Method and apparatus for adaptive control

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).sub.t=0 = ##EQU8## where d.sub.1 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 h.sub.1 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 .DELTA.u(t) is calculated generally as follows:
• ##EQU10## where (h) is a constant
• Y.sub.SP is the set point
• y(t) is the process value at time t
• .delta.=(A.sup..gamma.-1 +. . . +I
• .beta..sub.p (t)=C.sub.p.sup.T (t)›A.sup..gamma.-1 +A.sup..delta.-2 +. . . I!b
• .beta..sub.FFx (t)=C.sub.FFx.sup.T (t) ›A.sup..gamma.-1 +A.sup..delta.-2 +. . . I!b
• .beta..sub.S (t)=C.sub.S.sup.T (t)›A.sup..delta.-1 !b-1
• .DELTA.FF.sub.x (t)=FF.sub.x (t)-FF.sub.x (t-1)
• 1(t)=proxied stochastic error=(0.5)1(t-1)+(0.5) (estimated error(t),
• .DELTA.1.sub.s (t)=A.DELTA.1.sub.s (t-1)+b1(t).