Order Reduction of LTI Systems Using Balanced Truncation and Particle Swarm Optimization Algorithm

This paper presents a novel hybrid model reduction method to simplify large-scale continuous-time single-input–single-output and multi-input–multi-output dynamic systems using the advantages of the balanced truncation method and the particle swarm optimization (PSO) algorithm. The balanced truncation method obtains the reduced model denominator coefficients to ensure stability. The PSO algorithm minimizes the integral square error between the step responses of the original system and the reduced model as much as possible. It leads to the optimal numerator coefficients. The advantage of the proposed approach is that, for optimizing reduced model numerator coefficients, the search space boundaries of the PSO algorithm are not entirely random. They are selected using the balanced truncated reduced model numerator. So, the suggested method avoids two significant problems with evolutionary algorithms: the arbitrary choice of search space and the longer simulation time. Four power system models and four numerical examples from the literature are considered to assess the effectiveness of the proposed reduction method. The step responses and Bode diagrams for the higher-order system and its corresponding reduced models are displayed. For comparison, statistics are tabulated based on the rise time, the settling time, the peak overshoot, the integral square error, and the root-mean-square error. The proposed method ensures stability and other features of the higher-order system in the reduced model. The performance measure values and the time domain characteristics demonstrate the ability and effectiveness of the proposed approach. All the case studies use a MATLAB simulation environment.