Conditionally active min-max limit regulators
View Patent ↗A conditionally active limit regulator may be used to regulate the performance of engines or other limit regulated systems. A computing system may determine whether a variable to be limited is within a predetermined range of a limit value as a first condition. The computing system may also determine whether a current rate of increase or decrease of the variable to be limited is great enough that the variable will reach the limit within a predetermined period of time with no other changes as a second condition. When both conditions are true, the computing system may activate a simulated or physical limit regulator.
1. A computer-implemented method, comprising:
determining, by a computing system, whether a variable to be limited is within a predetermined range of a limit value as a first condition;
determining, by the computing system, whether a current rate of increase or decrease of the variable to be limited is great enough that the variable will reach the limit within a predetermined period of time with no other changes as a second condition; and
activating, by the computing system, a simulated or physical limit regulator when the first condition and the second condition are true.
2. The computer-implemented method of claim 1 , wherein the activating of the simulated or physical limit regulator further comprises:
passing, by the computing system, the simulated or physical limit regulator's output through appropriate minimum or maximum selection logic; and
modifying, by the computing system, a command regulating a fuel flow rate to a simulated or physical engine.
3. The computer-implemented method of claim 2 , wherein a third condition is defined by:
y 1 ≧(1−γ 1 )* y 1max
where γ 1 is a non-negative number that is less than a non-negative design parameter α 1 , and
to prevent chatter in the fuel flow rate command, the computing system only activates the simulated or physical limit regulator when the following Boolean expression is true:
(the first condition AND the second condition) OR the third condition.
4. The computer-implemented method of claim 1 , wherein when the simulated or physical limit regulator is a maximum limit regulator, the predetermined limit range is determined by:
e 1 ≦α 1 *y 1max
where e 1 is a maximum limit regulator error, α 1 is a non-negative design parameter, and y 1max is a maximum limit of the variable.
5. The computer-implemented method of claim 1 , wherein when the simulated or physical limit regulator is a maximum limit regulator, the current rate of increase of the variable to be limited is determined by:
ⅆ
ⅆ
t
e
1
≤
-
e
1
β
1
*
Δ
T
where e 1 is a maximum limit regulator error, β 1 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.
6. The computer-implemented method of claim 1 , wherein when the simulated or physical limit regulator is a minimum limit regulator, the predetermined limit range is determined by:
e 2 ≧−α 2 *y 2min
where e 2 is a minimum limit regulator error, α 2 is a non-negative design parameter, and y 2min is a minimum limit of the variable.
7. The computer-implemented method of claim 1 , wherein when the simulated or physical limit regulator is a minimum limit regulator, the current rate of decrease of the variable to be limited is determined by:
ⅆ
ⅆ
t
e
2
≥
-
e
2
β
2
*
Δ
T
where e 2 is a minimum limit regulator error, β 2 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.
8. A computer-implemented method, comprising:
determining, by a computing system, whether a variable to be limited is within a predetermined range of a limit value as a first condition using at least one discrete equation;
determining, by the computing system, whether a current rate of increase or decrease of the variable to be limited is great enough that the variable will reach the limit within a predetermined period of time with no other changes as a second condition using at least one discrete equation; and
activating, by the computing system, a simulated or physical limit regulator when the first condition and the second condition are true.
9. The computer-implemented method of claim 8 , wherein the activating of the simulated or physical limit regulator further comprises:
passing, by the computing system, the simulated or physical limit regulator's output through appropriate minimum or maximum selection logic; and
modifying, by the computing system, a command regulating a fuel flow rate to a simulated or physical engine.
10. The computer-implemented method of claim 9 , wherein a third condition is defined by:
y 1 ≧(1−γ 1 )* y 1max
where γ 1 is a non-negative number that is less than a non-negative design parameter α 1 , and
to prevent chatter in the fuel flow rate command, the computing system only activates the simulated or physical limit regulator when the following Boolean expression is true:
(the first condition AND the second condition) OR the third condition.
11. The computer-implemented method of claim 8 , wherein when the simulated or physical limit regulator is a maximum limit regulator, the predetermined limit range is determined by:
e 1 [k]≦α 1 *y 1max
where e 1 [k] is a limit regulator error at a current time index, α 1 is a non-negative design parameter, and y 1max is a maximum limit of the variable.
12. The computer-implemented method of claim 8 , wherein when the simulated or physical limit regulator is a maximum limit regulator, the current rate of increase of the variable to be limited is determined by:
1
Δ
T
(
e
1
[
k
]
-
e
1
[
k
-
1
]
)
≤
-
e
1
[
k
]
β
1
*
Δ
T
where e 1 [k] is a limit regulator error at a current time step, e 1 [k−1] is a limit regulator error at a previous time step, β 1 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.
13. The computer-implemented method of claim 8 , wherein when the simulated or physical limit regulator is a minimum limit regulator, the predetermined limit range is determined by:
e 2 [k]≧−α 2 *y 2min
where e 2 [k] is a limit regulator error at a current time step, α 2 is a non-negative design parameter, and y 2min is a minimum limit of the variable.
14. The computer-implemented method of claim 8 , wherein when the simulated or physical limit regulator is a minimum limit regulator, the current rate of decrease of the variable to be limited is determined by:
1
Δ
T
(
e
2
[
k
]
-
e
2
[
k
-
1
]
)
≥
-
e
2
[
k
]
β
2
*
Δ
T
where e 2 [k] is a limit regulator error at a current time step, e 2 [k−1] is a limit regulator error at a previous time step, β 2 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.
15. An apparatus, comprising:
memory storing computer program instructions; and
at least one processor configured to execute the computer program instructions stored in the memory, the at least one processor configured to:
determine whether a variable to be limited is within a predetermined range of a limit value as a first condition;
determine whether a current rate of increase or decrease of the variable to be limited is great enough that the variable will reach the limit within a predetermined period of time with no other changes as a second condition; and
activate a limit regulator when the first condition and the second condition are true.
16. The apparatus of claim 15 , wherein when activating the limit regulator, the at least one processor is further configured to:
pass the simulated or physical limit regulator's output through appropriate minimum or maximum selection logic; and
modify a command regulating a fuel flow rate to a simulated or physical engine.
17. The apparatus of claim 15 , wherein when the limit regulator is a maximum limit regulator, the at least one processor is further configured to determine the limit range by:
e 1 [k]≦α 1 *y 1max
where e 1 [k] is a limit regulator error at a current time index, α 1 is a non-negative design parameter, and y 1max is a maximum limit of the variable.
18. The apparatus of claim 15 , wherein when the limit regulator is a maximum limit regulator, the at least one processor is further configured to determine the current rate of increase of the variable to be limited by:
1
Δ
T
(
e
1
[
k
]
-
e
1
[
k
-
1
]
)
≤
-
e
1
[
k
]
β
1
*
Δ
T
where e 1 [k] is a limit regulator error at a current time step, e 1 [k−1] is a limit regulator error at a previous time step, β 1 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.
19. The apparatus of claim 15 , wherein when the limit regulator is a minimum limit regulator, the at least one processor is further configured to determine the limit range by:
e 2 [k]≧−α 2 *y 2min
where e 2 [k] is a limit regulator error at a current time step, α 2 is a non-negative design parameter, and y 2min is a minimum limit of the variable.
20. The apparatus of claim 15 , wherein when the limit regulator is a minimum limit regulator, the at least one processor is further configured to determine the current rate of decrease of the variable to be limited by:
1
Δ
T
(
e
2
[
k
]
-
e
2
[
k
-
1
]
)
≥
-
e
2
[
k
]
β
2
*
Δ
T
where e 2 [k] is a limit regulator error at a current time step, e 2 [k−1] is a limit regulator error at a previous time step, β 2 is an error derivative bound for the limit regulator, and ΔT is a controller step size for the computing system.