Adaptive control method that compensates for sign error in actuator response

• US 8,082,047 B1
• Filed: 11/09/2009
• Issued: 12/20/2011
• Est. Priority Date: 11/09/2009
• Status: Active Grant

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Sharma, Manu
• Primary Examiner(s): Masinick, Michael D
• Application Number:
  US12/615,169
• Time in Patent Office: 771 Days
• Field of Search: 700/54, 700/79, 701/3, 701/4, 244/164
• US Class Current: 700/54
• CPC Class Codes: G05B 13/025 using a perturbation signal

Abstract

An adaptive control method that provides the ability to address control uncertainties in both the sign and magnitude of the control power of the system to ensure stability and command tracking. The adaptive control system also functions correctly and remains internally stable in spite of control limits. The control system has the following elements: (i) a filter that smoothes the command to the plant and modifies the command when a control limit is reached, (ii) an element that receives command error input and constructs a nonlinear function of the accumulated error, (iii) an element that converts the nonlinear function of the accumulated error into a control signal to be added to the output of a baseline control system, and (iv) an element that computes the difference between the actuator command and the maximum achievable output.

Claims

1. An adaptive control system for controlling a plant, comprising:

a command filter that modifies a raw plant reference command to remove the effect of actuator saturation when a control limit is reached, said command filter outputting a filtered command and a time rate signal representing a time rate of said filtered command;

a linear controller that outputs a linear control signal component, said linear control signal component being a function of said time rate signal and a command tracking error signal;

control-reversal compensation means that output a nonlinear control signal component, said nonlinear control signal component being a function of said time rate signal and said command tracking error signal; and

a summer for outputting an actuator command that is a sum of said linear and nonlinear control signal components.

2. The system as recited in claim 1, wherein said control-reversal compensation means comprise an integrator that outputs a signal representing a parameter r computed using the function ∫

φ

{tilde over (ω

)}dt, where {tilde over (ω

)} is the command tracking error,

φ

({tilde over (ω

)},{dot over (ω

)}′

_c)=−

k{tilde over (ω

)}+{dot over (ω

)}′

_c

and {dot over (ω

)}′

_c is said time rate of said filtered command.

3. The system as recited in claim 2, wherein said control-reversal compensation means further comprise computing means connected to receive said parameter r signal from said integrator and a signal representing parameter φ

from said linear controller, said computing means outputting said nonlinear control signal component in accordance with a function Φ

r²(sin r).

4. The system as recited in claim 3, further comprising a deadzone switching element that prevents said integrator from receiving a signal representing the command tracking error {tilde over (ω

)} from said nonlinear controller when the magnitude of the command tracking error {tilde over (ω

)} is less than a predetermined threshold.

5. The system as recited in claim 3, further comprising a saturation element that receives said actuator command from said summer and passes it only if it has a magnitude within specified limits.

6. The system as recited in claim 5, wherein said saturation element outputs a clipped version of said actuator command when said actuator command has a magnitude greater than said limit.

7. The system as recited in claim 6, further comprising means for sending a signal to said command filter representing the product of a weighting factor and a difference between said actuator command and said clipped version of said actuator command, said weighting factor being a function of parameter r, and said command filter modifying said raw plant reference command as a function of said product.

8. The system as recited in claim 1, wherein said actuator is a reaction wheel aboard a spacecraft.

9. A method for adaptive control of a plant comprising the following steps:

filtering a raw plant reference command to remove the effect of actuator saturation when a control limit is reached;

outputting a filtered command and a time rate signal representing a time rate of said filtered command;

generating a linear control signal component that is a function of said time rate signal and a command tracking error;

computing a nonlinear function of an accumulated command tracking error;

converting said nonlinear function into a nonlinear control signal component;

summing said nonlinear control component and said linear control component to form an actuator command; and

outputting said actuator command to an actuator of said plant.

10. The method as recited in claim 9, wherein said computing step uses a function ∫

φ

{tilde over (ω

)}dt to compute a parameter r, where {tilde over (ω

)} is the command tracking error,

φ

({tilde over (ω

)},{dot over (ω

)}′

_c)=−

k{tilde over (ω

)}+{dot over (ω

)}′

_c

and {dot over (ω

)}_c is said time rate of said filtered command.

11. The method as recited in claim 10, wherein said converting step converts respective signals representing the parameters r and Φ

into said nonlinear control signal component in accordance with a function Φ

r²(sin r).

12. The method as recited in claim 11, further comprising the step of clipping said actuator command if said actuator command has a magnitude greater than a limit.

13. The method as recited in claim 12, further comprising the steps of forming a signal representing a difference between said actuator command and said clipped actuator command.

14. The method as recited in claim 13, wherein said filtering step is performed as a function of the product of a weighting factor and said difference between said actuator command and said clipped actuator command, said weighting factor being a function of parameter r.

15. A spacecraft comprising a reaction wheel and an adaptive control signal processing system for controlling said spacecraft, said adaptive control signal processing system being programmed to perform the following steps:

filtering a raw command reference to remove the effect of reaction wheel saturation when a control limit is reached;

outputting a filtered command and a time rate signal representing a time rate of said filtered command;

generating a linear control signal component that is a function of said time rate signal and a command tracking error;

computing a nonlinear function of an accumulated command tracking error;

converting said nonlinear function into a nonlinear control signal component;

summing said linear and nonlinear control signal components to form a control signal; and

outputting said control signal to said reaction wheel.

16. The spacecraft as recited in claim 15, further said adaptive control signal processing system is further programmed to clip said outputted control signal whenever its magnitude is greater than a limit, and to generate a signal representing a difference between said outputted control signal and said clipped control signal.

17. The spacecraft as recited in claim 15, wherein said computing step uses a function ∫

φ

{tilde over (ω

)}dt to compute a parameter r, where {tilde over (ω

)} is the command tracking error,

φ

({tilde over (ω

)},{dot over (ω

)}′

_c)=−

k{tilde over (ω

)}+{dot over (ω

)}′

_c

and {dot over (ω

)}′

_c is said time rate of said filtered control signal.

18. The spacecraft as recited in claim 17, wherein said converting step converts respective signals representing the parameters r and Φ

into said nonlinear control signal component in accordance with a function Φ

r²(sin r).

19. The spacecraft as recited in claim 16, wherein said filtering step is performed as a function of the product of a weighting factor and said difference between said outputted control signal and said clipped control signal, said weighting factor being a function of parameter r.

20. The spacecraft as recited in claim 15, wherein said step of computing said nonlinear function of an accumulated command tracking error is not performed when the magnitude of the command tracking error {tilde over (ω

)} is less than a predetermined threshold.