An Improved Passivity Preserving Model Order Reduction Technique

Abstract

The design of any system e.g. network systems and telecommunication systems contain mathematical model which are complex and require lot of computational power for analysis and simulation. For such scenarios, to make the analysis and design of these systems easier, model order reduction (MOR) is used which reduce the complexity of these models by reducing their order. It takes less computational power and simulation time when models with reduced orders are used. MOR methods are very useful when it comes to analyze large and complex systems such as space systems, state estimation in UAVs and high voltage systems etc. In feedback control systems theory, the major contribution of balanced truncation is its application in model reduction which gives the stable reduced models and an error bound within certain frequency limit. This is also known as frequency weighted MOR problem. For a given transfer function there are almost infinite state space realizations but a particular realization has been proved useful in control systems theory which is called internally balanced realization. It indicates the dominant system states and it is the minimal realization which is also asymptotically stable. The most wanted property in some systems is passivity which can be implied if the system’s transfer function is positive real. When the model is reduced to rth ROM using MOR it is desired to preserve the important features such as passivity, stability and input output behavior etc. Since passive systems are also stable systems and not vice versa, it is very important in MOR algorithms to preserve passivity. A lot of work has been done on passivity preserving model order reduction techniques in case of continuous time (CT) systems whereas no work is done in case of discrete time (DT) systems. Performance of a system can be enhanced by sampling and also the computational cost can be relatively reduced in this case. This research focuses on passivity preserving model order reduction (MOR) technique for discrete time systems. Balanced truncation along with extended Enns’ and Umair et al. technique proposed for continuous time systems are modified for discrete time systems. The proposed technique preserves passivity and yields reasonable approximation error.