Solving Implicit Equations

When a system contains an implicit equation, that is, an equation defined in terms of itself, you use unknown and constraint blocks to solve it. There may be one or more or no solutions for the system.

The key steps to setting and solving implicit equations follows:

      Define the variable that needs to be determined as an unknown using the unknown block. The order is very important: an unknown must be defined first and then given a variable name.

      Isolate 0 on the right side of the equation by moving all terms to the left side.

      Construct the left side of the equation and equate the right side using the constraint block to denote 0.

In the case of connections backward to earlier blocks already evaluated (often called feedback), Embed checks to see that such feedback loops contain at least one integrator, transferFunction, unitDelay (1/Z), or timeDelay block. If there is no such block in the feedback, the result is numerically ill-defined and is referred to as an algebraic loop. Embed detects such algebraic loops and produces a warning message.