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Poster: Rapid physical model deployment for real time embedded control

Physics based models are used in various control applications ranging from mechatronics to industrial systems controls. These models typically are described by a set of non-linear Differential Algebraic Equations (DAE) for which an analytical solution either is not known or does not exist. Modern numerical techniques are extremely efficient for these types of problems. For systems described by a set of Partial Differential Equations (PDE), spatial discretization schemes are employed to transform them into a set of DAEs.

Real-time control methods require such models to be ported into an embedded processor and solved in real time relative to the time constants of the controlled process. Some advanced control methods such as Model Reference Adaptive Control (MRAC) also involve model parameter updating in real time in order to minimize error or adapt to changes in the modeled system.

So far the process of model development/optimization and its embedded implementation has been a two-step process. First the model is developed and optimized in a general purpose Computer Aided Engineering (CAE) environment. After the model has been verified and optimized custom model code is generated either automatically or manually.

The two-step process has the following drawbacks:

1. The code produced does not contain all the functionality available in the CAE environment. For example the Embedded Coder of MATLAB does not translate essential numerical routines such as the DAE solver itself. The resulting software is compromised as it cannot benefit from features of such codes such as sensitivities which may be required in certain adaptive control applications. Other features that affect performance such as adaptive step-size are also not included.

2. Any change in the model itself requires repetition of the two-step process. If the code is produced manually, it adds significantly to the cost of the system.

Embedded dtSolve™ is a complete model solver. It is small enough and fast enough to reside on an embedded processor. It contains all the features of a State-of-the-Art solver including Automatic Differentiation (AD), complete DAE solver like IDAS or DASSL, sparse matrix techniques, sensitivities (computed analytically instead of finite differencing), AC small signal analysis and adaptive step-size. It accomplishes all these functions in a few hundred KB of code space (depending on features enabled). With Embedded dtSolve™ there is no need for creating custom embedded code. All you need to input are the model DAEs along with the boundary conditions and parameter information (values, bounds, optimizability, etc.), as you would input them in a general purpose CAE package.

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