State Space System Simulator Utilizing Bi-quadratic Blocks to Simulate Lightly Damped Resonances
A method for operating a data processing system to simulate a physical system is disclosed. The physical system receives a time-varying input and generates a time-varying output. A model of the physical system is provided. The model depends on values of the time-varying input and an internal state in the physical system, the internal state is not directly measurable. The model includes a bi-quad component that models a resonance or anti-resonance of the physical system. For each of a plurality of time points, a current input value for the time-varying input is received. An internal state vector having a value of the internal state at a current time point as one component thereof is computed and computing an estimate of a system output at that time point, the system output being directly measurable. In one aspect of the invention, the internal state vector depends on a previous value of the internal state vector and the current input value.
1 . A method for operating a data processing system to simulate a physical system, said method comprising:
providing a model of said physical system, said model depending on values of a time-varying input and an internal state in said physical system, said internal state not being directly measurable, said model including a bi-quad that models a resonance or anti-resonance of said physical system; and
for each of a plurality of time points, receiving a current input value for said time-varying input, computing an internal state vector having a value of said internal state at a current time point as one component thereof and computing an estimate of a system output at that time point, said system output being directly measurable.
2 . The method of claim 1 wherein said model comprises a plurality of bi-quads, each bi-quad being characterized by an input and an output, said input of one of said bi-quads being said output of another of said bi-quads.
3 . The method of claim 2 wherein each of said bi-quads comprises a plurality of parameters that specify a frequency for a resonance and a frequency for an anti-resonance and wherein said parameters are determined by comparing said model's output for particular inputs to experimental data from said physical system with said inputs.
4 . The method of claim 3 wherein said parameters are determined such that one of said bi-quads has a resonance or anti-resonance that matches a corresponding resonance or anti-resonance in said physical system.
5 . The method of claim 3 wherein said physical system has a plurality of resonances and anti-resonances and wherein said parameters are chosen such that a bi-quad having a resonance that matches one of said physical system resonances has an anti-resonance that matches a physical system anti-resonance that is closed to that resonance.
6 . The method of claim 1 wherein said internal state vector depends on a previous value of said internal state vector and said current input value.
7 . The method of claim 1 further comprising outputting a value indicative of a component of said internal state vector at each time point.
8 . The method of claim 1 wherein said model further includes a component that is not a bi-quad.
9 . The method of claim 1 wherein said bi-quad models a moving mass.
10 . The method of claim 1 wherein said model includes a state space model of a component that is not modeled by a bi-quad.
11 . An apparatus that emulates a physical system, said apparatus comprising:
a data processing system that includes hardware and software that emulates said physical system, said software providing a model of said physical system, said model depending on values of a time-varying input and an internal state in said physical system, said internal state not being directly measurable, said model including a bi-quad that models a resonance or anti-resonance of said physical system; and
for each of a plurality of time points, said data processing system receiving a current input value for said time-varying input, computing an internal state vector having a value of said internal state at a current time point as one component thereof and computing an estimate of a system output at that time point, said system output being directly measurable.
12 . The apparatus of claim 11 wherein said model comprises a plurality of bi-quads, each bi-quad being characterized by an input and an output, said input of one of said bi-quads being said output of another of said bi-quads.
13 . The apparatus of claim 12 wherein each of said bi-quads comprises a plurality of parameters that specify a frequency for a resonance and a frequency for an anti-resonance and wherein said parameters are determined by comparing said model's output for particular inputs to experimental data from said physical system with said inputs.
14 . The apparatus of claim 13 wherein said parameters are determined such that one of said bi-quads has a resonance or anti-resonance that matches a corresponding resonance or anti-resonance in said physical system.
15 . The apparatus of claim 13 wherein said physical system has a plurality of resonances and anti-resonances and wherein said parameters are chosen such that a bi-quad having a resonance that matches one of said physical system resonances has an anti-resonance that matches a physical system anti-resonance that is closed to that resonance.
16 . The apparatus of claim 11 wherein said internal state vector depends on a previous value of said internal state vector and said current input value.
17 . The apparatus of claim 11 further comprising outputting a value indicative of a component of said internal state vector at each time point.
18 . The apparatus of claim 11 wherein said model further includes a component that is not a bi-quad.
19 . The apparatus of claim 11 wherein said bi-quad models a moving mass.
20 . The apparatus of claim 11 wherein said model includes a state space model of a component that is not modeled by a bi-quad.