System and method for characterizing a system

• US 20030171901A1
• Filed: 03/08/2002
• Published: 09/11/2003
• Est. Priority Date: 03/08/2002
• Status: Active Grant

• Current Assignee: Johnson Controls Tyco IP Holdings LLP (Johnson Controls International plc)
• Original Assignee: Johnson Controls Technology Company (Johnson Controls International plc)
• Inventors: Salsbury, Timothy I.
• Granted Patent: US 7,505,877 B2
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: G06F 17/11 for solving equations , e.g. nonlinear equations, general mathematical optimization problems optimization specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06F 17/12 Simultaneous equations , e.g. systems of linear equations

Abstract

A method and apparatus of identifying a system is disclosed. The method comprises estimating at least one parameter in a second-order model of the system, and approximating at least one parameter in a first-order model of the system from the at least one second-order model parameter. The method may also comprise sampling an input to the system, sampling an output from the system. The apparatus comprises a device for estimating at least one parameter in a second-order model of the system, and device for approximating at least one parameter in a first-order model of the system from the at least one second-order model parameter.

Claims

1. A method of identifying a system, comprising:

estimating at least one parameter in a second-order model of the system; and

approximating at least one parameter in a first-order model of the system from the at least one second-order model parameter.

2. The method of claim 1 wherein the second-order model is a second-order continuous-time model.

3. The method of claim 1 wherein the at least one second-order model parameter is a plurality of second-order continuous-time parameters.

4. The method of claim 1 wherein the first-order model is a first-order plus time delay model.

5. The method of claim 1 wherein the at least one first-order model parameter includes one or more of a time delay parameter, a time constant parameter and a static gain parameter.

6. The method of claim 1 wherein the second-order model is a second-order transfer function model.

7. The method of claim 1 wherein the at least one second-order model parameter is estimated using sampled inputs and outputs of the system.

8. The method of claim 7 wherein the at least one second-order model parameter is estimated from the sampled inputs and outputs using a recursive least squares method.

9. The method of claim 7 wherein the output of the system is a continuous signal that is discretely sampled.

10. The method of claim 1 wherein the at least one first-order model parameter is approximated from the at least one second-order model parameter using a transformation function.

11. The method of claim 10 wherein the transformation function is a non-linear transformation.

12. The method of claim 1 wherein the at least one second-order model parameter is estimated using state variable filters.

13. The method of claim 1 wherein the at least one first-order model parameter is used for at least one of pre-tuning a feedback controller, configuring the feedback controller, reconfiguring the feedback controller, evaluating performance of the system, and validating performance of the system.

14. The method of claim 1 wherein the method is automated by a controller.

15. The method of claim 1 wherein the system is an HVAC system.

16. A method of analyzing a system to estimate at least one parameter in a first-order model of the system, the method comprising:

sampling an input to the system;

sampling an output from the system;

estimating at least one parameter in a second-order model of the system using the sampled inputs and outputs; and

approximating the at least one first-order model parameter based on the at least one second-order model parameter.

17. The method of claim 16 wherein the second-order model is a second-order continuous-time model, and the at least one second-order model parameter is a plurality of second-order continuous-time parameters.

19. The method of claim 16 wherein the at least one first-order model parameter comprises one or more of a time delay parameter, a time constant parameter and a static gain parameter.

20. The method of claim 16 wherein the at least one second-order model parameter is estimated from the sampled inputs and outputs using a recursive least squares method.

21. The method of claim 16 wherein the at least one first-order model parameter is approximated from the at least one second-order model parameter using a transformation function.

22. The method of claim 21 wherein the transformation function is a non-linear transformation.

23. The method of claim 16 wherein the at least one second-order model parameter is estimated using state variable filters.

24. The method of claim 16 wherein the at least one first-order model parameter is used to perform at least one of pre-tuning a feedback controller, configuring the feedback controller, reconfiguring the feedback controller, evaluating performance of the system, and validating performance of the system.

25. The method of claim 16 wherein the system is an HVAC system.

26. The method of claim 16 wherein the method is automated by a controller.

27. The method of claim 16, further comprising changing the input signal to the system.

28. The method of claim 27, wherein the change in the input signal is a step change made for purposes of identifying the system.

29. The method of claim 28 wherein the change in input signals is made during normal operation of the system.

30. A method of analyzing a non-first order system having inputs and outputs, the method comprising:

sampling the inputs;

sampling the outputs;

estimating at least one parameter for a first-order model of the system based on the sampled inputs and outputs.

31. The method of claim 30 wherein the first-order model is a first-order plus time delay model.

32. The method of claim 30 wherein the at least one first-order model parameter comprises one or more of a time delay parameter, a time constant parameter and a static gain parameter.

33. The method of claim 30, further comprising generating a test signal.

34. The method of claim 33 wherein the test signal is a step change in the inputs to the system.

35. The method of claim 34, further comprising determining when to terminate the test or apply another step change to the inputs by applying a convergence test to the at least one first order model parameter.

36. The method of claim 30 wherein the at least one first-order model parameter is estimated from at least one parameter of a second-order model of the system.

37. The method of claim 36 wherein the second-order model is a second-order transfer function model and the at least one parameter thereof is estimated using state variable filters.

38. The method of claim 37 wherein the at least one first-order model parameter is estimated from the at least one second-order model parameter using a transformation function.

39. The method of claim 38 wherein the transformation function is a non-linear transformation.

40. The method of claim 30 wherein the sampled outputs of the system are discrete measurements of a continuous output signal of the system.

41. The method of claim 40, further comprising passing the sampled outputs through a filter.

42. The method of claim 41 wherein the filter is a high-pass filter that focuses the estimation of at least one first-order parameter model on a frequency range of interest.

43. The method of claim 30 further comprising passing the at least one first-order model parameter through a filter.

44. The method of claim 43 wherein the filter is a low-pass filter that checks the viability of the first-order model.

45. The method of claim 30 wherein the step of estimating the at least one first-order model parameter is implemented in a digital controller.

46. The method of claim 30 wherein the non-first-order system is an HVAC system.

47. An apparatus for identifying a system, comprising:

means for estimating at least one parameter in a second-order model of the system; and

means for approximating at least one parameter in a first-order model of the system from the at least one second-order model parameter.

48. The apparatus of claim 47 wherein the second-order model is a second-order continuous-time model.

49. The apparatus of claim 47 wherein the at least one second-order model parameter is a plurality of second-order continuous-time parameters.

50. The apparatus of claim 47 wherein the first-order model is a first-order plus time delay model.

51. The apparatus of claim 47 wherein the at least one first-order model parameter includes one or more of a time delay parameter, a time constant parameter and a static gain parameter.

52. The apparatus of claim 47 wherein the second-order model is a second-order transfer function model.

53. The apparatus of claim 47, further including means for sampling inputs and outputs of the system, and wherein the at least one second-order model parameter is estimated using the sampled inputs and outputs.

54. The apparatus of claim 53 wherein the at least one second-order model parameter is estimated from the sampled inputs and outputs using a recursive least squares method.

55. The apparatus of claim 53 wherein the output of the system is a continuous signal that is discretely sampled.

56. The apparatus of claim 47 wherein the at least one first-order model parameter is approximated from the at least one second-order model parameter using a transformation function.

57. The apparatus of claim 56 wherein the transformation function is a non-linear transformation.

58. The apparatus of claim 47 wherein the at least one second-order model parameter is estimated using state variable filters.

59. The apparatus of claim 47 wherein the at least one first-order model parameter is used for at least one of pre-tuning a feedback controller, configuring the feedback controller, reconfiguring the feedback controller, evaluating performance of the system, and validating performance of the system.

60. The apparatus of claim 47, further including a controller running a program to perform the estimating means and the approximating means automatically.

61. The apparatus of claim 47 wherein the system is an HVAC system.