Fast plant test for model-based control

• US 7,194,317 B2
• Filed: 08/22/2002
• Issued: 03/20/2007
• Est. Priority Date: 08/22/2002
• Status: Expired due to Fees

• Current Assignee: Air Products and Chemicals Incorporated (Linde Plc)
• Original Assignee: Air Products and Chemicals Incorporated (Linde Plc)
• Inventors: Kothare, Simone L., Mandler, Jorge Anibal
• Primary Examiner(s): Knight; Anthony
• Assistant Examiner(s): Hartman, Jr.; Ronald D.
• Application Number:
  US10/225,675
• Publication Number:
  US 20040064202A1
• Time in Patent Office: 1,671 Days
• Field of Search: 700 28- 29, 700 38- 39, 702/108, 702/110
• US Class Current: 700/29
• CPC Class Codes: G05B 17/02 electric

Abstract

A method and apparatus for designing perturbation signals to excite a number of input variables of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller. The method begins with providing input parameters of the system. A plurality of binary multi-frequency (BMF) signals are generated based on these input parameters and the frequency spectra of these BMF signals are calculated. One BMF signal is selected out of the set of BMF signals so that the frequency spectrum of the selected BMF signal most closely matches a desired frequency spectrum specified by the input parameters. The selected BMF signal is used as a first perturbation signal for testing the system. The selected BMF signal is also shifted by predetermined amounts of samples to create delayed copies of the original BMF signal to be used as additional perturbation signals.

Claims

1. A method of producing perturbation signals adaptable to exciting a predetermined number of input variables of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing input parameters of the system;

b) generating a plurality of binary multi-frequency (BMF) signals based on the input parameters;

c) calculating the frequency spectra of the BMF signals generated in step (b);

d) selecting one of the BMF signals of the set of BMF signals of step (b), the frequency spectrum of the one selected BMF signal most closely matching a desired frequency spectrum specified by the input parameters;

e) using the selected BMF signal of step (d) as a first perturbation signal for system testing; and

f) shifting the selected BMF signal of step (d) by a delay time amount of samples to create a delayed copy of the selected BMF signal in step (e) to be used as a second perturbation signal for system testing.

2. The method of claim 1 further comprising the steps of:

g) increasing the delay time amount of samples; and

h) repeating steps (f) and (g) to generate a set of delayed copy of the selected BMF signal including one less delayed copy of the selected BMF signal than the predetermined number of input variables of the system.

3. A method of producing perturbation signals adaptable to exciting a predetermined number of input variables of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing input parameters of the system;

b) selecting a perturbation signal frequency spectrum;

c) generating a plurality of binary multi-frequency (BMF) signals through optimization based on the information of steps (a) and (b);

d) calculating the frequency spectra of the BMF signals generated in step (c);

e) selecting, based on the match between the signal frequency spectra calculated in step (d) and the perturbation signal frequency spectrum of step (b), a set of the BMF signals of step (c), each BMF signal of the selected set of BMF signals of step (c) containing substantially 100% of useful power;

f) selecting one of the BMF signals of the set of BMF signals of step (e), the frequency spectrum of the one selected BMF signal most closely matching the perturbation signal frequency spectrum selected in step (b);

g) using the selected BMF signal of step (f) as a first perturbation signal;

h) shifting the selected BMF signal of step (f) by a delay time amount of samples so that the original signal and its delayed copy are nearly stochastically uncorrelated during one system settling time; and

i) using the signal generated in step (h) as a second perturbation signal.

4. The method of claim 3, further comprising the steps of:

j) increasing the delay time amount of samples; and

k) repeating steps (h), (i), and (j) to generate a set of delayed copy of the selected BMF signal including one less delayed copy of the selected BMF signal than the predetermined number of input variables of the system.

5. The method of claim 3 wherein step (b) includes the steps of:

b1) selecting a control-relevant frequency window; and

b2) selecting a perturbation signal power distribution over the control-relevant frequency window.

6. The method of claim 3, wherein each of the set of the BMF signals selected in step (e) has a crest factor less than a predetermined crest factor.

7. A method of producing plant-friendly perturbation signals adaptable to exciting a predetermined number of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) determining the system settling time;

b) generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

c) executing a preliminary assignment of each BMF signal of step (b) to a system input channel;

d) selecting plant-friendliness criteria corresponding to a plurality of system outputs;

e) determining expected initial values corresponding to the plurality of system outputs in step (d);

f) determining approximate steady-state gains corresponding to the plurality of system outputs of step (d) with respect to the input channels;

g) selecting a set of amplitudes for the BMF signals of step (b);

h) determining a simplified system model of the system responses for the outputs of step (d), the simplified system model based on;

the system settling time of step (a);

the steady-state gains of step (f); and

linear dynamics of at least one predetermined order;

i) simulating the effect of the excitation of the input channels via the BMF signals on the system outputs using the simplified system model of step (h) and expected initial values corresponding to the plurality of system outputs in step (e);

j) judging the simulated responses in step (i) based on the plant-friendliness criteria in step (d); and

k) if the system responses of step (i) are judged in step (j) to exceed the plant-friendliness criteria;

changing, based on the judging of step (j), the assignment of BMF signals to input channels; and

repeating steps (i), (j) and (k).

8. A method of producing plant-friendly perturbation signals adaptable to exciting a predetermined number of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) determining a system settling time;

b) generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

c) executing an assignment of each BMF signal of step (b) to a system input channel;

d) selecting plant-friendliness criteria corresponding to a plurality of system outputs;

e) determining expected initial values corresponding to the plurality of system outputs in step (d);

f) determining approximate steady-state gains corresponding to the plurality of system outputs of step (d) with respect to the input channels;

g) selecting a set of amplitudes for the BMF signals of step (b);

h) determining a simplified system model of the system responses for the outputs of step (d), the simplified system model based on;

the system settling time of step (a);

the steady-state gains of step (f); and

linear dynamics of at least one predetermined order;

i) simulating the effect of the excitation of the input channels via the BMF signals on the system outputs using the simplified system model of step (h) and expected initial values corresponding to the plurality of system outputs in step (e);

j) judging the simulated responses in step (i) based on the plant-friendliness criteria in step (d); and

k) if the system responses of step (i) are judged in step (j) to exceed the plant-friendliness criteria;

changing, based on the judging of step (j), the amplitude of at least one BMF signal; and

repeating steps (i), (j) and (k).

9. The method of claim 8, wherein step (k) further includes changing the assignment of the BMF signals to the system input channels of step (c) for at least two BMF signals.

10. A method of producing plant-friendly perturbation signals adaptable to exciting a first predetermined number of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) determining a system settling time;

b) generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the first predetermined number of input channels of the system;

c) executing a candidate assignment of each BMF signal of step (b) to a system input channel;

d) selecting plant-friendliness criteria corresponding to a plurality of system outputs;

e) determining expected initial values corresponding to the plurality of system outputs in step (d);

f) determining approximate steady-state gains corresponding to the plurality of system outputs of step (d) with respect to the input channels;

g) selecting an initial set of amplitudes for the BMF signals of step (b);

h) determining a simplified system model of the system responses for the outputs of step (d), the simplified system model based on;

the system settling time of step (a);

the steady-state gains of step (f); and

linear dynamics of at least one predetermined order; and

i) solving a series of optimization problems to determine a calculated set of amplitudes of the BMF signals using the candidate assignment of perturbation signals to input channels of step (c), the initial set of amplitudes of step (g), the simplified system model of step (h), the expected initial output values of step (e), and the plant-friendliness criteria of step (d).

11. The method of claim 10, wherein solving the series of optimization problems in step (i) is based on maximizing excitation of the output responses within the plant-friendliness criteria of step (d).

12. The method of claim 10, further comprising the steps of:

j) changing the candidate assignment of perturbation signals to input channels;

k) repeating steps (i) and (j) to generate a second predetermined number of calculated sets of amplitudes of the BMF signals, each calculated set of amplitudes corresponding to one candidate assignment of perturbation signals to input channels; and

l) selecting a final assignment of perturbation signals to input channels and the corresponding calculated amplitudes of the BMF signals based on the plant friendliness criteria of step (d) and results of step (i).

13. A method of testing a system including a predetermined number of input channels and a plurality of output channels, for the purpose of obtaining a plurality of empirical models for the synthesis of a model-based controller, the model comprising the steps of:

a) generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

b) assigning the plurality of BMF signals generated in step (a);

input channels; and

amplitudes;

c) executing a test of the system using the BMF signal assignments of step (b);

d) collecting a plurality of output signals generated on the plurality of output channels during the test;

e) judging interactions of the plurality of output signals collected in step (d) with respect to each other;

f) generating a first set of the empirical models representing output signals judged in step (e) to be substantially interacting, the first set of the empirical models generated using multi-input multi-output (MIMO) parametric modeling tools and based on the BMF signal assignments of step (b) and the output signals collected in step (d); and

g) generating a second set of the empirical models representing output signals judged in step (e) not to be substantially interacting, the second set of the empirical models generated using multi-input single-output (MISO) parametric modeling tools and based on the BMF signal assignments of step (b) and the output signals collected in step (d).

14. The method of claim 13, wherein:

the MIMO parametric modeling tools include at least one of;

a state-space model;

or

an auto-regressive exogenous (ARX) model; and

the MISO parametric modeling tools include at least one of;

a state-space model;

an ARX model;

an auto-regressive moving average exogenous model;

an output-error model;

or

a Box-Jenkins model.

15. The method of claim 13, wherein the BMF signal to input channel assignments and BMF signal amplitude assignments of step (b) are selected to generate a plant-friendly test.

16. A method of producing plant-friendly perturbation signals adaptable to exciting a plurality of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing a settling time, a dominant time constant, an estimated first signal amplitude, an estimated second signal amplitude, and plant-friendliness criteria of the system;

b) providing an estimated perturbation signal frequency spectrum for the test signals;

c) generating a plurality of binary multi-frequency (BMF) signals based on the parameters provided in step (a);

d) calculating frequency spectra of the BMF signals generated in step (c);

e) selecting, based on the frequency spectra calculated in step (d), a set of the BMF signals of step (c), each BMF signal of the selected set of BMF signals including substantially 100% useful power;

f) selecting one of the BMF signals of the set of BMF signals of step (e), the frequency spectrum of the one selected BMF signal substantially matching the estimated perturbation signal frequency spectrum of step (b);

g) using the selected BMF signal of step (f) as a first test signal;

h) setting a first test signal amplitude to the estimated first signal amplitude;

i) shifting the selected BMF signal of step (f) by one settling time of the system to use as a second test signal having an estimated second signal amplitude;

j) setting a second test signal amplitude to the estimated second signal amplitude;

k) simulating responses of the system using the first test signal and the second test signal;

l) judging the responses of step (k) based on the plant-friendliness criteria; and

m) if the responses of step (k) are judged in step (l) to exceed the plant-friendliness criteria;

changing, based on the judging of step (l), at least one of the first test signal amplitude or the second test signal amplitude; and

repeating steps (k), (l), and (m).

17. The method of claim 16, wherein step (m) further includes exchanging the first test signal and the second test signal.

18. A method of producing plant-friendly perturbation signals adaptable to exciting a plurality of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing an estimated first signal amplitude, an estimated second signal amplitude, and plant-friendliness criteria of the system;

b) providing a first test signal and a second test signal, the second test signal being nearly stochastically uncorrelated to the first test signal;

c) setting a first test signal amplitude to the estimated first signal amplitude;

d) selling a second test signal amplitude to the estimated second signal amplitude;

e) simulating responses of the system using the first test signal and the second test signal;

f) judging the responses of step (e) based on the plant-friendliness criteria; and

g) if the responses of step (e) are judged in step (f) to exceed the plant-friendliness criteria;

changing, based on the judging of step (f), at least one of the first test signal amplitude or the second test signal amplitude; and

repeating steps (e), (f), and (g).

19. The method of claim 18, wherein step (g) further includes exchanging the first test signal and the second test signal.

20. A method of producing plant-friendly perturbation signals adaptable to exciting a predetermined number of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) determining a system setting time;

b) generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

c) executing an assignment of each BMF signal of step (b) to a system input channel;

d) selecting plant-friendliness criteria corresponding to a plurality of system outputs;

e) determining expected initial values corresponding to the plurality of system outputs in step (d);

f) determining approximate steady-state gains corresponding to the plurality of system outputs of step (d) with respect to the input channels;

g) selecting a set of amplitudes for the BMF signals of step (b);

h) determining a simplified system model of the system responses for the outputs of step (d), the simplified system model based on;

the system settling time of step (a);

the steady-state gains of step (f); and

linear dynamics of at least one predetermined order;

i) simulating the effect of the excitation of the input channels via the BMF signals on the system outputs using the simplified system model of step (h) and expected initial values corresponding to the plurality of system outputs in step (e);

j) judging the simulated responses in step (i) based on the plant-friendliness criteria in step (d); and

k) if the system responses of step (i) are judged in step (j) to exceed the plant-friendliness criteria;

changing, based on the judging of step (j), the assignment of the BMF signals to the system input channels of step (c) for at least two BMF signals; and

repeating steps (i), (j) and (k).

21. A method of producing plant-friendly perturbation signals adaptable to exciting a plurality of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing a settling time, a dominant time constant, an estimated first signal amplitude, an estimated second signal amplitude, and plant-friendliness criteria of the system;

b) providing an estimated perturbation signal frequency spectrum for the test signals;

c) generating a plurality of binary multi-frequency (BMF) signals based on the parameters provided in step (a);

d) calculating frequency spectra of the BMF signals generated in step (c);

e) selecting, based on the frequency spectra calculated in step (d), a set of the BMF signals of step (c), each BMF signal of the selected set of BMF signals including substantially 100% useful power;

f) selecting one of the BMF signals of the set of BMF signals of step (e), the frequency spectrum of the one selected BMF signal substantially matching the estimated perturbation signal frequency spectrum of step (b);

g) using the selected BMF signal of step (f) as a first test signal;

h) setting a first test signal amplitude to the estimated first signal amplitude;

i) shifting the selected BMF signal of step (f) by one settling time of the system to use as a second test signal having an estimated second signal amplitude;

j) selling a second test signal amplitude to the estimated second signal amplitude;

k) simulating responses of the system using the first test signal and the second test signal;

l) judging the responses of step (k) based on the plant-friendliness criteria; and

m) if the responses of step (k) are judged in step (l) to exceed the plant-friendliness criteria;

exchanging, based on the judging of step (l), the first test signal and the second test signal; and

repeating steps (k), (l), and (m).

22. A method of producing plant-friendly perturbation signals adaptable to exciting a plurality of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, a method comprising the steps of:

a) providing an estimated first signal amplitude, an estimated second signal amplitude, and plant-friendliness criteria of the system;

b) providing a first test signal and a second test signal, the second test signal being nearly stochastically uncorrelated to the first test signal;

c) setting a first test signal amplitude to the estimated first signal amplitude;

d) setting a second test signal amplitude to the estimated second signal amplitude;

e) simulating responses of the system using the first test signal and the second test signal;

f) judging the responses of step (e) based on the plant-friendliness criteria; and

g) if the responses of step (e) are Judged in step (f) to exceed the plant-friendliness criteria;

exchanging, based on the judging of step (f), the first test signal and the second test signal; and

repeating steps (e), (f), and (g).

23. An apparatus for producing perturbation signals adaptable to exciting a predetermined number of input variables of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, comprising:

means of providing input parameters of the system;

means of generating a plurality of binary multi-frequency (BMF) signals based on the input parameters;

means of calculating the frequency spectra of the generated BMF signals;

means of comparing the frequency spectra of the generated BMF signals to a desired frequency spectrum specified by the input parameters;

means of selecting one of the BMF signals of the set of BMF signals, the frequency spectrum of the one selected BMF signal most closely matching the desired frequency spectrum;

means of using the one selected BMF signal as a first perturbation signal for system testing; and

means of shifting the one selected BMF signal by a delay time amount of samples to create a delayed copy of the one selected BMF signal to be used as a second perturbation signal for system testing.

24. An apparatus for producing plant-friendly perturbation signals adaptable to exciting a predetermined number of input channels of a system, in order to test that system for the purpose of obtaining models for the synthesis of a model-based controller, comprising:

means of determining the system settling time;

means of generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

means of executing a candidate assignment of each BMF signal to a system input channel;

means of selecting plant-friendliness criteria corresponding to a plurality of system outputs;

means of determining expected initial values corresponding to the plurality of system outputs;

means of determining approximate steady-state gains corresponding to the plurality of system outputs with respect to the input channels;

means of selecting an initial set of amplitudes for the BMF signals;

means of determining a simplified led system model of the system responses for the outputs, the simplified system model based on;

the system settling time;

the steady-state gains; and

linear dynamics of at least one predetermined order;

means of simulating the effect of the excitation of the input channels via the BMF signals on the system outputs using the simplified system model and expected initial values corresponding to the plurality of system outputs;

means of judging the simulated responses based on the plant-friendliness criteria and the expected initial values corresponding to the plurality of system outputs;

optimizing means of changing at least one of;

the assignment of BMF signals to input channels based on the judged simulated responses;

or

the amplitude of at least one BMF signal based on the judged simulated responses.

25. The apparatus of claim 24, wherein the optimizing means includes means of solving a series of optimization problems to determine a calculated set of amplitudes of the BMF signals using the candidate assignment of perturbation signals to input channels, the initial set of amplitudes of the BMF signals, the simplified system model, the expected initial output values, and the plant-friendliness criteria.

26. The apparatus of claim 25, wherein the means of solving the series of optimization problems maximizes excitation of the output responses within the plant-friendliness criteria.

27. An apparatus for testing a system including a predetermined number of input channels and a plurality of output channels, for the purpose of obtaining a plurality of empirical models for the synthesis of a model-based controller, comprising:

means of generating a plurality of nearly stochastically uncorrelated binary multi-frequency (BMF) signals to match the predetermined number of input channels of the system;

means of assigning the plurality of BMF signals;

input channels; and

amplitudes;

means of executing a test of the system using the BMF signal assignments;

means of collecting a plurality of. output signals generated on the plurality of output channels during the test;

means of judging interactions of the plurality of collected output signals with respect to each other;

means of generating a first set of the empirical models representing output signals judged to be substantially interacting, the first set of the empirical models generated using multi-input multi-output (MIMO) parametric modeling tools and based on the BMF signal assignments and the collected output signals; and

means of generating a second set of the empirical models representing output signals judged not to be substantially interacting, the second set of the empirical models generated using multi-input single-output (MISO) parametric modeling tools and based on the BMF signal assignments and the collected output signals.

28. The apparatus of claim 27, wherein:

the MIMO parametric modeling tools include at least one of;

a state-space model;

or

an auto-regressive exogenous (ARX) model; and

the MISO parametric modeling tools include at least one of;

a state-space model;

an ARX model;

an auto-regressive moving average exogenous model;

an output-error model;

or

a Box-Jenkins model.

29. The apparatus at claim 27, wherein the BMF signal to input channel assignments and BMF signal amplitude assignments are selected to generate a plant-friendly test.