Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems (original) (raw)
Related papers
Radioengineering, 2021
Frequency limited model order reduction algorithm presented by Wang & Zilouchian for discrete-time systems provide unstable reduced-order models and also do not provide a priori error bound formula. Many stabilitypreserving model order reduction algorithms were presented; however, these methods produce significant approximation errors in the desired frequency interval. An improved algorithm of model order reduction for the discrete-time systems is presented. The proposed technique gives the stable reduced-order model and also provides less approximation error as compared with other algorithms and also provides the formula for the frequency response a priori error bound. Numerical examples provided at the end of the section show the efficacy of the proposed technique.
A frequency weighted model order reduction technique and error bounds
Automatica, 2014
A new frequency weighted technique for balanced model reduction is proposed. The proposed technique not only provides stable reduced order models for the case when both input and output weightings are included but also yields frequency response error bounds. The method is illustrated using numerical examples and the results are compared with other frequency weighted model reduction techniques.
A frequency limited model reduction technique for linear discrete systems
2013 Australian Control Conference, 2013
This paper describes the model reduction framework for single-input single-output (SISO) discrete-time systems based on the preservation parameters such as Markov properties of the original system by applying a Frequency-Limited Impulse Response Gramian based Balanced Truncation method. This proposed method extends the Frequency-Limited Impulse Response Gramians model reduction method for continuous systems described in the recent paper in [20] to be applicable for discrete time systems. A numerical example is provided to compare the performances between various frequency limited model reduction methods at an arbitrarily selected frequency range within the passband of a digital filter. The stability of the reduced order models are also checked for each scenario.
Discrete-time model reduction in limited frequency ranges
Journal of Guidance, Control, and Dynamics, 1993
A mathematical formulation for model reduction of discrete-time systems such that the reduced-order model represents the system in a particular frequency range is discussed. The algorithm transforms the full-order system into balanced coordinates using frequency-weighted discrete controllability and ohservahility grammians. In this form a criterion is derived to guide truncation of states based on their contribution to the frequency range of inlerest. Minimization of the criterion is accomplished without need for numerical optimization. Balancing requires the computation of discrete frequency-weighted grammians. Closed-form solutions for the computation of frequency-weighted grammians are developed. Numerical examples are discussed to demonstrate the algorithm.
International Journal of Control, 2018
A new technique for frequency limited model order reduction of discrete time second-order systems is presented. Discrete time frequency limited Gramians (DFLGs) and corresponding discrete algebraic Lyapunov equations are developed. An efficient technique for the computation of DFLGs and their Cholesky factors is presented. Computed DFLGs are partitioned to obtain position and velocity Gramians. These Gramians are balanced with different combinations to obtain various balanced transformations that yield Hankel singular values (HSVs) for order reduction. Frequency limited discrete time balanced truncation framework is proposed and truncation based on magnitudes of HSVs is applied to obtain the reduced order model. Moreover, stability conditions for reduced order models are stated. Results of the proposed technique are compared with infinite Gramians balancing scheme in order to certify the usefulness of the presented technique for frequency limited applications.
Frequency Limited Model Reduction Techniques with Error Bounds
—The main issue with the pioneer frequency limited interval Gramian based technique by Gawronski and Jaung is that it yields unstable reduced order models. There exist some techniques in literature that yield stable reduced order models, however these techniques yield relatively more frequency response errors. In this paper, three frequency limited interval Gramians based model order reduction techniques are proposed. The proposed techniques ensure the stability of the reduced order models, produce relatively lower frequency response error (as compared with existing stability preserving techniques) and yield the frequency response error bounds. Numerical examples along with comparison among different techniques are presented which show the effectiveness (relatively low approximation error as compared with other existing stability preserving model order reduction techniques) of the proposed techniques. Index Terms—Model order reduction, limited frequency interval Gramians, error bound, frequency response error.
A Novel Approach for Model Order Reduction in Discrete Time System
International Journal of Intelligent Engineering and Systems, 2021
In modern digital control system such as model reference control and model predictive control, where the real time calculation is the main challenge, the model order reduction has become very important issue to minimize the execution time. In this work, our aim is to construct a novel technique for reduction of high order discrete time systems. This could be achieved by computation algorithm model from a given high order pulse transfer function. The proposed model is based on matching the weighting sequence of the original parameters with those adopted in the low-order model. The generalized least squares method is then used to determine the reduced model parameters. The efficiency of the proposed algorithm is validated by using the integral squared error minimization between the original system and the reduced model. An example is presented and discussed to validate the efficiency of the proposed low-order model. Performance comparisons with many recent related works showed that the proposed model is promising in terms of low error indices and time responses.
Frequency Weighted Controller Order Reduction (Part I)
Journal of Electrical Engineering, 2000
In this paper, a new method for controller reduction of linear time invariant systems is presented. The method is based on newly defined controllability and observability grammians which are calculated from input to state and state to output characteristics of the controller in a certain frequency domain. These grammians are defined for the closed loop system to keep the performance of original controller. The main idea of this method is based on Moores model reduction. The relation of this method with weighted frequency model reduction of Enns will be described by a commutative diagram. The stability property of the new method is investigated. It is shown that the stability for two sided weights can be preserved under certain conditions. The simulation results show the effectiveness of this novel technique.
Model Reduction of Large-Scale Systems using Perturbed Frequency-Domain Balanced Structure
2004
The technique described in this paper uses singular perturbation and balanced structure to reduce the order of a large-scale plant model over a finite frequency range of operations pre-specified by the designer. This method reduces error rate in model reduction of real equipment that has to operate within a finite frequency range. The outcome of reducing the model within a specified frequency range of operation provides a better estimate of the full order plant model. To illustrate the effectiveness of the technique, a fourth order open-loop plant model is reduced to a second order over several different frequency ranges of operation. Also a sixth and a seventh order controller is designed using H ∞ and reduced to a third order while maintaining a robust stability for the closed loop system. A singular value Bode diagram and a Nyquist diagram comparing the original and the reduced order system illustrate the effectiveness of the model reduction technique both in the open-loop and closed-loop sense.
Asian Journal of Control, 2017
A new structure preserving model order reduction technique for second order systems in limited frequency interval is presented. Frequency limited Gramians (FLGs) and corresponding continuous time algebraic lyapunov equations (CALEs) are developed. For solution of CALEs and Cholesky factorization of FLGs, computationally efficient approximation scheme is proposed. Multiple transformations based on balancing of frequency limited position or velocity Gramians are defined in order to compute Hankel singular values (HSVs). Frequency limited second order balanced truncation based on magnitudes of HSVs is performed for order reduction. Moreover, stability conditions for reduced order models (ROMs) are stated and algorithms for achieving stability in ROMs are proposed. Results are compared with existing technique to certify the usefulness of the proposed technique.