Self-Tuning Control of a Difficult Process

Modelling and adaptive control of fed‐batch penicillin fermentation

“…In this process accurate tracking of a time varying biomass set point profile is essential, with an absolute minimum of overshoot or oscillation; both of which are detrimental to high penicillin yields. Further details of the development and assessment of the algorithms to be discussed below can be found in Clarke et al (1985) and Montague (1986).…”

“…As a result of this classification, from a range of possible algorithms: implicit Generalized minimum variance (Clarke and Gawthrop 1979), explicit polynomial pole placement self tuning (Wellstead et al 1979(Wellstead et al , 1981, explicit state space pole placement self tuning (Warwick, 1981), sub-optimal iterative solution of the discrete Riccati equation to produce an explicit LQG control law, and the explicit Generalized Predictive Controller (Clarke et al, 1985), only the last two techniques were found to be amenable to application on the fed-batch fermentation process being studied. In this process accurate tracking of a time varying biomass set point profile is essential, with an absolute minimum of overshoot or oscillation; both of which are detrimental to high penicillin yields.…”

Adaptive multivariable optimal predictive control

“…In the case where the model is not known, or where the plant has changed sufficiently such that the model does not adequately describe the dynamics, a new model can be identified on-line. Recursive least squares with upper-diagonal factorization of the covariance matrix can be used to estimate the parameters of equation (1). In this case, A Y ( t ) should be used in the data vector so that the data vector contains zero mean data (Clarke et a/.…”

“…In this case, A Y ( t ) should be used in the data vector so that the data vector contains zero mean data (Clarke et a/. 1 …”

“…Assume that the process can be described by the following linear, discrete time model: (1) where Y ( I ) is an n vector of the deviations of the process outputs from the mean values at sampling instant t ; f i ( f ) is an rn vector of the changes in the process inputs between sampling instants t -1 and 1; v ( t ) is an r vector of the changes in the measurable process disturbances between sampling instants I -1 and I ; kf is the integral time delay between the i -j output -input pair; kfj is the integral time delay between the i-j output-disturbance pair; A = ( Iz-I); and A(Z-'), B(z-') and n(z-') are n x n, n x rn and n x r matrix polynomials (respectively) in the backward shift operator z -I .…”