Towards a joint process control design for batch processes: application to semibatch polymer reactors

Matrix inequality-based observer design for a class of distributed transport-reaction systems

“…The proposed design method is rather simple, as the observer design amounts to calculating the output injection gains that render feasible the MI (28). It is rather flexible, as semi-linear systems with constant or varying coefficients, different boundary conditions, and boundary and/or distributed injection can be used.…”

Linear PI control of batch exothermic reactors with temperature measurement

“…Since mass can be added but not removed, the initial concentration deviations may manifest themselves as some concentrations with growing bounded deviations, yielding product compositions with some offset referred to its mean value specification. If the batch motion deviations occur within prescribed limits, industrial batch control practitioners say that the batch-to-batch operation is repeatable with an admissible product quality variability [17], or equivalently, in our terminology, that the batch motion is practically stable.…”

“…Since the majority of the industrial batch reactors are controlled with (possibly gain scheduled) linear PI-type temperature controllers combined with ratio feedforward schemes, without needing the (typically uncertain or unknown) reaction and heat exchange rate nonlinear model functions [17], such observer-based strongly nonlinear and highly model dependent FF-SF control scheme should seem unduly complex and fragile. Motivated by the preceding comments, in this section, a measurement-driven controller to recover the behaviour of the nonlinear FF-FB controller (4) is designed under the following premises: (i) only the reactor temperature is measured, (ii) the reaction rate is unknown, (iii) a mean value estimate of the heat exchange nonlinear function can be used, (iv) the controller must be linear and easy to tune in terms of existing rules for linear single-output filters and single-input controllers, and (iv) the closed-loop behaviour must be assessed on the basis of a robust stability framework.…”

“…In particular, (a) Statement (ii) of Theorem 1 indicates that after certain time t n ðt e Þ; the performance of the exact I/O linearizing feedback is recovered for sufficiently small values of the estimation time-constant t e : In practice, the convergence time t n ðt e Þ should be about 3-10 times smaller than the batch operating time. Hence, practical temperature tracking in batch reactors may require high-gain compensation when the reactor dynamics are fast dynamics, as in the case of some exothermic reactions [8,9,17]. (b) The stability results described above show that good temperature tracking performance in batch reactors can be obtained with relatively simple controllers.…”

“…Over the batch-to-batch operation, gradually decrease the estimator time constant until the ultimate value t e;min is reached when the loop response becomes oscillatory. Back off and set t e ¼ t e;min =3: Gradually decrease the control time constant t c until oscillatory response is reached at the ultimate time constant t n c : Back off and set t c ¼ t n c =3: As proposed in Reference [17], the preceding stability assessment and tuning rules say that the equipment, batch motion, and the control design must be jointly performed. In particular, the control tuning affects and is affected by the batch duration.…”