Method and apparatus for adaptive control
First Claim
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1. A method of generating a control signal for controlling a process, during each of a plurality of sampling instants, said process having at least one input variable and one output variable, the application of said control signal to said process constituting a control action causing a variation of said input variable, said method comprising:
- a) providing an adaptive controller adapted to store a model of said process comprising a state vector and a model parameter vector and to generate said control action;
b) providing means for measuring said output variable of said process, generating a signal representing said measurement and communicating said measurement to said adaptive controller;
c) selecting a number n of orthonormal series functions to model said process;
d) providing a signal to define an initial state vector 1(t)t=0 = ##EQU8## where d1 is a constant, and storing said initial state vector in said adaptive controller;
e) providing a signal to define an initial predicted model parameter vector= ##EQU9## where h1 is a constant, and storing said initial predicted model parameter vector in said adaptive controller;
f) performing an update of said state vector in said controller using said orthonormal series functions to provide a history of said control actions and any feedforward input variables up to that sampling instant;
g) measuring said process output variable and calculating a model error in the predicted model parameter vector by comparing said predicted model parameter vector to said measured process output variable;
h) updating the model parameter vector with said model error by a Kalman filter recursive least squares method;
i) calculating the change in controller output required to bring said process output variables to a desired value based on a predicted process output variable obtained from said updated model parameter vector and said updated state vector;
j) generating a control action based on said calculated required change in controller output;
k) repeating steps f) through j) at each sampling instant;
l) storing a reference model parameter vector in said controller during a period of satisfactory controller operation; and
m) periodically replacing said model parameter vector in said controller with said reference vector if a steadily decreasing prediction parameter gain is detectedwhere said change in controller output Δ
u(t) is calculated generally as follows;
##EQU10## where (h) is a constantYSP is the set pointy(t) is the process value at time tδ
=(A.sup.γ
-1 +. . . +Iβ
p (t)=CpT (t) A.sup.γ
-1 +A.sup.δ
-2 +. . . I!bβ
FFx (t)=CFFxT (t) A.sup.γ
-1 +A.sup.δ
-2 +. . . I!bβ
S (t)=CST (t) A.sup.δ
-1 !b-1Δ
FFx (t)=FFx (t)-FFx (t-1)1(t)=proxied stochastic error=(0.5)1(t-1)+(0.5) (estimated error(t),Δ
1s (t)=AΔ
1s (t-1)+b1(t).
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Abstract
The present invention provides a method and apparatus for adaptive control which does not require a predetermined model of the process to be controlled. The method comprises the steps of 1) setting an initial state vector; 2) setting an initial parameter vector; 3) setting an initial prediction parameter gain between 2 and 10; 4) set the initial covariance matrix; 5) performing a state update 6) estimating the model error; 7) updating the parameter vector, 8) updating the co-variance matrix, and 9) updating the controller output.
271 Citations
8 Claims
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1. A method of generating a control signal for controlling a process, during each of a plurality of sampling instants, said process having at least one input variable and one output variable, the application of said control signal to said process constituting a control action causing a variation of said input variable, said method comprising:
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a) providing an adaptive controller adapted to store a model of said process comprising a state vector and a model parameter vector and to generate said control action; b) providing means for measuring said output variable of said process, generating a signal representing said measurement and communicating said measurement to said adaptive controller; c) selecting a number n of orthonormal series functions to model said process; d) providing a signal to define an initial state vector 1(t)t=0 = ##EQU8## where d1 is a constant, and storing said initial state vector in said adaptive controller; e) providing a signal to define an initial predicted model parameter vector= ##EQU9## where h1 is a constant, and storing said initial predicted model parameter vector in said adaptive controller; f) performing an update of said state vector in said controller using said orthonormal series functions to provide a history of said control actions and any feedforward input variables up to that sampling instant; g) measuring said process output variable and calculating a model error in the predicted model parameter vector by comparing said predicted model parameter vector to said measured process output variable; h) updating the model parameter vector with said model error by a Kalman filter recursive least squares method; i) calculating the change in controller output required to bring said process output variables to a desired value based on a predicted process output variable obtained from said updated model parameter vector and said updated state vector; j) generating a control action based on said calculated required change in controller output; k) repeating steps f) through j) at each sampling instant; l) storing a reference model parameter vector in said controller during a period of satisfactory controller operation; and m) periodically replacing said model parameter vector in said controller with said reference vector if a steadily decreasing prediction parameter gain is detected where said change in controller output Δ
u(t) is calculated generally as follows;
##EQU10## where (h) is a constantYSP is the set point y(t) is the process value at time t δ
=(A.sup.γ
-1 +. . . +Iβ
p (t)=CpT (t) A.sup.γ
-1 +A.sup.δ
-2 +. . . I!bβ
FFx (t)=CFFxT (t) A.sup.γ
-1 +A.sup.δ
-2 +. . . I!bβ
S (t)=CST (t) A.sup.δ
-1 !b-1Δ
FFx (t)=FFx (t)-FFx (t-1)1(t)=proxied stochastic error=(0.5)1(t-1)+(0.5) (estimated error(t), Δ
1s (t)=AΔ
1s (t-1)+b1(t). - View Dependent Claims (2, 3, 4, 5, 6, 7, 8)
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Current AssigneeUniversal Dynamics, Inc. (Pentafin SpA)
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Original AssigneeUniversal Dynamics, Inc. (Pentafin SpA)
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InventorsGough, William Albert Gordon Jr.
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Primary Examiner(s)Gordon, Paul P.
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Application NumberUS08/548,682Time in Patent Office754 DaysField of Search364/148, 364/149, 364/150, 364/151, 364/153, 364/162, 364/163, 364/164US Class Current700/29CPC Class CodesG05B 13/042 in which a parameter or coe...
