the state. To model this algorithm, we use a process SimulinkMAlgorithm, which is similar to ClassicMAlgorithm, but has another monitor VaryStep, specified in Fig. 8. It is composed in parallel with Interaction to define a process VariableStepInteraction used in SimulinkMAlgorithm. VaryStep takes as parameters a threshold for change and the initial value of the step size initialSS . Taking a simple approach, we define a state that records the old (oldOuts) and new (newOuts) values of the outputs, besides the current step size currentSS . After the state is initialised (using the action Init) to record undefined (s) old values for the outputs, no new values (empty function ∅), and the initial step size, the monitor steps by recording the new output values (Monitor ) and then changing the step size (Adjust ). Adjust- ment is based just on a comparison between the old and new values defined by an (omitted) function delta. If the threshold is reached, a new step size is defined by another function newstep and informed to the Timer . We have established that SimulinkMAlgorithm is valid, that is, it refines MAlgorithm, by proving that the new action VariableStepInteraction refines Interaction. We have also proved termination, deadlock freedom, and deter- minism.
