TAILIEUCHUNG - Model-Based Design for Embedded Systems- P56

Model-Based Design for Embedded Systems- P56: This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. | 526 Model-Based Design for Embedded Systems The execution of continuous model described by differential and algebraic equations requires solving these equations numerically. A widely used class of algorithms discretizes the continuous time line into an increasing set of discrete time instants and numerically computes values of state variables at these ordered time instants. The next state of derivative systems cannot be specified directly but the derivative functions are used to specify the rate of change of state variables 34 . The execution of a continuous system raises problems because given a state qk and a vector x for a time tk the derivative offers information only for dqk dt but not the system s behavior over time. For a nonzero interval tk tk i the computation has to be realized without knowing the behavior in the interval tk tk 1 . This problem can be solved using numerical integration methods. Some of the most commonly used methods are Euler method that consists in signal integration dq t lim q t h - q t dt h h For an h small enough in order to obtain accurate results the following approximation can be used q t h q t h dq t d t This solution has low efficiency and does not have stability problems for small enough h and it is very robust 34 . Causal methods that are a linear combination of states and derivative values at time instants with coefficients chosen to minimize errors from the computed estimate to the real value 34 . This solution has high efficiency but it has stability and robustness problems. Noncausal methods that use future values of states derivative and inputs. In order to do that the model is executed past the needed time and the values that are necessary are stored to estimate the present values 34 . Methodology This section introduces a methodology for the design of continuous dis-crete co-simulation tools as shown in Figure . To enable the design of co-simulation tools this methodology presents several steps that are .

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