1/10/2024 0 Comments Mathmod 2018In comparison, MORLAB can be applied to way larger systems due to its efficient underlying spectral projection routines, which also often allow MORLAB to outperform the routines from the default MATLAB toolboxes by far. ![]() It should be noted that also the default MATLAB toolboxes provide some model reduction routines for small-scale dense standard systems in the Control System Toolbox and the Robust Control Toolbox™. Overviews about supported methods for ( 2) can be found inīesides the continuous-time version ( 2), the ss object supports discrete-time linear time-invariant standard systems, which are also implemented in the MORLAB toolbox with appropriate model reduction routines. 1 can be replaced by any model order reduction routine of choice from MORLAB. The important point here is that the model reduction with MORLAB only concerns the ss object to be exchanged but the surrounding process is untouched. Due to the consistent data type of rom, the reduced-order model can now directly replace the original sys object for the acceleration of the surrounding process. This object can be directly put into a MORLAB routine (here ml_ct_ss_bt), which produces a new ss object, namely rom. Let sys be the original ss object, e.g., in a Simulink LTI system block. An example of the resulting workflow is given in Fig. Besides an interface for the single matrices of ( 2) and one using structs, MORLAB fully supports ss objects. Therefore, MORLAB provides consistent interfaces for the model order reduction routines, i.e., the reduced-order models will be of the same data type as the original models. With, , and, which belongs to the same system class as ( 2). Concerning the model order reduction of ( 2), the reduced-order surrogate model reads as Now, the task is the integration of model order reduction into the computer-aided control system design workflow. Complete dynamical processes are usually modeled here, especially embedding LTI system blocks, which correspond to ( 2) and use the ss object in its backend. On the other hand, Simulink is a modeling toolkit for hierarchical system design and numerical experiments using graphical blocks. The toolbox uses the ss object as its main interface. It provides a lot of important system-theoretic routines for the analysis and simulation of ( 2). The Control System Toolbox is the main toolbox for dealing with dynamical systems in MATLAB. ![]() Those objects are, in principle, a collection of the most important properties of ( 2), e.g., the matrices A, B, C, D, corresponding measured data, units of the state variables and so forth. The way in MATLAB to efficiently deal with ( 2) are so-called state-space model objects (ss objects). To support the work with linear dynamical systems, the toolbox also implements a number of system-theoretic subroutines, e.g., the additive decomposition of dynamical systems, and evaluation tools for the time and frequency domain with support for the different implemented system structures.Īn overview of the basic principles of the MORLAB toolbox can be found in Therefore, the toolbox comes with many different solvers for different types of matrix equations, e.g., for continuous- and discrete-time algebraic Riccati or Lyapunov equations. , which are used for the solution of underlying matrix equations. and the right matrix pencil disk function The implementation of the toolbox is based on spectral projection methods, like the matrix sign function comes with 10 different model reduction techniques for continuous- and discrete-time standard, descriptor and second-order systems. As a repository of MATLAB codes for model order reduction of linear standard systems.
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