28TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES AIRCRAFT SYSTEM SIMULATION FOR PRELIMINARY DESIGN Petter Krus, Robert Braun, Peter Nordin, and Björn Eriksson Linköping University, SE-58183 Linköping, Sweden [email protected] Keywords: aircraft conceptual design, system modeling, mission simulation Abstract subsystem as early in preliminary design as possible, and then use this model to develop the Developments in computational hardware and design further. In this way the simulation model simulation software have come to a point where becomes a point of convergence for the aircraft it is possible to use whole mission simulation in conceptual design as well as the conceptual a framework for conceptual/preliminary design. design of the subsystem as well as a tool for This paper is about the implementation of full further development in preliminary design. system simulation software for Using simulation performance conceptual/preliminary aircraft design. It is characteristics at the whole aircraft level can be based on the new Hopsan NG simulation evaluated very straightforwardly, and things like package, developed at the Linköping University. trim drag are accounted for as a byproduct. The Hopsan NG software is implemented in Furthermore, as the design progress into sub C++. Hopsan NG is the first simulation system design, systems such as actuation software that has support for multi-core systems, fuel systems etc, can also be included simulation for high speed simulation of multi and verified together in the actual flight profile. domain systems. Using simulation models of whole aircraft with In this paper this is demonstrated on a subsystems, it is then possible to do design flight simulation model with subsystems, such as analysis, e.g. sensitivity analysis and trade of control surface actuators. analysis, as well as design optimization. In this paper this is demonstrated on a flight simulation model with subsystems, such as control surface 1 Introduction actuators. Traditionally aircraft conceptual design involves In recent years there has been a lot of very few aspects of system design. There is, development in methods and tools suitable for however, a great advantage if system subsystem simulation of systems. One example is the design also can be involved early on. There are Hopsan-NG simulation package developed at several reasons for that. Modern aircraft are Linköping University. This means for example very compact so system installation is important that it is possible to model basic aircraft to take into consideration, and this cannot systems, such as hydraulic system, air system properly be done unless there is a preliminary and fuel system, much more efficiently than design of the systems. Furthermore, energy before and that a lot of systems can even be efficiency and the impact of subsystem on the simulated in real time or faster than real time. In energy efficiency of the whole aircraft are this paper it is shown how subsystem models becoming important in order to select the proper also can be coupled to models of flight subsystem concept. The aim here is to allow the dynamics, propulsion, and flight control, to whole aircraft to be simulated with its produce a more complete aircraft system model. Such a model can be used already in 1 KRUS P., et al. preliminary design, thus allowing the and O'Brien (Ref. [2]) for simulation of preliminary subsystem designs to be designed electrical networks. concurrently with the aircraft layout. Johns and O'Brien pointed out that an One problem when dealing with large important aspect of modelling using complex systems, however, is that most transmission line elements is that most of the simulation packages rely on centralized numerical errors introduced by an ordinary integration algorithms that scale rather poorly solver are avoided. The errors made due to the with respect to system size. For large-scale introduction of transmission line elements, are systems it is an advantage if the system can be better described as modelling errors. partitioned in such a way that the parts can be An attractive feature with this is that laws of evaluated with only a minimum of interaction. conservation of mass and energy still hold for The reason that centralized solver dominates is the solution, since there always exist a plausible most likely, that until recently, the typical physical system for the model although the line system simulation has been of a moderate size. lengths may vary compared to the original In this paper, distributed solvers with linear system. This also implies that the user may scaling properties is used, which means that tolerate a larger numerical error since, generally, simulation speeds, orders of magnitude higher quite large modelling errors are present anyway than real time, can be achieved for system (errors of the order of 10% are generally simulation Furthermore, development in single considered acceptable from an engineering point processor performance is leveling out. On the of view). other hand, multi-core architectures have A key feature of the transmission line is the become the norm. However, using conventional finite signal propagation speed (speed of sound) simulation software, the simulation can only use of the signal travelling through the line. This one core for the simulation, thus not exploiting means that events at one component do not that potential. The distributed modeling affect another immediately. Using this approach approach used in here, however, makes it the subsystems can be solved independently in intrinsically suitable for multi-core simulation, each time step in contrast to using conventional and Hopsan already has that capability solver. The implementation of the numerical implemented. solver of differential algebraic equations can therefore be implemented in the subsystem rather than at a central level. This approach is 2 Distributed modelling sometimes referred to as distributed modelling for several reasons. The simulation of waves in A very suitable method for modelling and transmission lines means that distributed simulation of large complex dynamic systems is parameters are used in the lines, secondly it represented by distributed modelling using allows for distributed solver of differential transmission line elements. The origin of this algebraic equations in component and concept goes back at least to Auslander 1968 [1] subsystems. There is also the possibility of who first introduced transmission lines (or bi- using distributed processing by allocating lateral delay lines). This method evolves subsystems to different processors. naturally for calculation of pressures when In this way the system is divided into pipelines are modelled with distributed subsystems that generally are of limited size and parameters. This approach was adopted for the very robust method for DAE:s described simulation of fluid power systems with long earlier, can be used. lines in the HYTRAN program [2]. already in the seventies. The method can be generalised to both mechanical and electrical systems. 2.1 The unit transmission line A related method is the transmission line In transmission line modelling the basic modelling method (TLM) presented by Johns dynamic element is the unit transmission line. In the Hopsan package this is used to connect 2 AIRCRAFT SYSTEM SIMULATION FOR PRELIMINARY DESIGN different components to each other. In the An interesting observation is found if c2 in general case it can be used to model both Eq. (18) is substituted with Eq. (19) and the capacitances and inductances. In the Hopsan- outlet at 2 is blocked. package, however, it is used only to represent =−+ −+ capacitances (oil volumes and mechanical p22()(2)[(2)()]t ptTZqtTqTc 1 1(7) springs). q 1 q 2 Compared to the trapezoidal method for p p integration (h is the time step). 1 2 1 (8) Figure 1. Transmission line yh+t = yt + h f ut, t + f uh+t , h + t 2 The complete set of equations that describes where a lossless transmission line are: ° =−+ + − y = f u, t (9) p12()tptTZqtZqtT ( )cc 1 () 2 ( ) (1) p ()tptTZqtZqtT=−+ ( ) () + ( − ) (2) 21cc 2 1 These equations are the same if Th= /2 Here Zc is the characteristic impedance of the line, p and q are pressures and flows The relationship between flow entering a respectively. T is the time delay in the line. Note volume and the pressure can be written as: q that the main property of these equations is the p° = (10) time delay they introduce in the communication C between the ends. where C is the capacitance. Identification yields h (11) Introducing Zc = C =−+− ct12()() pt T ZqtTc 2 () (3) ct()()=−+ pt T ZqtT () − (4) 21c 1 The implication of this is that if we use the Here c is the wave variables that represent trapezoidal method to integrate pressure in a information that has been transmitted from the volume (capacitance) between two components, other side of the transmission line. With these, this corresponds to introducing a short pipe the following set of equations is obtained. instead of a pure capacitance. This can also be =+ p12()tctZqt ()c 1 () (5) extended to other domains such as mechanical =+ and electric. p21()tctZqt ()c 2 () (6) Laminar restrictor q1 Σ c 3 Differential algebraic systems 2Z2Zc Delay h 2 c c c r1 i2 Zc In order to solve the dynamics of the individual Zc c Σ components and subsystems any type of solver 1 Delay h 2Zc q 2Zc 2 ci1 cr2 can be used. A general approach to represent a system is to represent it as a differential algebraic system. This also allows for algebraic Figure 2. Block diagram of transmission line. loops. With this method the system can be ° F x, x, t = 0 (12) partitioned since there is no direct communication between the two sides of the where x is the variable vector. transmission line, there is always a time delay However, Eq. (1) implies that the system that can be used to partition the model.