SYSTEM AND METHOD FOR GENERATING DISCRETE-TIME MODEL (DTM) OF CONTINUOUS-TIME MODEL (CTM) FOR A DYNAMICAL SYSTEM
First Claim
1. A method for execution by a processor of converting a continuous-time model (CTM) to a discrete time model (DTM), the method comprising:
- determining a sampling time and CTM state-space matrices [A, B, C, D] defined for a dynamical system ordinary differential equation mathematical formulation;
determining an order of approximation [i,j,k] parameters of the coefficients of an Obreshkov integration formula, to be used in determining the DTM [Adm, Bdm, Cdm, Ddm] to provide an approximation of accuracy and to meet A- or L-stability requirements defined for the dynamical system; and
discretizing the CTM into a DTM using the selected order of approximation [i,j,k], and the CTM state-space matrices [A, B, C, D] and sampling time (T) by calculating Obreshkob-coefficient and matrices [Adm, Bdm, Cdm, Ddm] using Obreshkov-based polynomial matrices.
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Abstract
Method and apparatus for processing continuous-time models (CTM) in a digital processing architecture is disclosed. The discrete state-space technique maps the CTM into the discrete-time model (DTM) and stores the states of the system in a sample time independent discrete state space set of matrices. The resulting state-space matrices can be processed in software or directly in hardware. The method disclosed is particularly suited to be used in automatic synthesis algorithms where a digital circuit is generated from an algorithm described in a high level language or model representation such as, for example, data flow or bond graph into a hardware description language (HDL), and the HDL model can be synthesized using system specific tools to generate an application specific integrated circuit (ASIC) or an FPGA configuration.
13 Citations
29 Claims
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1. A method for execution by a processor of converting a continuous-time model (CTM) to a discrete time model (DTM), the method comprising:
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determining a sampling time and CTM state-space matrices [A, B, C, D] defined for a dynamical system ordinary differential equation mathematical formulation; determining an order of approximation [i,j,k] parameters of the coefficients of an Obreshkov integration formula, to be used in determining the DTM [Adm, Bdm, Cdm, Ddm] to provide an approximation of accuracy and to meet A- or L-stability requirements defined for the dynamical system; and discretizing the CTM into a DTM using the selected order of approximation [i,j,k], and the CTM state-space matrices [A, B, C, D] and sampling time (T) by calculating Obreshkob-coefficient and matrices [Adm, Bdm, Cdm, Ddm] using Obreshkov-based polynomial matrices. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. An apparatus for converting a continuous-time model (CTM) to a discrete time model (DTM), the apparatus comprising:
a processor for executing the instructions for performing; receiving a DTM output, input signals determining a sampling time (T) and CTM state-space matrices [A, B, C, D] defined for a dynamical system ordinary differential equation mathematical formulation; determining an order of approximation [i,j,k] parameters of the coefficients of an Obreshkov integration formula, to be used in determining the DTM [Adm, Bdm, Cdm, Ddm] to provide an approximation of accuracy and to meet A- or L-stability requirements defined for the dynamical system; and discretizing the CTM into a DTM using the selected order of approximation [i,j,k], and the CTM state-space matrices [A, B, C, D] and sampling time by calculating Obreshkov coefficients and matrices [Adm, Bdm, Cdm, Ddm] using Obreshkov polynomial matrices. - View Dependent Claims (17, 18, 19, 20, 21)
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22. An apparatus for executing a discrete time model (DTM) the apparatus comprising:
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a processor for executing the instructions for performing; computing an approximation for the output signals y(nT) at the sampling time (T) comprising;
wm(n+1,T)=Admwm(n,T)+BdmU(n,T)
x*m(n,T)=Cdmwm(n,T)+Ddmu(n,T)where the DTM output is defined by; - View Dependent Claims (23, 24, 25, 26, 27, 28, 29)
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Specification