Hardware-in-the-Loop simulation is widely used in the automotive industry for testing of electronic control units. As hardware is involved, simulations have to be performed in real time. Special methods and tools for real time simulations have been developed at the institute. Results contributed to the hybrid modelling technique. Additionally, methods have been developed and implemented that overcome the kinematic closed loops in suspension subsystems. Thus the resulting equations of motion of the vehicle form systems of ordinary differential equations that can be solved efficiently in real time.

An electronic control unit (ECU) acts as a hardware component designated to be tested. The ECU sends its output signals to the model, which represents the remaining vehicle (engine, gearbox, axle etc.), the driver and the environment. The ECU’s input signals are computed by the model in real time instead of being measured in a real vehicle.

Handling of kinematic loops in suspension subsystems

For the real time simulation of vehicles (e.g. for Hardware-in-the-Loop or vehicle simulators) very fast multibody system models are used today. Since vehicle suspension models with kinematic closed loops requiring an iterative solution of equations of motion is a factor that increases significantly the dynamic simulation of the vehicle, reduction techniques are applied to the suspension submodels to avoid the algebraic constraints in equations of motion of the vehicle.

The model reduction approach is based on the formulation of the equations of motion in the independent coordinates together with subsystem-local solution of constraint equations describing kinematic loops. Thus the resulting equations of motion of the vehicle form system of ordinary differential equations (ODE) that that can be solved efficiently in real time.

For the local solution of algebraic equations the iterative method or the stabilised solution of time integrated (local) dependent coordinates have been used. The former has been proven to be less favourable due to the extra computing time consumption compared with the latter. The algebraic equations have been defined both in relative and natural coordinates. The first is preferred due to less computing time, the second one requires less input parameters (just absolute coordinates of linking points between rods and chassis or wheel carrier, respectively) thus being more user-friendly.

The simulation results in the time domain have indicated just small deviations of reduced models compared to the complete reference model of suspension, see graph.

Real-Time Simulation

Sparsing techniques

Modelling of mechatronic systems often leads to stiff differential-algebraic equations. In real time simulation neither implicit nor explicit methods can cope with such systems in an efficient way: explicit methods have to employ too small steps and implicit methods have to solve too large systems of equations. A solution of this general problem is to use a method that allows manipulations of the Jacobian by computing only those parts that are necessary for the stability of the method.

Specifically, a priori manipulation by sparsing aims at zeroing out certain elements of the Jacobian leading to a structure that can be exploited using sparse matrix techniques.

At the institute, a sparsing criterion for the linearly implicit Euler method was derived. A stiff real time simulator has been implemented and tested with real life problems.

HIL test environment

In order to be able to test and demonstrate methods and tools on site, a HIL test environment was set up. Its main component is a real time computer system. Scripts for automatic test procedures have been implemented. The connection with the institute’s optimization environment MOPS enables HIL optimization of hardware parameters.

The HIL environment was kept flexible, such that e.g. Rapid Control Prototyping is possible, too, which has been demonstrated for an aircraft actuator.