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Modelica describes physical systems on a high level, using model objects, multi-dimensional arrays and other data structures as well as graphical representations. Modelica models are translated to differential-algebraic equation systems and compiled to executable code prior to their execution in numerical solvers. The translation gives a lot of possibilities for code optimization. This is particularly important for model-based control applications. This paper investigates the exploitation of C++ for Modelica code optimization. C++ supports advanced programming concepts and at the same time aims to “leave no room for a lower-level language … (except for assembly code in rare cases)” (B. Stroustrup: The C++ Programming Language, 2014). The features exploited here include polymorphism, templates, built-in exception handling and object destructors. The ideas have been implemented in the OpenModelica C++ runtime. The paper describes its enhancement with new array features and with an FMI 2.0 interface. FMI serves as interface between modeling tools and control applications. In particular the new FMI 2.0 meets requirements of numerical optimization solvers in modelbased control. A publically available application example demonstrates the achievements. CPU times obtained with the OpenModelica C++ runtime are significantly faster than CPU times obtained with the C runtime or with Dymola.

Efficient calculation of the solutions of nonlinear optimal control problems (NOCPs) is becoming more and more important for today’s control engineers. The systems to be controlled are typically described using differential-algebraic equations (DAEs), which can be conveniently formulated in Modelica. In addition, the corresponding optimization problem can be expressed using Optimica. Solution algorithms based on collocation methods are highly suitable for discretizing the underlying dynamic model formulation. Thereafter, the corresponding discretized optimization problem can be solved, e.g. by the interior-point optimizer Ipopt. The performance of the optimizer heavily depends on the availability of derivative information for the underlying optimization problem. Typically, the gradient of the objective function, the Jacobian of the DAEs as well as the Hessian matrix of the corresponding Lagrangian formulation need to be determined. If only some or none of these derivatives are provided, usually numerical approximations are used by the optimizer internally. OpenModelica supports the Optimica language and is capable of automatically generating the discretized optimization problem using collocation methods as well as the whole symbolic machinery available. In addition, all necessary derivative information is determined using the automatic differentiation capabilities of ADOL-C, which has now been integrated into the OpenModelica environment.

Derivatives, or Jacobians, are commonly required by numerical algorithms. Access to accurate Jacobians often improves the performance and robustness of algorithms, and in addition, efficient implementation of Jacobian computations can reduce the over-all execution time. In this paper, we present methods for computing Jacobians in the context of the Functional Mock-up Interface (FMI), and Modelica. Two prototype implementations, in JModelica.org and OpenModelica are presented and compared in industrial benchmarks.

The industrial usage of the open-source Modelica tool OpenModelica was limited so far for power plant applications, due to the performance of large fluid systems. This paper presents some efforts to improve the simulation time on benchmark fluid models proposed by Siemens Energy. The main aspects presented here to achieve a faster simulation are an efficient evaluation of the jacobian matrix by a coloring technique, that exploits the sparsity pattern of a modelica model. Therefore the techniques are scratched and applied to

Modelica is well suited for modelling complex physical systems due to the acausal description it is using. The causalisation of the model is carried out prior to each simulation. A significant part of the causalisation process is the symbolic manipulation and optimisation of the model. Despite the growing interest in Modelica, the capabilities of symbolic manipulation and optimisation are not fully utilized. This paper presents an approach to increase the customisability, access, and reuse of symbolic optimisation by a more modular and flexible design concept. An overview of the common symbolic manipulation and optimisation algorithms of a typical Modelica compiler is presented as well as a general modular design concept for a Modelica compiler backend. The modularisation concept will be implemented in a future version of the OpenModelica compiler.

Jacobian matrices are used in a wide range of applications - from solving the original DAEs to sensitivity analysis. Using Automatic Dierentiation the necessary partial derivatives can be provided eciently within a Modelica-Tool. This paper describes the corresponding implementation work within the OpenModelica Compiler (OMC) to create a symbolic derivative module. This new OMC-feature generates symbolically partial derivatives in order to calculate Jacobian matrices with respect to dierent variables. Applications