Method for simulating discontinuous physical systems

• US 6,243,663 B1
• Filed: 04/30/1998
• Issued: 06/05/2001
• Est. Priority Date: 04/30/1998
• Status: Expired due to Fees

• Current Assignee: Sandia Corporation (Martin Marietta Corporation)
• Original Assignee: Sandia Corporation (Martin Marietta Corporation)
• Inventors: Baty, Roy S., Vaughn, Mark R.
• Primary Examiner(s): Teska, Kevin J.
• Assistant Examiner(s): Phan, Thai
• Application Number:
  US09/071,134
• Time in Patent Office: 1,132 Days
• Field of Search: 395/500.23, 395/500.27, 708/207, 708/400, 703/14, 703/22, 703/1, 703/2
• US Class Current: 703/2
• CPC Class Codes: G05B 17/02 electric

Abstract

The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and well-behaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.

Claims

1. A method for simulating on a computer the physical behavior of a physical system, comprising the steps of:

a) generating a description of the physical system and the physical laws controlling the physical properties of the physical system in terms of a well-posed problem in generalized function theory for the behavior of a set of system variables and a set of system parameters;

b) converting the well-posed problem into a hyperreal well-posed problem by steps comprising extending system variables and system parameters into the hyperreal number system;

c) discretizing the hyperreal well-posed problem by steps comprising replacing infinitesimal and hyperreal infinite system variables and parameters with small and large real numbers, respectively; and

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d) approximating the physical behavior of the physical system by steps comprising creating a software implementation of the discretized hyperreal well-posed problem, mounting said software implementation on a suitable electronic computer, and operating said computer so as to perform said approximation.

2. The method of claim 1, wherein the step of generating a description comprises simplifying the set of system variables and the set of system parameters so that a subset of the physical behavior of the physical system is simulated.

3. The method of claim 1, wherein the step of converting the well-posed problem into a hyperreal well-posed problem comprises converting limit processes contained in the well-posed problem to algebraic relations within the hyperreal well-posed problem.

4. The method of claim 1, wherein the physical system is discontinuous.

5. The method of claim 1, wherein the physical system is nonconservative.

6. The method of claim 1, wherein the physical system includes frictional forces.

7. A process control system to control a physical process, comprising:

a) a process apparatus controlled by input of a set of adjustable control parameters, and comprising diagnostic devices to measure and output values of a set of process parameters;

b) a process control computer, comprising a central processing unit, a memory, means to accept process parameters input from the process apparatus, and means to output adjustable control parameters to the process apparatus;

c) a control program, loaded in said memory and operating in said process control computer, comprising;

1) a set of desired process parameters describing a desired process path;

2) a routine to input and store in the memory the set of process parameters from the process apparatus;

3) a software implementation of a discretized well-posed hyperreal problem generated using the method of claim 1, such that said software implementation generates an approximation of the physical response of said physical process when run on the process control computer;

4) a process correcting routine, comprising;

a) a predictor which uses said software implementation to approximate a future state of the physical process, said future state being described in terms of a set of predicted process parameters;

b) a corrector which compares the set of predicted process parameters to the set of desired process parameters, and alters the set of adjustable control parameters such that the physical process is directed more closely along the desired process path; and

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5) a routine to output the altered adjustable control parameters to the process apparatus.

8. The process control system of claim 7, wherein the discretized well-posed hyperreal problem is generated using the method of claim 4.

9. The process control system of claim 7, wherein the physical process comprises control of a robotic mechanism.

10. An apparatus design optimizer, said apparatus design optimizer comprising:

a) a computer comprising a central processing unit, memory, and output means;

b) a design optimization program, loaded in said memory and operating in said computer, comprising;

i) a set of design parameters describing a proposed apparatus;

ii) a set of environmental parameters describing external conditions to which the proposed apparatus is subjected;

iii) a set of design response parameters describing the physical response desired from the proposed apparatus when subjected to said external conditions;

iv) a software implementation of a discretized well-posed hyperreal problem generated using the method of claim 1, such that said software implementation generates an approximation of the physical response of the proposed apparatus to the external conditions when run on the computer, said approximation being expressed as a set of test response parameters;

v) a response error routine to calculate the response error between the physical response described by the set of test response parameters and the desired physical response described by the set of design response parameters;

vi) a design corrector which uses the approximation error to generate a new set of trial design parameters such that the physical response of the new apparatus design is closer to the desired physical response;

vii) an iterative routine to repeat steps iv, v, and vi, until the approximation error for the current set of trial design parameters falls below a predefined level, whereupon the iterative routine terminates; and

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viii) an output routine to direct the computer to transmit trial design parameters to the computer output.

11. The apparatus design optimizer of claim 10, wherein the software implementation of the discretized well-posed hyperreal problem is generated using the method of claim 4.

12. An apparatus response simulator to numerically simulate the response of a physical system to an external environment, said apparatus response simulator comprising:

a) a computer comprising a central processing unit, memory, and output means;

b) a response simulation program, loaded in said memory and operating in said computer, comprising;

i) a set of apparatus parameters describing the physical system;

ii) a set of environmental parameters describing external conditions to which the physical system is subjected;

iii) a software implementation of a discretized well-posed hyperreal problem generated using the method of claim 1, such that said software implementation generates an approximation of the physical response of the proposed apparatus to the external conditions when run on the computer, said approximation being expressed as a set of response parameters; and

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iv) an output routine to direct the computer to transmit the set of response parameters to the computer output.

13. The apparatus response simulator of claim 12, wherein the software implementation of the discretized well-posed problem is generated using the method of claim 4.