Linear time invariant system simulation with iterative model
OwnerTan Duinventor
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Abstract
Disclosed are systems, methods and algorithms for simulating a Linear Time Invariant (LTI) system, such as a circuit, using an iterative model. A settle time is determined for a LTI system. Standard step response data is collected reflecting the step response of the system for a period equal to the settle time. A particular section of standard step response data is then used for modeling the LTI system for an arbitrary input and providing simulated output results.
Claims24
A method of modeling a linear time invariant (LTI) system comprising the steps of:
- providing a first step input, x0(t), to the LTI system for producing a first output, y0(t);
- measuring a settle time, Tsettle, from the first step input, x0(t), and the first output, y0(t);
- providing a second step input, x1(t), to the LTI system for producing a second output, y1(t);
- measuring the second input, x1(t), and the second output, y1(t), for a period consisting of the settle time, Tsettle;
- saving the ratio of the second output to the second input, y1(t):x1(t), as standard step response data;
- and
- modeling the LTI system using the standard step response data.
A system for constructing a simulation of a linear time invariant (LTI) circuit comprising:
- means for determining a settle time, Tsettle, of the LTI circuit;
- means for measuring a step response of the LTI circuit;
- means for storing standard step response data of the LTI circuit;
- means for modeling the LTI circuit using the standard step response data;
- and
- means for providing LTI circuit simulation results.
An algorithm for modeling a linear time invariant (LTI) circuit comprising the steps of:
- providing a first step input, x0(t), to the LTI circuit for producing a first output, y0(t);
- measuring a settle time, Tsettle, from the first step input, x0(t), and the first output, y0(t), the settle time being approximately the time interval within which the LTI circuit reaches a steady state;
- providing a second step input, x1(t), to the LTI circuit for producing a second output, y1(t);
- measuring the second input, x1(t), and the second output, y1(t), for a period consisting of the settle time, Tsettle;
- saving the ratio of the second output to the second input, y1(t):x1(t), as standard step response data;
- modeling the LTI circuit using the standard step response data according to the formula:
- 13 y ( t k ) = y ( t k - 1 ) + Δ x k - 1 p ( t k - t k - 1 ) + ∑ k - M k - 2 Δ x j [ p ( t k - t j ) - p ( t k - 1 - t j ) ] ,
- wherein;
- a maximum sample time interval, max(Ts)<Tsettle/2, and;
- (tk−1−tk−M)<XTe, where X consists of a selected system constant.
An algorithm for modeling a linear time invariant (LTI) circuit comprising the steps of:
- providing a first step input, x0(t), to the LTI circuit for producing a first output, y0(t);
- measuring a settle time, Tsettle, from the first step input, x0(t), and the first output, y0(t), the settle time being approximately the time interval required for the LTI circuit to reach a steady state;
- providing a second step input, x1(t), to the LTI circuit for producing a second output, y1(t);
- measuring the second input, x1(t), and the second output, y1(t), for a period consisting of the settle time, Tsettle;
- saving the ratio of the second output to the second input, y1(t):x1(t), as standard step response data;
- modeling the LTI circuit using the standard step response data according to the formula:
- y(tk)=y(tk−1)+a1Δxk−1+a2Δxk−2+ . . . +aMΔxk−M, wherein;
- sample length Ts=XTe/M, where X consists of a selected system constant, Te consists of a time constant associated with the LTI circuit, and M consists of a selected accuracy constant.
Dependencies are inferred from the claim text.