Comprehensive helicopter simulation has been an important subject of research ever since the rise of the first helicopters. Numerous modeling approaches and software frameworks emerged, each with its individual advantages and drawbacks. However, a comprehensive approach that yields an efficient and effective simulation adaptable for research is still missing. Comprehensive here means that all relevant aspects are taken into account, e. g. vortex dynamics, rotor behavior, vibrations, etc. The German Aerospace Center (DLR) is working on a new solution using general state-space models for submodels of the helicopter which are coupled to a comprehensive model. This coupling yields an index-1 differential algebraic equation (DAE) system. ududIn this thesis, we analyze existing numerical algorithms for the solution of index-1 DAE systems and define a new familiy of methods that suits the challenges of helicopter simulation best. The challenges here consist in the interaction of large systems that are complex and individual in their behavior on their own. We focus our analysis on half-explicit Runge-Kutta HERK) methods. Their explicit approach delivers the efficiency we seek. However, these methods are not able to handle stiff systems like the highly vibratory helicopter well. Stiff ordinary differential equation (ODE) problems can be solved by explicit exponential Runge-Kutta (EERK) methods. In order to apply them to index-1 DAE systems, we derive the new half-explicit exponential Runge-Kutta (HEERK) methods.ududWe test our HEERK methods in comparison to HERK methods on a mechanical model of the main rotor. The results show that HEERK methods need substantially fewer time steps than HERK methods for the same approximation quality. We also see that a good choice of submodels, hereudthe stiff variables are solely placed in the state function, boosts this effect. So, HEERK methods constitute an essential step towards an effective real-time simulation in comprehensive rotorcraft simulation.
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机译：自从第一架直升机问世以来，全面的直升机模拟一直是研究的重要课题。出现了许多建模方法和软件框架，每种方法都有其各自的优点和缺点。但是，仍然缺少能够产生适用于研究的高效且有效的模拟的综合方法。这里的全面意味着将所有相关方面都考虑在内。 G。涡旋动力学，旋翼行为，振动等。德国航空航天中心（DLR）正在研究一种新的解决方案，它使用直升机的子模型的通用状态空间模型，并与综合模型耦合。这种耦合产生了一个指数为1的微分代数方程（DAE）系统。 ud ud在本文中，我们分析了现有的用于索引1 DAE系统解决方案的数值算法，并定义了一种最适合直升机模拟挑战的新方法。这里的挑战在于大型系统的相互作用，这些系统本身是复杂的且行为各异。我们将分析重点放在半显式Runge-Kutta HERK方法上。他们明确的方法可以提供我们寻求的效率。但是，这些方法无法处理像高振动直升机这样的刚性系统。可以通过显式指数Runge-Kutta（EERK）方法解决刚性常微分方程（ODE）问题。为了将它们应用于index-1 DAE系统，我们推导了新的半显式指数Runge-Kutta（HEERK）方法。 ud ud我们在主转子的机械模型上测试了HEERK方法与HERK方法的比较。结果表明，对于相同的近似质量，HEERK方法所需的时间步长明显少于HERK方法。我们还看到，很好的子模型选择（这里 udst变量仅放置在状态函数中）可以增强这种效果。因此，HEERK方法构成全面旋翼飞机仿真中有效实时仿真必不可少的步骤。
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