Method and apparatus for adaptive control of marginally stable systems

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).