Complex Frequency Domain Model Reduction: A Comparison of Techniques

Abstract

A mathematical model of the plant to be controlled must first be identified in order to design a controller to improve the process’ performance and stability. This mathematical model usually is in the form of complex frequency domain state-space realization or continuous/ discrete time domain regression algorithm. This paper works on the complex frequency domain state-space realization. Reducing the order of the state-space model of the physical plant is usually desirable since it reduces computational time and hardware implementation for the resulting controller designed based on the model. For a frequency domain state space realization of a linear time-invariant and non-causal plant, there are numerous methods available to reduce its order. These include Balancing Model Reduction, Frequency-Weighted Balancing, Low-Frequency Approximation and Balanced Truncation with Reduced Error Bound. Besides background information and a summary, the model-reduction methodology for each of the above-said techniques is also presented. Using a two-input two-output six-state model for a large turbo-generator and a large industrial boiler with 8 states, 2 inputs and 2 outputs model, this paper provides a comparison between three of the four methodologies mentioned above in terms of the spectral norms of the model reduction error.