Method and apparatus for adaptive control of marginally stable systems

Claim 1

In a method of controlling a marginally stable industrial process comprising the steps of 1) setting an initial state vector; 2) setting an initial parameter vector; 3) setting an initial prediction parameter gain; 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, the improvement comprising the steps of: a) Reading the process input, process output, process measured disturbance and the set point at the previous sample tine; b) Scaling the process input, process output, process measured disturbance to internal variables corresponding for process input, process output and process measured disturbances, respectively; c) When the controller is just enabled or a reset flag is raised ten Reading the tuning parameters from the configuration file; d) Computing a state space form of the orthonormal Laguerre network A, B, C(k), A_FFX, B_FFX, C_FFX(k), A_STS, B_STS, C_STS(k) where C(k), C_FFX(k), C_STS(k) are calculated from one of the following: loaded from a previously saved model; loaded from an initial model; initialised to [0,0,0, . . . 0] e) Computing control related matrices SB, SA, SS, K, SB_FFX, SA_FFX, SS_FFX, K_FFX, SB_STS, SA_STS SS_STS, K_STS; f) Initializing C_M(k) with C(k), C_M_STS(k) with C_STS(k) and C_M_FFX(k) with C_FFX(k); g) Clearing the state vector L(k), L_FFX(k), L_STS(k) used during control; and h) Updating the models states as follows: L  ( k ) = A * L  ( k - 1 ) + B * CV  ( k - 1 ) L_FFX  ( k ) = A_FFX * L_FFX  ( k - 1 ) + B_FFX * FFX  ( k - 1 ) L_STS  ( k ) = A_STS * L_STS  ( k - 1 ) + B_STS * DV  ( k - 1 ) where A, A_FFX, A_STS represent the state and B, B_FFX, B_STS the input matrices of the corresponding state space representation of the Laguerre networks generated for the same pole but different number of filters, if required; i) Calculating the models output estimation: Y_EST  ( k ) = Y_EST  ( k - 1 ) + C  ( k ) * L  ( k ) Y_EST   _FFX   ( k ) =  Y_EST   _FFX   ( k -  1 ) +  C_FFX   ( k ) *  L_FFX   ( k )   Y_EST  _STS  ( k ) = Y_EST  _STS  ( k - 1 ) + C_STS  ( k ) * L_STS  ( k ) j) Updating the input of the unknown disturbance model: DV ( k )=( Y — EST ( k )+ Y — EST — FFX ( k )+ Y — EST — STS ( k ))− PV ( k ); k) Repeating steps h. to j. a plurality of times for the convergence of the state estimators; l) Iterate the computation of the input to the unknown disturbance model also for convergence purposes; m) Computation of the prediction parameter gain: BETA(k) C(k)*SB(k).